Clara_v4_stage1 — memorisation

37,806,408 tokens · pre-tokenised uint16 bins · zero traces. Stage 1 of a staged curriculum: this is the fact itself. Stage 2 is how to get it.

⚠️ Verify the tokenizer before you mount anything:

python3 CLARA_TOKENIZER/verify_tokenizer.py CLARA_TOKENIZER/tokenizer.json clara_v4_stage1_memorize

pool	tokens	docs	max_doc
clara_v4_stage1_memorize	1,662,722	—	—

Shards: 97 / 33 / 35. ⚠️ Sharded so that n_shards >= world_size x 4 — with shards[rank::world] a pool with fewer shards than ranks leaves some ranks with zero shards for that lane and it is served at a fraction of its configured dose, silently. The original 4/1/1 sharding would have been served by 4, 1 and 1 rank of 8. | clara_v4_stage1_formulas | 1,037,357 | 685 | 1,720 | | clara_v4_stage1_reference | 131,503 | 279 | 557 |

Contents

_memorize — 36,502 facts, THE TABLES ONLY, enumerated and proven present in the bins.

⛔ This pool was 4,119,364 facts (exhaustive to 3 digits) and that version FAILED, measurably. Trained 40 epochs it scored 0/250 on recall and emitted degenerate repetition. The comparison that explains it:

arith_atoms_s512  3,000,000 problems · ~10 exposures · TRACED -> 98% recall
the 3-digit pool  4,119,364 facts    · ~40 exposures · BARE   ->  0% recall

Not the count, not the exposures — the FORMAT. 999*999 is not a fact anyone memorises, it is a procedure; a bare pool asks the model to induce the algorithm from answers alone with the working deliberately removed. ⇒ bare covers what is genuinely LOOKUP (through the 2-digit tables); everything at 3 digits and above belongs in the TRACED stage-2 pool.

⚠️ The negative-operand NOTATION forms are sampled, not exhaustive — + - meaning - is ONE systematic rule, and exhaustively it was 70.8% of this pool, outnumbering the real table facts 2.4:1. A rule needs a few thousand examples; the tables need every one.

Contents: every + − × pair over 0..99 (negatives included) · division with remainder · every negative-operand form in both spaced and unspaced notation · squares, cubes, powers. (superseded) a 4,079,962-fact core. EVERY combination of + − × for both operands over 0..999 (1,000,000 pairs each, negatives included), division with remainder for every dividend 0..9,999 over divisors 1..99, every + − × pair over −99..99, squares to 1000², cubes to 100³, powers of 2/3/10. ⛔ Exhaustive stops at 3 digits and that is arithmetic not choice: 4-digit would be 300,000,000 facts = 4.2B tokens = 36% of a 116B run. Above 3 digits the pool samples.

Syntax: one space either side of =. 0-1=-1 tokenises =- as a single fused token; 0-1 = -1 gives ' =' then ' -'. Negative operands are written canonically — -3-3 = -6, not -3+-3 — and the translation is itself taught as a fact: 3 + -2 = 3 - 2 = 1, so the model can accept either form. Both surface forms are taught — spaced 3 + -2 = 3 - 2 = 1 and unspaced 3+-1 = 3-1 = 2. Unspaced, +- and -- each tokenise as a SINGLE token, so these lines define that token's meaning directly.

(superseded) a 17,381-fact core: all a+b, a−b, a*b for a,b ∈ 0..9 · times tables to 12×12 · exact division tables (divisor 1..12, quotient 0..99) · all a±b for a,b ∈ 0..99 · all a*b for a ∈ 0..99, b ∈ 0..9 · squares 1..50 · cubes 1..20 · 2^1..16 · 10^1..10. Plus 2,000,000 sampled: 3–6 digit + − ×, division with 6-digit answers, multi-component chains, exponents, fractions, decimals, percents.

_formulas — geometry, algebra identities, trig (incl. unit-circle exact values), derivative and integral tables, physics, combinatorics. 25,248 sympy-verified assertions; every formula ships with computed worked instances.

_reference — all 118 elements (via periodictable), scipy.constants, 24 SI prefixes, primes < 1000, roman numerals, factorials, exact unit conversions, Greek alphabet.

Format

uint16 little-endian token ids. BOS = 65463, EOS = 65464. Tokenizer tok_64k_singledigit, sha256 0c9c6d8c528d5aae542e27276ef9c48000dc32a8e3edab76071438d3be40d706, with the Digits pre-tokenizer stage — digits tokenise individually (1234 → [16,17,18,19]).

Gates — each names an input that would fail it

1. Independent second evaluation path — every item recomputed from its emitted string by a different route; rejects 2+2=5, 1/2+1/2=2, 100/4=24.
2. All-shard single-digit census — 0 multi-digit tokens.
3. Decode-and-recompute from the written bins — 0 failures.
4. Zero-trace assert — 0 documents contain S(/P(/carry=/Step.
5. Completeness proven — all 17,381 core facts and all 118 elements verified present in the bins.

Dosing

Memorisation is bought in repetitions (~10), not tokens: pool ≤ frac × RUN / 10. Under random-offset sampling a pool served at 3 epochs shows only 1−e⁻³ = 95% of itself, so the core block is already repeated 10× inside the pool.

Provenance

Entirely synthetic — generated by computation and verified against sympy, periodictable and scipy.constants. No third-party corpus content. Nothing was typed from recall; categories with no authoritative offline source (country capitals, planetary data, historical dates) are deliberately absent, because a wrong memorised fact is worse than a missing one.