Disposition receipt for the Gaussian halo-exponent PR chain (13 open PRs; none retained; one unchecked)

research/halo-chain-receipt/README.md

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+# Disposition receipt: the Gaussian halo-exponent PR chain
+
+**Claim type:** a source-bound overlap and disposition receipt (the overlap-receipt card). **No new κ.**
+It makes no closures and no merge recommendations. It covers 13 open PRs submitted on 2026-10-21 against
+base `2a13eb18`. The verifier checks the receipt's internal consistency and its retention claims.
+`RECEIPT.json` records exact heads and package-file blobs.
+
+## Disposition
+
+All 13 PRs are single-package additions on base `2a13eb18`. **None is retained on main**: each package
+path is absent at the base.
+
+| PR | Author | Head | Role | Depends on | Independent check |
+| --- | --- | --- | --- | --- | --- |
+| #4437 | jwr404 | `7ca94e97` | ideal column majorant across `g = 2`; ideal gap `> 1/(8p²)` | — | #4468 |
+| #4438 | jwr404 | `6157a47b` | within-cell gauge transfer, `1/(1−ε)`; `C = 3` | #4437 | #4469 |
+| #4439 | jwr404 | `26af8afb` | within-cell ε exponents 12, 26, 28, 28, 6 | #4438, #4437 | #4471 |
+| #4442 | jwr404 | `d079c2b0` | across-cell ε exponents (downward reading) | #4439, #4449 | #4471 |
+| #4449 | mihir-s-05 | `1fb77b37` | across-cell rounding `0 ≤ H ≤ n`, `n − H < 4η` | — | #4472 |
+| #4451 | jwr404 | `be243a28` | weight error is relative `δ = 2^{2−32760p}` | — | #4460 |
+| #4452 | jwr404 | `af68f597` | within-cell δ exponents 11, 24, 26, 26, 6 | #4451, #4437 | #4460 |
+| #4462 | pinterbanget | `c8fd7f81` | across-cell δ transfer; "rounded"-reading robustness | #4452, #4449, #4442 | **none yet** |
+| #4460 | pinterbanget | `6aaf4810` | check of #4451/#4452 | | |
+| #4468 | pinterbanget | `b5f7fbbb` | check of #4437 | | |
+| #4469 | pinterbanget | `baf56b16` | check of #4438 | | |
+| #4471 | pinterbanget | `0cf8e2b0` | check of #4439/#4442 | | |
+| #4472 | pinterbanget | `dcf680a1` | check of #4449 | | |
+
+## Relations
+
+- **The two routes.** The δ route (#4451, #4452, #4462) implies the ε route's weight hypothesis with
+  room, since #4451 shows `δ < 1/(16p²)`. It gives smaller exponents: 11, 24, 26, 26, 6, against 12,
+  26, 28, 28, 6. The ε results remain valid but are coarser. Neither route is on main.
+- **Coverage.** Every author PR in the set has at least one independent check, by separately written
+  code. All checks are by one contributor, so a second, different reviewer is still missing.
+- **The one gap.** The open transfer #4462 has no independent check yet.
+- **Hypotheses common to the whole chain.** The ideal gaps (GAUSSIAN's "eventually" statements, #4402)
+  and the page-generator implementation are not discharged by any PR in the set.
+
+## Not covered
+
+- PRs outside the named set, for example #4402 and #4406 already on main, and the downstream report.
+- Any judgement of merge priority.
+
+## Reproduce
+
+```sh
+python3.12 -B scripts/research_package.py --package research/halo-chain-receipt --check-only
+python3.12 -B scripts/research_package.py --package research/halo-chain-receipt
+git fetch origin pull/4452/head && git ls-tree -r FETCH_HEAD research/gaussian-delta-exponents   # compare a recorded blob
+```
+
+The verifier prints `PASS_HALO_CHAIN_RECEIPT`.
+
+## Open next questions
+
+1. **An independent check of #4462 by a different contributor.**
+   - *First step:* replay Lemma A's split with δ, and Lemma B's `10p²` ceiling.
+
+## Credit
+
+- jwr404 (James Reed) and mihir-s-05 (Mihir Srivastava) wrote the author PRs.
+
+Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.
+Apache-2.0.