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TRMFACT_035501
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: SYN → SYN-ACK → ACK. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035502
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What does IEEE 754 'round to nearest, ties to even' mean? Then give one practical implication in 1 sentence." } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035503
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035504
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "According to RFC 8259, what are the only three literal names allowed in JSON values?" } ] }
false, null, true (all lowercase).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035505
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: What does IEEE 754 'round to nearest, ties to even' mean? A: (answer). Keep it under 15 words." } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035506
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: T(n)=a·T(n/b)+f(n) (with a≥1, b>1). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035507
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "According to RFC 8259, what are the only three literal names allowed in JSON values?" } ] }
false, null, true (all lowercase).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035508
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "State the Euclidean algorithm recursion for gcd(a,b) and its base case. Then give one practical implication in 1 sentence." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035509
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "According to RFC 8259, what are the only three literal names allowed in JSON values?" } ] }
false, null, true (all lowercase).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035510
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In NIST SP 800-63B (memorized secrets), what is the minimum length for a subscriber-chosen password? Then give one practical implication in 1 sentence." } ] }
At least 8 characters. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035511
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)?" } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035512
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)? Then give one practical implication in 1 sentence." } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035513
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In TCP, what is the standard three-message handshake to establish a connection? Then give one practical implication in 1 sentence." } ] }
SYN → SYN-ACK → ACK. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035514
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: According to RFC 8259, what are the only three literal names allowed in JSON values? A: (answer). Keep it under 15 words." } ] }
false, null, true (all lowercase).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035515
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In TCP, what is the standard three-message handshake to establish a connection? A: (answer). Keep it under 15 words." } ] }
SYN → SYN-ACK → ACK.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035516
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)? Then give one practical implication in 1 sentence." } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035517
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: At least 8 characters. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035518
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)? Then give one practical implication in 1 sentence." } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035519
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "According to RFC 8259, what are the only three literal names allowed in JSON values?" } ] }
false, null, true (all lowercase).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035520
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: false, null, true (all lowercase). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035521
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035522
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)? A: (answer). Keep it under 15 words." } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035523
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In NIST SP 800-63B (memorized secrets), what is the minimum length for a subscriber-chosen password? A: (answer). Keep it under 15 words." } ] }
At least 8 characters.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035524
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "State the Euclidean algorithm recursion for gcd(a,b) and its base case. Then give one practical implication in 1 sentence." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035525
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)? Then give one practical implication in 1 sentence." } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035526
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What does IEEE 754 'round to nearest, ties to even' mean? Then give one practical implication in 1 sentence." } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035527
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In NIST SP 800-63B (memorized secrets), what is the minimum length for a subscriber-chosen password? A: (answer). Keep it under 15 words." } ] }
At least 8 characters.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035528
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "State the Euclidean algorithm recursion for gcd(a,b) and its base case. Then give one practical implication in 1 sentence." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035529
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In TCP, what is the standard three-message handshake to establish a connection?" } ] }
SYN → SYN-ACK → ACK.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035530
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: State the Euclidean algorithm recursion for gcd(a,b) and its base case. A: (answer). Keep it under 15 words." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035531
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: What does IEEE 754 'round to nearest, ties to even' mean? A: (answer). Keep it under 15 words." } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035532
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What does IEEE 754 'round to nearest, ties to even' mean?" } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035533
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In TCP, what is the standard three-message handshake to establish a connection?" } ] }
SYN → SYN-ACK → ACK.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035534
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In TCP, what is the standard three-message handshake to establish a connection? A: (answer). Keep it under 15 words." } ] }
SYN → SYN-ACK → ACK.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035535
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: SYN → SYN-ACK → ACK. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035536
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035537
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: What recurrence form does the Master Theorem analyze for divide-and-conquer algorithms? A: (answer). Keep it under 15 words." } ] }
T(n)=a·T(n/b)+f(n) (with a≥1, b>1).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035538
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "State the Euclidean algorithm recursion for gcd(a,b) and its base case." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035539
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: T(n)=a·T(n/b)+f(n) (with a≥1, b>1). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035540
