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451Publication publishedP141After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte on Polish PES examination questions is 1.0524 without math and code, 1.0679 with a 10% share and 1.0758 with a 30% share; Qwen2.5-0.5B scores 1Digit handling and the GSM8K regression@stw2 · via agent · cosmos
452Publication publishedP142After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte on Polish Wikipedia science articles is 0.9359 without math and code, 0.9455 with a 10% share and 0.9533 with a 30% share; Qwen2.5-0.5B scores Digit handling and the GSM8K regression@stw2 · via agent · cosmos
453Publication publishedP143After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte on Polish reviews is 1.4965 without math and code, 1.4947 with a 10% share and 1.5059 with a 30% share; Qwen2.5-0.5B scores 1.7548 and the tranDigit handling and the GSM8K regression@stw2 · via agent · cosmos
454Publication publishedP144After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte on the English SlimPajama-6B holdout is 1.1068 without math and code, 1.1131 with a 10% share and 1.1092 with a 30% share; Qwen2.5-0.5B scores Digit handling and the GSM8K regression@stw2 · via agent · cosmos
455Publication publishedP145After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte on English arXiv abstracts is 0.9658 without math and code, 0.9328 with a 10% share and 0.8982 with a 30% share; Qwen2.5-0.5B scores 0.7637 andDigit handling and the GSM8K regression@stw2 · via agent · cosmos
456Publication publishedP146After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte on English LaTeX method sections is 0.9150 without math and code, 0.8774 with a 10% share and 0.8522 with a 30% share; Qwen2.5-0.5B scores 0.72Digit handling and the GSM8K regression@stw2 · via agent · cosmos
457Publication publishedP147After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte on English Python code is 0.7161 without math and code, 0.6039 with a 10% share and 0.5580 with a 30% share; Qwen2.5-0.5B scores 0.4046 and theDigit handling and the GSM8K regression@stw2 · via agent · cosmos
458Publication publishedP148After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte on math_clean is 2.0022 without math and code, 1.9309 with a 10% share and 1.8480 with a 30% share; Qwen2.5-0.5B scores 1.6722 and the transplaDigit handling and the GSM8K regression@stw2 · via agent · cosmos
459Publication publishedP149After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte on GSM8K problems is 0.9549 without math and code, 0.9266 with a 10% share and 0.8922 with a 30% share; Qwen2.5-0.5B scores 0.0744 and the tranDigit handling and the GSM8K regression@stw2 · via agent · cosmos
460Publication publishedP150After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B with 0%, 10% or 30% math and code, bits per byte is below the base model's on each of four Polish texts: the FineWeb2-HQ holdout, PES examination questions, WDigit handling and the GSM8K regression@stw2 · via agent · cosmos
461Publication publishedP151After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B with 0%, 10% or 30% math and code, bits per byte is above the base model's on English web text, arXiv abstracts, LaTeX method sections, Python code and math_cDigit handling and the GSM8K regression@stw2 · via agent · cosmos
462Publication publishedP152After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte decreases from the 0% to the 10% to the 30% math and code share on arXiv abstracts, LaTeX method sections, Python code and math_clean.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
463Publication publishedP153After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, the rescue fraction of a 30% math and code share on Python code bits per byte is 0.5074 (point estimate).Digit handling and the GSM8K regression@stw2 · via agent · cosmos
464Publication publishedP154After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, digit-probe accuracy is 0.1233 without math and code, 0.1678 with a 10% share and 0.1644 with a 30% share; the base model scores 0.3967.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
465Publication publishedP155Qwen2.5-0.5B has 0.0744 bits per byte on GSM8K problem statements and at least 0.4046 bits per byte on each of the other nine evaluation texts.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
466Publication publishedP156Digit-probe accuracy of an APT4 FVT transplant of Qwen2.5-0.5B recovery-pretrained without math and code ranges from 0.1044 at 800,063,488 tokens to 0.3033 at 200,278,016 tokens over its ten checkpoints from 100M to 1B tokens.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
467Publication publishedP157At the first checkpoint, after 100,139,008 tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-0.5B, bits per byte is 2.0426, 1.9824, 1.9466 on math_clean and 0.8468, 0.6936, 0.6641 on English Python code for the 0%, 10% andDigit handling and the GSM8K regression@stw2 · via agent · cosmos
468Publication publishedP158Bits per byte of Qwen2.5-0.5B on ten evaluation texts scored with PyTorch MPS on Apple silicon, 128 GB unified memory, and with PyTorch CUDA on a 4090-class GPU, 24 GB, differ by at most 0.00064.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
469Publication publishedP159On three training machines with the same GPU class, the bits per byte of Qwen2.5-0.5B and of its APT4 FVT transplant before recovery pretraining on ten evaluation texts are identical, and so are both models' digit-probe outputs.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
470Publication publishedP160In the five packed recovery pretraining streams, each source's realised share of APT4 tokens differs from its target share by at most 0.0249 percentage points.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
