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values | record_ids stringlengths 0 305 | token_ids listlengths 512 512 |
|---|---|---|---|
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prod100x:direct_sp:153184 | direct_sp | mul_sub:8d873ca1,sub_add:ac01fd88,mul_add:627875f5,sub_mul:184116a1,sub_add:a198450d,sub_add:2ff39f1a,add_sub:3c37c9ff | [
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prod100x:code:007830 | code | sub_add:4c213927,sub_add:bff9db81,sub_add:41ac2b88,add_sub:8f17a631,sub_mul:fd73812b,sub_mul:a18fe7eb,mul_sub:0da26f28,mul_sub:9dc9ac6b,mul_sub:4d1e57f2 | [
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108,
... | |
real_web-0478718 | real_web | [
67,
101,
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116,
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32,
119,
105,
116,
104,
32,
112,
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111,
103,
114,
97,
112,
104,
115,
44,
32,
100,
111,
99,
117,
109,
101,
110,
116,
115,
32,
97,
110,
100,
32,
97,
114,
116,
105,
102,
97,
... | |
real_web-0859821 | real_web | [
256,
10,
97,
110,
110,
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97,
108,
32,
115,
97,
108,
97,
114,
121,
32,
40,
36,
41,
32,
61,
32,
261,
256,
44,
256,
256,
256,
274,
84,
104,
101,
32,
102,
105,
114,
115,
116,
32,
65,
115,
116,
101,
114,
111,
105,
100,
32,
... | |
real_web-0534641 | real_web | [
105,
116,
32,
99,
101,
114,
116,
97,
105,
110,
108,
121,
32,
119,
97,
115,
32,
97,
110,
32,
101,
110,
116,
101,
114,
116,
97,
105,
110,
105,
110,
103,
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97,
102,
116,
101,
114,
110,
111,
111,
110,
32,
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110,
115,
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... |
End of preview. Expand in Data Studio
magic-cap1b training data
~1B tokens, 1,953,123 blocks of 512 tokens (uint16 ids, vocab 276): 50% FineWeb-Edu sample-10BT (byte-level, digits atomic) + 50% synthetic arithmetic in 4 evidence families (direct_sp scratchpad / verbal / code with computed values / primitive). Widened spec: starts 0-999, mult 2-5, addsub 1-99; 300k distinct programs per family, ~1-3x reuse.
generation/ holds the exact code + tokenizer that produced (and
decodes) the tokens; record_ids maps synthetic blocks to programs.
Rebuild deterministically: modal_app.py --phase build --variant cap in
the project repo, https://github.com/HCAI-Lab-GT/mathamagical. Trained model:
leejason2025/magic-cap1b. Web text under ODC-By (FineWeb-Edu).
Contamination screen of the web half
Run on the exact bytes in this dataset. shard0.parquet verifies to
b1ba7b2ce4cb5ea6ef42dca40263eabb85f37700d01693a68e9b30a31d78e871 and
the build consumes docs in file order until the background budget is
filled, so the screened set is exactly the web half: 103,966 docs /
500,031,637 bytes, the first 14.3% of the shard. Nothing later in the
shard and nothing from any other shard is in this dataset.
| Definition of "contaminated" | Docs |
|---|---|
Contains the record format (STEP_1: or START: n |) |
0 |
| Contains a held-out prompt verbatim | 0 |
| States a full held-out chain (both steps of one item) | 0 |
States only the answer step (mid x k2 = t) |
5 |
| Contains any arithmetic equation at all | 168 |
The screen asserts a positive control (the format pattern must fire on a real training record and on a held-out prompt) before scanning, so the zeros are verified rather than a dead pattern.
The 5 answer-step matches are incidental times-table facts in unrelated
documents (1 * 3 = 3 inside an RSA worked example, 3 x 2 = 6 inside
JMeter loop counts, 8 x 2 = 16 inside a guess-your-age trick). None
states the held-out problem. All belong to the three held-out items whose
intermediate arithmetic is common knowledge, which is a held-out design
weakness rather than contamination; later held-out sets raise the
starting range and should exclude single-digit intermediates by
construction.
Scope: the screen covers the direct/scratchpad format that the held-out claim is stated in. Verbal and code families were not separately screened. Scripts and raw results: see the project repo, https://github.com/HCAI-Lab-GT/mathamagical.
Known issue: 8-char program_ids
program_id in this release is an 8-hex-char sha256 prefix (32 bits),
namespaced by composition. Measured on this exact build: 29 colliding
ids covering 58 distinct programs, 0.005% of records, roughly 6-7 pairs
per composition, which is what the birthday bound predicts at ~240k
programs per composition.
This affects record_ids, the block-to-program map used for attribution,
so a handful of blocks are 2-way ambiguous about which program they came
from. It does not affect training or the capability evaluations, which
never read record_ids. The generator has since moved to 16 hex chars;
ids are a pure function of the program signature and the build is
deterministic from seed 0, so a rebuild regenerates them with no other
change.
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