docs/DATA_DICTIONARY.md

Data dictionary

The files in results/ are outputs of fixed-design synthetic finite known-model studies. They are neither human gameplay records nor model weights. There are no training/validation/test splits, no learned neural model, and no commercial-game benchmark. Trial tables expose simulation draws; aggregate tables summarize those draws or exact finite computations. Combining rows from different designs does not create a shared benchmark population.

All counts below describe the delivered v3 reference outputs. Deterministic reproduction can regenerate the main files. Scientific definitions are implemented in experiments/run_all.py and the modules under src/infinite_players/.

Shared conventions

Convention	Meaning
Probabilities, accuracy, TV, gain fractions	Dimensionless numbers, usually represented on the 0–1 scale rather than as percentages
ci_low, ci_high in binomial studies	Two-sided nominal 95% Wilson interval for the simulated success proportion
paired_gain_ci_low, paired_gain_ci_high	Descriptive paired t interval over 16 arena-seed gains, not an external population guarantee
trial, seed, revision, index	Zero-based identifiers within the stated study design unless otherwise stated
iteration in nullspace_updates.csv	One-based projected-policy update number, from 1 through 24
Event/lag/horizon counts	Simulation events or decisions; they are not seconds, milliseconds, frames, or a proposed universal AI clock
theta, world	Synthetic signs in {-1,+1}; binary type and mechanics hypothesis labels
Floating residuals	Absolute numerical errors in the indicated probability, logscore, or equality-constraint quantity
Payload bytes	NumPy array payload only where specified; excludes Python objects, allocator overhead, and unrelated input storage

The main pseudorandom seed is 1,860,317. Different studies use offsets from it; the arena family separately calls make_arena(4100 + seed). results/config.json records the main experimental design. Study definitions are fixed rather than selected by searching for the strongest displayed outcome.

Result-file map

Family	Aggregate/diagnostic files	Trial or structured detail
Temporal alignment	continuous_lag.csv	continuous_lag_trials.csv
Sequence inference	sequence_inference.csv, sequence_inference_audit.json	sequence_inference_trials.csv
Local source correction	local_revisions.csv, runtime_telemetry.json	local_revision_trials.csv
Future-query memory	memory_graphs.csv, retrospective_memory.csv, lossy_memory_bound.json	No separate retrospective-query trial CSV is retained
Semantic-law policy improvement	shield_summary.csv, semantic_horizons.csv, calibration_unlock.json	shield_arena.csv, nullspace_updates.csv, policy_examples.json
Approximate operators	approximation_summary.json	approximation_trials.csv
Lifetime promotion audits	lifetime_audit.csv	No separate lifetime-history trial CSV is retained
Exact finite verification	exact_audits.json	Enumerated assertions and rational values, not a generic gameplay dataset
Combined configuration/results	config.json, summary.json	These duplicate or collect study outputs rather than introducing extra independent evidence

Temporal alignment and lag

continuous_lag.csv has 7 rows, one each for lags 0, 1, 2, 3, 4, 6, and 9. Each condition contains 16,000 trajectories of 64 events, for 112,000 trajectories overall. The generator uses Markov persistence 0.72 and sign reliabilities 0.6 and 0.75. Overlapping trajectory segments are generated jointly; endpoint pairs are not assumed independent.

Fields	Definition and units
lag	Offset between observation streams, in simulation events
n	Events contributing to each signed score; 64 here
trials, correct	Trajectory count and number classified correctly
accuracy	correct / trials; ties are resolved by a random fair sign
ci_low, ci_high	Wilson interval for simulated classification accuracy
mean_score, theory_mean	Observed mean and exact declared-model mean of the sum of n signed products; score units
variance, theory_variance	Sample variance with ddof=1 and exact declared-model variance of that score; squared-score units
error_bound	Conservative one-trajectory classification-error upper bound returned by lag_moments; dimensionless and not an empirical error rate

continuous_lag_trials.csv has 112,000 rows. Its key is (lag, trial); score is the signed integer score and correct is 0 or 1. These trajectories are synthetic alignment fixtures, not measurements of human response latency.