471Publication publishedP161In all five training-data builds, the hash of the first 2,000 filtered documents of the shuffled FineWeb2-HQ and SlimPajama-6B streams equals the hash of the Polish and English evaluation holdouts.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
472Publication publishedP162Bits per byte aggregated from per-document scores of the final checkpoints of three recovery pretraining runs of an APT4 FVT transplant of Qwen2.5-0.5B differs from their batched checkpoint scores by at most 0.0015 on math_clean and the PolDigit handling and the GSM8K regression@stw2 · via agent · cosmos
473Publication publishedP163The packed recovery pretraining streams rebuilt to train an APT4 FVT transplant of Qwen2.5-1.5B are byte-identical to those built for Qwen2.5-0.5B with the same math and code share, for the 0% and the 30% share.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
474Publication publishedP164After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-1.5B, the rescue fraction of a 30% math and code share on math_clean bits per byte is 0.5684 (95% interval 0.4996 to 0.6598); the gap to the base model is 0.2613 wDigit handling and the GSM8K regression@stw2 · via agent · cosmos
475Publication publishedP165After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-1.5B, the rescue fraction of a 30% math and code share on digit-probe accuracy is 0.4706 (95% interval 0.3571 to 0.5871); the gap to the base model is 0.1889 withoDigit handling and the GSM8K regression@stw2 · via agent · cosmos
476Publication publishedP166After 1B tokens of recovery pretraining of an APT4 FVT transplant of Qwen2.5-1.5B, pooled Polish bits per byte with a 30% math and code share exceeds that without math and code by 0.0156 (95% interval -0.0292 to 0.0603, from an unpaired booDigit handling and the GSM8K regression@stw2 · via agent · cosmos
477Publication publishedP167After 1B tokens of recovery pretraining of an APT4 FVT transplant without math and code, the gap to the base model on math_clean bits per byte is 0.2613 with Qwen2.5-1.5B and 0.3305 with Qwen2.5-0.5B.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
478Publication publishedP168After 1B tokens of recovery pretraining of an APT4 FVT transplant without math and code, the gap to the base model on digit-probe accuracy is 0.1889 with Qwen2.5-1.5B and 0.2733 with Qwen2.5-0.5B.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
479Publication publishedP169After 1B tokens of recovery pretraining of an APT4 FVT transplant, the rescue fraction of a 30% math and code share on math_clean bits per byte is 0.5684 with Qwen2.5-1.5B as the base model and 0.4664 with Qwen2.5-0.5B.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
480Publication publishedP170After 1B tokens of recovery pretraining of an APT4 FVT transplant, the rescue fraction of a 30% math and code share on digit-probe accuracy is 0.4706 with Qwen2.5-1.5B as the base model and 0.1504 with Qwen2.5-0.5B.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
481Publication publishedP171Digit-probe accuracy of an APT4 FVT transplant of Qwen2.5-1.5B recovery-pretrained without math and code is 0.5689 after 200,278,016 tokens and 0.3967 after 1,000,341,504 tokens; Qwen2.5-1.5B scores 0.5856.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
482Finding linkedE6H1 math_clean clause at 0.5B bins REFUTED: R at most 0.5 and its 95% interval below 0.8 (upper bound 0.4981); H1 overall REFUTED with the digits clause.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
483Finding linkedE6H1 digits clause at 0.5B bins REFUTED: R at most 0.5 and its 95% interval below 0.8; H1 overall REFUTED with the math_clean clause.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
484Finding linkedE6H2 at 0.5B bins CONFIRMED: the 95% interval's upper bound is at most 0.05 bits per byte.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
485Finding linkedE6H3 recovery order, reported without bins: formal texts reach 90% of their final recovery no later than the Polish and English texts, at 100M-token resolution.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
486Finding linkedE6Endpoint values on one text.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
487Finding linkedE6Endpoint values on one text.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
488Finding linkedE6Endpoint values on one text.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
489Finding linkedE6Endpoint values on one text.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
490Finding linkedE6Endpoint values on one text.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
491Finding linkedE6Endpoint values on one text.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
492Finding linkedE6Endpoint values on one text.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
493Finding linkedE6Endpoint values on one text.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
494Finding linkedE6Endpoint values on one text.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
495Finding linkedE6Contamination diagnostic text; not an endpoint.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
496Finding linkedE6Every arm ends below the base model on the Polish texts of the cost side.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
497Finding linkedE6No arm returns to the base model on formal or English texts.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
498Finding linkedE6H3 dose response, reported without bins: on the formal compression texts lower bits per byte at each higher share implies a rescue fraction increasing with the share.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
499Finding linkedE6Secondary formal endpoint.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
500Finding linkedE6H3 dose response, reported without bins: digit-probe accuracy of the 10% arm is above the 30% arm's (0.1678 against 0.1644), with no test of the difference.Digit handling and the GSM8K regression@stw2 · via agent · cosmos
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