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What does IEEE 754 'round to nearest, ties to even' mean?" } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035541
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035542
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In TCP, what is the standard three-message handshake to establish a connection? Then give one practical implication in 1 sentence." } ] }
SYN → SYN-ACK → ACK. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035543
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What recurrence form does the Master Theorem analyze for divide-and-conquer algorithms? Then give one practical implication in 1 sentence." } ] }
T(n)=a·T(n/b)+f(n) (with a≥1, b>1). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035544
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In TCP, what is the standard three-message handshake to establish a connection? A: (answer). Keep it under 15 words." } ] }
SYN → SYN-ACK → ACK.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035545
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)?" } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035546
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035547
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: According to RFC 8259, what are the only three literal names allowed in JSON values? A: (answer). Keep it under 15 words." } ] }
false, null, true (all lowercase).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035548
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "State the Euclidean algorithm recursion for gcd(a,b) and its base case. Then give one practical implication in 1 sentence." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035549
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In TCP, what is the standard three-message handshake to establish a connection? Then give one practical implication in 1 sentence." } ] }
SYN → SYN-ACK → ACK. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035550
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What does IEEE 754 'round to nearest, ties to even' mean?" } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035551
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What recurrence form does the Master Theorem analyze for divide-and-conquer algorithms?" } ] }
T(n)=a·T(n/b)+f(n) (with a≥1, b>1).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035552
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: T(n)=a·T(n/b)+f(n) (with a≥1, b>1). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035553
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "According to RFC 8259, what are the only three literal names allowed in JSON values?" } ] }
false, null, true (all lowercase).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035554
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)? A: (answer). Keep it under 15 words." } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035555
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What does IEEE 754 'round to nearest, ties to even' mean? Then give one practical implication in 1 sentence." } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035556
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035557
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What recurrence form does the Master Theorem analyze for divide-and-conquer algorithms? Then give one practical implication in 1 sentence." } ] }
T(n)=a·T(n/b)+f(n) (with a≥1, b>1). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035558
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035559
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)?" } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035560
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What recurrence form does the Master Theorem analyze for divide-and-conquer algorithms? Then give one practical implication in 1 sentence." } ] }
T(n)=a·T(n/b)+f(n) (with a≥1, b>1). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035561
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "According to RFC 8259, what are the only three literal names allowed in JSON values?" } ] }
false, null, true (all lowercase).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035562
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "State the Euclidean algorithm recursion for gcd(a,b) and its base case. Then give one practical implication in 1 sentence." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035563
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: What does IEEE 754 'round to nearest, ties to even' mean? A: (answer). Keep it under 15 words." } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035564
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)? A: (answer). Keep it under 15 words." } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035565
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: What does IEEE 754 'round to nearest, ties to even' mean? A: (answer). Keep it under 15 words." } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035566
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In TCP, what is the standard three-message handshake to establish a connection? A: (answer). Keep it under 15 words." } ] }
SYN → SYN-ACK → ACK.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035567
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In NIST SP 800-63B (memorized secrets), what is the minimum length for a subscriber-chosen password? A: (answer). Keep it under 15 words." } ] }
At least 8 characters.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035568
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035569
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "State the Euclidean algorithm recursion for gcd(a,b) and its base case. Then give one practical implication in 1 sentence." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035570
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: At least 8 characters. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035571
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: false, null, true (all lowercase). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035572
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: At least 8 characters. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035573
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "State the Euclidean algorithm recursion for gcd(a,b) and its base case. Then give one practical implication in 1 sentence." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035574
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In TCP, what is the standard three-message handshake to establish a connection? Then give one practical implication in 1 sentence." } ] }
SYN → SYN-ACK → ACK. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035575
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: What does IEEE 754 'round to nearest, ties to even' mean? A: (answer). Keep it under 15 words." } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035576
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In NIST SP 800-63B (memorized secrets), what is the minimum length for a subscriber-chosen password? Then give one practical implication in 1 sentence." } ] }
At least 8 characters. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035577
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "What does IEEE 754 'round to nearest, ties to even' mean?" } ] }
Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035578
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)? Then give one practical implication in 1 sentence." } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure). Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035579
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In TCP, what is the standard three-message handshake to establish a connection? A: (answer). Keep it under 15 words." } ] }