Sequence inference

sequence_inference.csv has 9 rows: three methods at each of 8, 16, and 32 events per record. There are 1,000 records at each length, for 3,000 underlying records. The three method rows within each length are evaluated on the same records, so they are paired comparisons rather than 9,000 independent recordings.

method	Meaning
operator_tree	Ordered scaled-operator tree inference after the simulated mechanics calibration
full_HMM_replay	Separately implemented exact full forward replay using the same hypotheses, likelihoods, and calibration
paired_product	Simpler sign-product estimator on those same synthetic records

Aggregate fields are events, method, trials, correct, accuracy, ci_low, and ci_high. events is the source-record length. Accuracy is correct recovery of the synthetic binary theta after the actual simulated world sign is supplied as a calibration probe. These values do not measure human identity reconstruction.

sequence_inference_trials.csv has 3,000 rows, keyed by (n, trial):

Fields	Meaning
n	Events in this record; corresponds to aggregate events
trial	Record index within this length condition
theta, world	Generating type and mechanics signs
posterior_positive	Tree posterior probability of theta = +1 after the mechanics probe
tree_correct, full_replay_correct, product_correct	Per-method 0/1 correctness on the same record

sequence_inference_audit.json records independent_records (3,000), maximum_tree_replay_posterior_error (maximum coordinatewise posterior discrepancy), and maximum_precalibration_identity_error_from_half (largest departure from the symmetric 0.5 type posterior before calibration). The tree is an update/inference organization, not a better posterior than the same exact Bayesian model.

Local evidence correction and resource cost

local_revisions.csv has 3 rows, for archived lengths 256, 2,048, and 16,384 events. Each length receives 16 local factor replacements under a fixed four-hypothesis, two-hidden-state model.

Fields	Meaning and units
events, hypotheses, hidden_states, revisions	Archive length and the finite inference dimensions/counts
tree_compositions_per_revision	Tree-depth count of batched operator compositions after replacing one leaf
replay_steps_per_revision	Event-wise vector-forward steps for full replay
tree_payload_bytes	Reported conceptual operator-node payload bytes, including scaling arrays and padding/unused node slots
raw_two_sign_payload_bytes	Baseline payload of two raw int8 sign streams, 2 * events bytes
max_posterior_error	Maximum absolute posterior-coordinate discrepancy across 16 replacements
max_centered_logscore_error	Maximum error after subtracting each implementation's first hypothesis logscore; distinguishes accumulated relative-logscore error from posterior saturation

Tree compositions and forward steps are different work units, with additional hypothesis/state arithmetic factors. The depth reduction is not an equal-unit FLOP comparison. The tree payload is 160 times the minimal raw two-sign payload on these fixtures, excluding overhead; do not describe it as a compression result.

local_revision_trials.csv has 48 rows, keyed by (events, revision). It contains index (replaced event position), posterior_max_error, centered_logscore_error, tree_compositions, and forward_steps for each replacement. Replacements within one archive are sequentially related and are not 48 independent archives.

runtime_telemetry.json is a list of 3 entries. Fields are events, build_seconds, tree_16_revisions_seconds, replay_16_revisions_seconds, and measured_revision_speed_ratio (replay update time divided by tree update time). Durations use wall-clock seconds. The ratio excludes tree construction and measures a single local execution. This file is intentionally excluded from deterministic reference hashing. Original reference telemetry and fresh audit telemetry are distinct retained observations.

Future-query memory

memory_graphs.csv has 7 exact finite cases for record lengths 1 through 4 bits. queried_coordinates is either the first coordinate alone or every coordinate; the one-bit case appears once.

Fields	Meaning
record_bits	Length n of a binary historical record
queried_coordinates	Number of prefix coordinates that a future query may request
records	Number of possible input records, 2 ** record_bits
minimum_memory_states	Exact chromatic number of the constructed confusability graph
minimum_fixed_bits	Ceiling of log2 of that state count; fixed-length exact-storage requirement in bits

retrospective_memory.csv has 6 aggregate rows for retained prefixes of 0, 8, 32, 64, 128, and 256 bits from a 256-bit synthetic history. Each storage condition is evaluated on the same 16,000 generated histories/coordinate queries; conditions are paired, not six unrelated datasets. The implemented strategy stores a prefix and guesses outside it.

Fields: history_bits, retained_prefix_bits, trials, correct, accuracy, ci_low, ci_high, analytic_accuracy, and evidential_coverage. The latter two equal 0.5 + 0.5 * retained_prefix_bits / history_bits and retained_prefix_bits / history_bits, respectively. This is a disclosed prefix-retention baseline, not a claim of optimal approximate coding at every bit budget.

lossy_memory_bound.json contains history_bits and a bounds list with average_error and minimum_bits_lower_bound. The lower bound is n * (1 - h2(error)), measured in bits, under the declared random-access setting. It is an information-theoretic lower bound, not an implemented encoder size or compression benchmark.

