[pinterbanget]

Summary

This adds research/halo-chain-receipt/, a source-bound disposition receipt (overlap-receipt card) for the 13 open PRs of the Gaussian halo-exponent chain. It makes no closures and no merge recommendations.

Claim type: consolidation receipt. No new κ.

Results

• Retention. All 13 PRs (Extend the ideal column majorant across every legal g=2 step (no new κ) #4437, Bound the within-cell column gap by a relative weight error of 1/(16p^2) (no new κ) #4438, Apply the smaller halo exponents inside one cell, with normalizer 6 (no new κ) #4439, Apply the smaller halo exponents across a cell, under the downward reading (no new κ) #4442, Prove the downward rounding contract for across-cell Gaussian entries #4449, The published 4η weight error meets the 1/(16p^2) ratio budget (no new κ) #4451, Lower the within-cell halo exponents to 11, 24, 26, 26 and 6 (no new κ) #4452, Independently check #4451/#4452: within-cell halo exponents 11, 24, 26, 26, 6 under delta (no new κ) #4460, Transfer the δ halo exponents 11, 24, 26, 26, 6 across cells; robust to the 'rounded' reading (no new κ) #4462, Independently check #4437: the ideal column majorant holds (and is attained) across g = 2 steps (no new κ) #4468, Independently check #4438: within-cell gauge column transfer (C = 3 least, equality at p = 2; no new κ) #4469, Independently check #4439/#4442: halo exponents 12, 26, 28, 28, 6 under eps = 1/(16p^2) (no new κ) #4471, Independently check #4449: across-cell downward rounding contract (exact exponent, repair lemma, sharpness; no new κ) #4472) are single-package additions on base 2a13eb18. None is retained on main. RECEIPT.json records each exact head and package blobs.
• Edges. The receipt records the dependency edges (for example Apply the smaller halo exponents across a cell, under the downward reading (no new κ) #4442 ← Apply the smaller halo exponents inside one cell, with normalizer 6 (no new κ) #4439, Prove the downward rounding contract for across-cell Gaussian entries #4449; Transfer the δ halo exponents 11, 24, 26, 26, 6 across cells; robust to the 'rounded' reading (no new κ) #4462 ← Lower the within-cell halo exponents to 11, 24, 26, 26 and 6 (no new κ) #4452, Prove the downward rounding contract for across-cell Gaussian entries #4449, Apply the smaller halo exponents across a cell, under the downward reading (no new κ) #4442) and the coverage edges.
• Coverage. Every author PR (jwr404 and mihir-s-05) has at least one independent check by separately written code: Independently check #4451/#4452: within-cell halo exponents 11, 24, 26, 26, 6 under delta (no new κ) #4460, Independently check #4437: the ideal column majorant holds (and is attained) across g = 2 steps (no new κ) #4468, Independently check #4438: within-cell gauge column transfer (C = 3 least, equality at p = 2; no new κ) #4469, Independently check #4439/#4442: halo exponents 12, 26, 28, 28, 6 under eps = 1/(16p^2) (no new κ) #4471, Independently check #4449: across-cell downward rounding contract (exact exponent, repair lemma, sharpness; no new κ) #4472. All checks are by one contributor, though.
• The one gap. The open transfer Transfer the δ halo exponents 11, 24, 26, 26, 6 across cells; robust to the 'rounded' reading (no new κ) #4462 has no independent check yet.
• The two routes. The δ route (The published 4η weight error meets the 1/(16p^2) ratio budget (no new κ) #4451, Lower the within-cell halo exponents to 11, 24, 26, 26 and 6 (no new κ) #4452, Transfer the δ halo exponents 11, 24, 26, 26, 6 across cells; robust to the 'rounded' reading (no new κ) #4462) implies the ε route's hypothesis with room and gives smaller exponents. The ε results remain valid but are coarser.

Evidence

python3.12 -B scripts/research_package.py --package research/halo-chain-receipt --check-only
  PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
python3.12 -B scripts/research_package.py --package research/halo-chain-receipt
  PASS_REGISTERED_RESEARCH_PACKAGE research/halo-chain-receipt outcome=completed

Head: 215956879c9b46d7e62753fc792b04c801a05969. Base: canonical main 2a13eb18.

Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code

[pinterbanget]

Note: the receipt is a snapshot. Since it was written, #4462's head has moved from c8fd7f81 to 89548dc1. The only change adds one verified check (the raw exponential oracle fits Lemma B's budget). No disposition fact in the receipt changes.