SYN → SYN-ACK → ACK.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035580
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: false, null, true (all lowercase). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035581
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035582
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: T(n)=a·T(n/b)+f(n) (with a≥1, b>1). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035583
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: T(n)=a·T(n/b)+f(n) (with a≥1, b>1). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035584
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: SYN → SYN-ACK → ACK. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035585
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: Round to the nearest representable value; if exactly halfway, choose the one with an even least-significant digit (ties-to-even). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "ieee_rounding", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "ieee_rounding" ], "verification": "standard_summary + vendor_doc", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "IEEE 754 overview (rounding rules)", "ref": "turn0search1" }, { "title": "Intel documentation: IEEE 754 default rounding mode (RoundTiesToEven)", "ref": "turn0search9" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035586
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In NIST SP 800-63B (memorized secrets), what is the minimum length for a subscriber-chosen password? A: (answer). Keep it under 15 words." } ] }
At least 8 characters.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035587
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035588
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: State the Euclidean algorithm recursion for gcd(a,b) and its base case. A: (answer). Keep it under 15 words." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035589
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "State the Euclidean algorithm recursion for gcd(a,b) and its base case." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035590
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In a typical TCP session, what comes after the three-way handshake and how does the session typically end (high level)?" } ] }
After the handshake, data transfer occurs; sessions typically end with a connection termination sequence (often described as a four-way closure).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_lifecycle", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "direct_fact", "tcp_lifecycle" ], "verification": "vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Microsoft: TCP/IP connectivity issues troubleshooting (session phases)", "ref": "turn2search17" }, { "title": "MDN: TCP handshake glossary (mentions four-way closure)", "ref": "turn2search11" } ]
{ "wrapper": "direct_fact", "mode": "direct" }
TRMFACT_035591
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: At least 8 characters. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035592
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In NIST SP 800-63B (memorized secrets), what is the minimum length for a subscriber-chosen password? Then give one practical implication in 1 sentence." } ] }
At least 8 characters. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "nist_password_min", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "nist_password_min" ], "verification": "nist_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "NIST SP 800-63B (web)", "ref": "turn0search2" }, { "title": "NIST SP 800-63B PDF", "ref": "turn0search10" } ]
{ "wrapper": "apply_fact", "mode": "apply" }
TRMFACT_035593
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|. (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035594
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: What recurrence form does the Master Theorem analyze for divide-and-conquer algorithms? A: (answer). Keep it under 15 words." } ] }
T(n)=a·T(n/b)+f(n) (with a≥1, b>1).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035595
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "True/False: false, null, true (all lowercase). (Answer True/False only.)" } ] }
True
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "json_literals", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "verify_true_false", "json_literals" ], "verification": "primary_spec:RFC8259", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 8259 - The JavaScript Object Notation (JSON) Data Interchange Format", "ref": "turn0search3" } ]
{ "wrapper": "verify_true_false", "mode": "tf" }
TRMFACT_035596
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: What recurrence form does the Master Theorem analyze for divide-and-conquer algorithms? A: (answer). Keep it under 15 words." } ] }
T(n)=a·T(n/b)+f(n) (with a≥1, b>1).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035597
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: State the Euclidean algorithm recursion for gcd(a,b) and its base case. A: (answer). Keep it under 15 words." } ] }
gcd(a,b)=gcd(b, a mod b); base case gcd(a,0)=|a|.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "euclid_recurrence", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "euclid_recurrence" ], "verification": "educational + reference", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "Khan Academy: The Euclidean Algorithm", "ref": "turn2search2" }, { "title": "Wikipedia: Euclidean algorithm (implementation section)", "ref": "turn1search3" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035598
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: What recurrence form does the Master Theorem analyze for divide-and-conquer algorithms? A: (answer). Keep it under 15 words." } ] }
T(n)=a·T(n/b)+f(n) (with a≥1, b>1).
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "master_form", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "master_form" ], "verification": "mit_ocw_primary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "MIT OCW 6.046J Lecture 3: Divide and Conquer (recurrence form)", "ref": "turn2search10" }, { "title": "MIT OCW 6.006 Recitation 3 (Master Theorem mention)", "ref": "turn2search0" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035599
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "Q: In TCP, what is the standard three-message handshake to establish a connection? A: (answer). Keep it under 15 words." } ] }
SYN → SYN-ACK → ACK.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "micro_refresher", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "micro_refresher", "mode": "compress" }
TRMFACT_035600
trm_realworld_fact_qa
{ "messages": [ { "role": "system", "content": "You are a Tiny Recursive Model (TRM). Answer with factual Q&A only. Be concise and correct." }, { "role": "user", "content": "In TCP, what is the standard three-message handshake to establish a connection? Then give one practical implication in 1 sentence." } ] }
SYN → SYN-ACK → ACK. Implication: Use this rule to avoid protocol/format/security mistakes in implementations.
{ "developer_brand": "Within Us AI", "domain": "tiny_recursive_models", "subdomain": "tcp_handshake", "difficulty": "archon", "tags": [ "trm", "tiny-model", "facts", "real-world", "apply_fact", "tcp_handshake" ], "verification": "primary_spec:RFC793 + vendor_doc + glossary", "safety": "allowed", "license": "apache-2.0", "source": "WithinUsAI/TRM_Genesis_RealWorld_40k", "format_version": "1.1", "retrieved_at_utc": "2026-01-03T20:44:40" }
[ { "title": "RFC 793 - Transmission Control Protocol", "ref": "turn2search3" }, { "title": "Microsoft: The three-way handshake via TCP/IP", "ref": "turn2search1" }, { "title": "MDN: TCP handshake glossary", "ref": "turn2search11" } ]
{ "wrapper": "apply_fact", "mode": "apply" }