Semantic-law policy improvement

The arena has six ground states, six ground actions, two semantic posture labels, and two semantic tactic labels, with discount factor gamma = 0.9. Each tactic has three motor realizations. Rewards in FiniteMDP are expected per-decision rewards; the demo environment samples Bernoulli rewards from them.

method	Delivered controller
source_anchor	Original interior tactic/motor-mixture policy
path_shield_LP	Exact finite policy iteration using LP-constrained joint next-tactic/next-posture signatures
conditional_class_only	Policy iteration preserving current-state tactic probabilities, with no full semantic-path contract
unconstrained	Policy iteration without those semantic constraints
nullspace_24_updates	24 feasible projected-Q updates from the source anchor

shield_arena.csv has 80 rows: five methods across 16 seeded arenas. seed is the replicate index 0–15; the generator receives 4100 + seed, with synthetic source type alternating by parity.

Fields	Definition
discounted_value	Mean of exact infinite-horizon discounted state values over all six initial ground states, equally weighted
normalized_value	(1 - gamma) * discounted_value; comparable per-decision reward scale
normalized_gain	Mean normalized state-value improvement relative to the same seed's anchor
minimum_state_value_gain	Minimum unnormalized discounted-value gain over the six ground states
class_probability_error	Maximum absolute departure from target current-state tactic probabilities
signature_error	Maximum absolute departure from the full target joint semantic-action/next-semantic-state kernel
semantic_path_TV_h6	Half the L1 difference between exact enumerated six-step semantic-word laws, starting specifically at ground state zero

Initial conditions differ across metrics: the value metric averages all six starting ground states; path TV starts at state zero. They must not be described as the same trajectory-return measurement. semantic_law enumerates sequences of (semantic action, next semantic state) pairs; it does not enumerate motor actions or require ground-state distributions to match.

shield_summary.csv has 5 rows, one per controller. normalized_value, normalized_gain, and semantic_path_TV_h6 are means over 16 seeds. paired_gain_ci_low and paired_gain_ci_high are the mean gain plus/minus a Student-t standard-error interval with 15 degrees of freedom. max_signature_error is the maximum over seeds, not the mean. seeds records the replicate count.

nullspace_updates.csv has 384 rows, keyed by (seed, iteration):

Fields	Meaning
mean_value	Mean unnormalized discounted value after this update, over six ground states
minimum_value_gain	Minimum state-value change relative to the immediately previous update, in unnormalized discounted-value units
signature_residual	Maximum absolute signature-constraint residual after this update

Its sequential iterations are not independent trials. Compare normalized values only after applying the explicit (1 - gamma) factor.

semantic_horizons.csv has 32 rows: four methods (source_anchor, path_shield_LP, conditional_class_only, unconstrained) at horizons 1–8, for arena seed index zero only. semantic_path_TV uses exact law enumeration from ground state zero. This file is neither a 16-seed average nor a sample-size/accuracy curve; the projected-update method is not included in it.

policy_examples.json contains 15 entries: the five controller policies for seed indices 0, 1, and 2. Each has seed, method, a 6-by-6 row-stochastic policy matrix, and audit where applicable. LP audit objects report iteration count, Bellman residual, and per-state primal residual, dual violation, and duality gap. Source-anchor/projected examples may have null audit fields. Tiny negative zeros are floating serialization artifacts, not negative probability claims.

calibration_unlock.json contains:

• calibration: three named entries, before_calibration_robust, true_world_0, and true_world_1. Each contains a three-action policy, expected one-decision reward, constraint rank, nullity, and numerical LP audit with primal/dual residuals and duality gap. This small fixture is separate from the six-state averaged arena.
• no_headroom_max_absolute_gain: maximum absolute discounted state-value difference between optimized and anchor policies in the separate constant-reward no-headroom arena.

The positive world control's reward 0.85 and negative world's 0.4 are finite constructed controls. They are not human player returns or a general empirical calibration effect.

Approximate operator circuits

approximation_trials.csv has 1,000 rows, one per positive-circuit perturbation trial. Each trial uses eight factors, four hypotheses, and two hidden states.

