[pinterbanget]

Summary

This adds research/pr4416-padding-check/. It is an independent check of 1337isnot1337's #4416, which proposes conditional κ = 0.00268647. The construction tensors zxv's p7 controller v = 6240 times, completes small targets to 11^v and splits paid jobs at 10^v.

Claim type: a written proof check of TENSOR.md §1–3 and §5, plus certified exact arithmetic. No new κ. #4416 is not accepted, and the native p7 audit is not re-checked.

Results

• The proof steps hold.
  • Product moments multiply.
  • Completion to 11^v loses moment by concavity but buys separation; the bound conservatively keeps T_τ^v.
  • The split tails qJ^τ + r^τ ≤ 2RJ^{−C} and charge(D) < 2L/J^C hold.
  • The rank formula's general exit constant 2^{(111/26)v}, its −log₂η bound, θ < 25/26 and H0 ≥ 7v all hold.
• The arithmetic is certified.
  • The p7 invoice totals match: 7,688 fields, 55,998 calls, rank-one masses 131,723 and 131,115.
  • At C = 0.00268648: α < 0.999999984404, γ < 0.99819171 and δ < 0.64382471.
  • The p7 mixed root lies in (0.0026864890486, 0.0026864890492).
  • The v = 6240 inequality holds by both routes.
  • Conditional κ = 0.00268647 via paid target padding after native composition #4416's H0 = 4,307,773,805,920 and H1 = 16,201,843,136,005,340,321 reproduce exactly.
• Margins and minor improvements.
  • γ sits only 8·10⁻⁶ below its stated bound 4991/5000, and the tested saving is 9·10⁻⁹ below the root.
  • The least v for (b, c) = (11, 10) under the direct certified route is 5,745.
  • The same induction, with certified −log₂η, the exact exit constant and θ̄ = 145/151, gives H1 = 15,370,312,178,898,752,926, which is 5.4% smaller.

Evidence

python3.12 -B scripts/research_package.py --package research/pr4416-padding-check --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/pr4416-padding-check
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4416-padding-check outcome=completed   (~10 s, stdlib only)

Head: ba0efeaac4e62d1757d7a9be6fd8aaf8f9bd35dc. Base: canonical main 12fa8c5c, priority revision 7. The audited files' SHA256 prefixes are in the README.

Not covered

• The native p7 word.
• The analytic, precision, tape and outer premises.
• FOLLOWUP.md's 209-profile screen.

Task and overlap

• Card: independent-moment, refined.
• Claim: Handoffs and requests for independent checks #1166 (comment)
• Overlap: no other review of Conditional κ = 0.00268647 via paid target padding after native composition #4416.

Credit

@1337isnot1337 (#4416, #4414, #4412), @zxv (#4359), and Jacob Alan Sussman (#4268).

Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance; no independent human review. Apache-2.0. This PR does not merge anything or change the frontier.

🤖 Generated with Claude Code