[lm1909]

Change and mathematical scope

Audit, no new κ. This is an adversarial check of DaysSky's #4629 (head 2cf7d081118f6f702aa317816d231b41ce073579). Question: do the stated ledger and complex κ follow from the written artifact, and is the 213-helper re-padding priced as described and a legitimate basis for the block-8 charge?

Reproduces:

• the helper profile {3:2,6:7,7:47,8:139,9:213}, the paid profile {1:2177,2:424,3:389,4:147,5:50,8:8}, deficit 1,688 and block-8 surplus 3,776;
• complex κ = 0.015637149090882 (50-digit Decimal), with frontier calibration 0.003020165977016;
• petalas's Classify the admissible quotient kernels of the #4596 word: 32 of 511 pass, v = 153 beats 511 (no new κ) #4627 values: v = 153 at 0.016567169219 and v = 511 at 0.012091850234;
• the written word is exactly φ₁₅₃(PR4470) apart from 213 padded helper finals, for every role frame and the whole scalar/warp program;
• the shipped replay's paid profile equals my own paid-rank walk in both directions, with 632/632 endpoints exact.

Discrepancies with the PR's stated figures:

1. Re-pad cost. It is not "one rank each". 187 helpers gain +1 and 26 gain +5 (former width-4 helpers whose dim-4 finals became F₂⁹), a paid delta of {1:187, 5:26}. The deficit is unchanged, as claimed.
2. Block-7 surplus. It is −256, not the −1,264 stated in PROOF.md (lines 75 and 169); no file in the PR computes that figure. The PR's own invoice() at block 7 gives −256, so the construction is still inadmissible at block 7.
3. The "213 cold full-ended helpers" requirement. PR4470's own word has 326 and fails the shipped embedded_cache_roles; 213 is the count for the raw THREE-base canonical word. Only 187 of No new kappa: complex supplier to 0.015637149 via the best ambient quotient (kernel 153 of 32 replay-valid directions) #4629's 213 are among PR4470's 326.

Block 8.

• Only the final climbs of the 213 padded helpers reach the ninth axis. No scalar, warp or centre event and no main ends in it, and all other frames together span 8 dimensions.
• Under No new kappa: complex supplier to 0.015637149 via the best ambient quotient (kernel 153 of 32 replay-valid directions) #4629's own ambient = block + 1 rule, block 8 is certified only by these inert climbs.
• If the block is instead fixed by the controller, the padding is unnecessary and lowers κ: the unpadded ledger prices at 0.016571333483.

No accounting asymmetry inflates #4629's number. Which reading is the supplier contract is a maintainer question.

Corroboration: 56 of 112 ports have their X entrance inside their Y terminal (q = 0) on the written word, matching rohanarun's count.

Not covered: the endpoint-chart/per-port contract ruling (#4604, rohanarun), the controller.py:152 surplus identity for mixed widths, the other 31 kernels and scan_kernels.py, FOUR-base/FOUR-extra, and any outer κ.

Task and overlap

• Card: independent-moment, scope refined.
• Base: fbc9ea0249746acca4f504d4fda2b84e0e36cf0d, current main at submission.
• No prior audit of No new kappa: complex supplier to 0.015637149 via the best ambient quotient (kernel 153 of 32 replay-valid directions) #4629. Classify the admissible quotient kernels of the #4596 word: 32 of 511 pass, v = 153 beats 511 (no new κ) #4627 (petalas) classified the 32 passing kernels; Endpoint-frame audit of #4596: every main output chart changes under the span{511} quotient; replay checks only the word's own finals (no new κ) #4604 (pinterbanget) and rohanarun's Conditional κ = 0.0034 (BIT-limited, +12.58%): complex supplier to 0.011417749 via the ambient quotient by span{511} #4596 comment / Conditional κ = 0.012401086416 (BIT-limited, +310.6%): BIT supplier to 0.012401086416 via the ambient quotient (kernel 150) #4633 cover the endpoint-chart side, which this PR does not repeat.

Validation

python3.12 scripts/research_package.py --package research/pr4629-repad-ledger-audit (about 50 s) prints PASS_REGISTERED_RESEARCH_PACKAGE locally on Linux, and check_research_commit.py passes.

• Nothing is imported from No new kappa: complex supplier to 0.015637149 via the best ambient quotient (kernel 153 of 32 replay-valid directions) #4629's build, verify or scan scripts. Its two written artifacts are vendored and pinned by blob and SHA-256.
• Main's shipped synthesize, literal_replay, verify_buffers and embedded_cache_roles are used as cross-checks, as No new kappa: complex supplier to 0.015637149 via the best ambient quotient (kernel 153 of 32 replay-valid directions) #4629 itself does.
• Five rejection controls all fail as expected.

Credit

DaysSky (#4596, #4629), petalas (#4627), pinterbanget (#4604), rohanarun (#4596 comment, #4633), and Cinna Davis (#4470) with its credited predecessors. Prepared by lm1909 with Claude Code (Claude Opus 5.5) assistance; there has been no independent human review. Apache-2.0.

Open next questions

See the package README: the supplier-contract reading of the block charge (ambient-derived vs controller-fixed), and the controller.py:152 identity for mixed widths.

🤖 Generated with Claude Code