Fields	Meaning
trial	Perturbation-trial index
log_error_budget	Sum of entrywise multiplicative log-error allowances over factors; natural-log scale
posterior_TV	Total variation between exact and perturbed posterior distributions
uniform_bound	tanh(log_error_budget / 2) bound used by this declared positive-operator construction

approximation_summary.json records trials, violations, maximum_posterior_TV, and maximum_error_bound_ratio, the largest observed posterior_TV / uniform_bound. Zero violations in these simulations supports the implemented fixture check; the mathematical theorem and its assumptions must be assessed separately.

Lifetime promotion audit

lifetime_audit.csv has 2 aggregate rows, for true mean session gains 0 and 0.3. Each condition simulates 10,000 histories, 40 candidate versions, and 256 bounded audit observations per version. Gains are synthetic independent signs with the declared mean. The version budget is lifetime_budget / (version * (version + 1)) for one-based versions.

Fields	Meaning
true_gain	Generating expected bounded session-level gain
trials	Simulated lifetime histories, not individual session observations
versions	Number of candidate versions tested per history
audit_sessions_per_version	Audit sample count used by each version's decision rule
lifetime_budget	Total nominal error allocation, 0.05
any_promotion_count, any_promotion_rate	Number and fraction of histories with at least one accepted promotion
ci_low, ci_high	Wilson interval for that any-promotion fraction
mean_promotions	Mean count of accepted versions per history

This is a statistical acceptance-rule fixture. It does not simulate a learning system discovering 40 successively improved algorithms, and is not evidence of sustained recursive self-improvement.

Exact audits, combined JSON, and retained reports

exact_audits.json records separate finite checks under lag, operator, memory, shield, and composition, plus status. It includes exact rational quantities as strings, enumerated-case counts, and selected floating discrepancies. Cases include 2,550 lag atoms, 16 hidden operator paths, 276 deterministic encoders, 2,046 semantic words, and 72 posterior/horizon composition cases. These are internal exact-arithmetic implementations, not external proof review.

config.json records design counts, sizes, seed, and the synthetic-study scope. summary.json collects the outputs of the seven study functions. Some entries are nested pairs, such as [sequence_aggregate_rows, sequence_audit] and [shield_aggregate_rows, calibration_report]; the JSON is a study report, not a tabular split. Values already present in CSVs are duplicated summaries, not additional observations.

v3_source_reproduction.json and final_zip_reproduction.json are retained original execution reports. Their comparisons entries contain file, expected/actual SHA-256 digests, and match; top-level fields count the declared deterministic files and matches. legacy_v2_reproduction.json and final_zip_legacy_reproduction.json similarly retain the original v2 execution evidence. Original test logs (tests.txt, v3_reproduced_tests.txt, and legacy_v2_run.txt) are text diagnostics, not study data. The legacy archive is omitted from this curated edition; see REPRODUCIBILITY.md for restoration instructions.

Fresh release-preparation outcomes are separately identified under validation/. The original report descriptions, source paths, and timestamps are provenance and must not be interpreted as a fresh run performed by every downloader.

Demonstration artifacts

The three files under examples/demo/ are known synthetic fixtures rather than dataset splits:

File	Structure and meaning
synthetic_recording.jsonl	32 source events. Fields: nonempty event_id, integer simulation tick, signs action_signal and context_signal, asserted source_kind = synthetic_fixture, clock_domain = shared_simulation_tick, and source_epoch. The exact contract is in schemas/fixture_event.schema.json.
descendant_trace.jsonl	1,000 execution decisions with tick, ground state, chosen ground action, semantic_action, sampled 0/1 reward, and next_state. A single stochastic continuation trace, not 1,000 independent agent evaluations.
player_capsule.json	Source digest/epoch and event count, finite hypothesis catalog, coupled pre/post-calibration posterior, persistent sampled type branch, anchor/descendant policies, declared protected semantic kernel, exclusions, numerical optimizer audit, and evaluation summary.

The capsule's normalized analytic values average the finite state-value vectors; its path TV uses the default state-zero initial law; its sampled_reward_mean is the arithmetic mean of one 1,000-step sampled trace. They have different estimands. Source-kind labels and event identifiers are caller assertions, not cryptographic proof of human origin or observation independence. Distinct IDs do not by themselves establish independent observations.