XllentAI
/

modular_arithmetic

@@ -147,7 +147,7 @@ Reproduce any row with `modchallenge evaluate horner_rnn --total 1100 --seed <he
 This matches the larger faithful 5-prime bootstrap on the shipped weights
 (`diag_5prime_boot.py` in the research repo): `P(tier < 0.90) ≈ 0.000 %` for tiers 1–9 and
 ≈ 0.002 % for tier 10; `E[tier10] ≈ 0.991`, worst observed near-max tier-10 prime ≈ 0.875. A
-40k-draw width sweep (`audit_width_robustness.py`) finds **no accuracy "knee"** anywhere in the
 samplable range — the residual misses are rare per-`(a,b)` reduction-boundary events scattered
 ≈ uniformly, in the deep tail only.

 This matches the larger faithful 5-prime bootstrap on the shipped weights
 (`diag_5prime_boot.py` in the research repo): `P(tier < 0.90) ≈ 0.000 %` for tiers 1–9 and
 ≈ 0.002 % for tier 10; `E[tier10] ≈ 0.991`, worst observed near-max tier-10 prime ≈ 0.875. A
+40k-draw width sweep (`audit_width_robustness.py`, research repo) finds **no accuracy "knee"** anywhere in the
 samplable range — the residual misses are rare per-`(a,b)` reduction-boundary events scattered
 ≈ uniformly, in the deep tail only.

README.md CHANGED Viewed

@@ -125,9 +125,10 @@ accuracy, and both are about *matching the test distribution*:
 ### Tier 9 and the reduction-boundary position
 The tier-9 prime range is value-uniform on `[2^513, 2^1024)`, so a large fraction of tier-9
-primes are **shorter than 1024 bits**, and the conditional-subtraction reduction boundary
-lands at `p`'s most-significant set bit — at a *different position* for each prime width. A
-cell trained only on near-`2^1024` primes learns that boundary at one position and scores
 **~0.00 on shorter primes**: tier 9 started at **0.73**, dominated by a single ~1020-bit
 benchmark prime failing entirely (0/22). The fix is to train on a mix of value-uniform primes
 (benchmark-faithful) and **bit-length-uniform primes over [990, 1024]** (equal weight to every
@@ -136,8 +137,11 @@ position. Combined with gradient accumulation (effective batch ~26k) and the wor
 loss, this took tier 9 from **0.73 -> 0.99**, even across prime widths (held-out value-uniform
 validation 0.99; per-width 1015-1024 all ~0.99).
-The training scripts live in the companion research repo (not shipped in this model repo); the
-commands below document *how the weights were obtained* (the provenance the rules ask for):
 ```bash
 # Historical small-prime cells were first trained width-matched, then absorbed into the shared cell.

 ### Tier 9 and the reduction-boundary position
 The tier-9 prime range is value-uniform on `[2^513, 2^1024)`, so a large fraction of tier-9
+primes are **shorter than 1024 bits**, and the position where the modular reduction must occur
+(`p`'s most-significant set bit) differs per prime width, so the trained convolution must learn
+that boundary at every position. A cell trained only on near-`2^1024` primes learns it at one
+position and scores
 **~0.00 on shorter primes**: tier 9 started at **0.73**, dominated by a single ~1020-bit
 benchmark prime failing entirely (0/22). The fix is to train on a mix of value-uniform primes
 (benchmark-faithful) and **bit-length-uniform primes over [990, 1024]** (equal weight to every
 loss, this took tier 9 from **0.73 -> 0.99**, even across prime widths (held-out value-uniform
 validation 0.99; per-width 1015-1024 all ~0.99).
+The training scripts and the intermediate checkpoints they reference live in the companion
+research repo (not shipped in this model repo); the commands below document *how the weights were
+obtained* (the provenance the rules ask for) and are not runnable as-is from this repo alone.
+Intermediate warm-start files such as `weights_shared_64_512.pt` are prior in-flight cells, not
+redistributed here.
 ```bash
 # Historical small-prime cells were first trained width-matched, then absorbed into the shared cell.