Research: group B native residual widths under #2979 joint W (no new kappa)

research/rank7-group-b-native-widths-audit/MASTER-HANDOFF.md

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+# Master handoff: rank7-group-b-native-widths-audit
+
+## Result
+
+Group B of #2979: both providers and both orientations emit residual pairs
+`0:260` (helper 299, cold, width **7**) and `114:260` (helpers 448/449/484/485,
+entrance `[51]`, width **6**) under shared
+`W = ⟨256,128,64,34,17,11,4⟩`. Adapter and `LOCAL-CHECKS` hashes match the
+retained `FULL-NATIVE-RECEIPT.json`. These widths join all **3330** T74 fill
+placements. No new kappa.
+
+**Not headlined (soft-overlap trap):** guide margins `+42541` / single-299
+`-58943` — already on deferred tip `f795116d` and in `#2979` `STAGE-PRICES.json`
+/ group-A registered margins. Do not open a CrocSwap PR that reprints them.
+
+## Pins
+
+- Base / selected main: `6f100d4bb5083f8c35d96fd95a539811c62f245c`
+- Selected κ: `0.001672660197076918`
+- Task card: `independent-moment` (priority revision 6)
+- Predecessor head #2979: `be191346391661f4d35fc0d1508d0a6029572576`
+- Branch: `cursor/group-b-native-widths-60b9`
+- Content tip SHA: `5241640244d2521818a6fe3b1f6c34e99d67a4e3`
+- Publish tip (package+handoff): branch HEAD of `cursor/group-b-native-widths-60b9` (content package commit `5241640244d2521818a6fe3b1f6c34e99d67a4e3`; docs-only handoff commits may follow)
+- Package: `research/rank7-group-b-native-widths-audit/`
+
+## Exact commands
+
+```sh
+python3 -I -B research/rank7-group-b-native-widths-audit/verify.py
+python3 -I -O -B research/rank7-group-b-native-widths-audit/verify.py
+python3 -I -B research/rank7-group-b-native-widths-audit/test_verify.py -v
+python3 -I -B scripts/research_package.py --package research/rank7-group-b-native-widths-audit --check-only
+python3 -I -B scripts/research_package.py --package research/rank7-group-b-native-widths-audit
+```
+
+## Expected PASS lines
+
+```text
+PASS_GROUP_B_NATIVE_WIDTHS providers=2 helpers=5 residual_widths=7,6,6,6,6 pairs=299:0:260,448:114:260,449:114:260,484:114:260,485:114:260 placements=3330 adapter_pinned both_orientations no_new_kappa
+PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)
+PASS_REGISTERED_RESEARCH_PACKAGE research/rank7-group-b-native-widths-audit outcome=partial
+```
+
+(`-O` verify must print the same `PASS_GROUP_B_NATIVE_WIDTHS` line; `need`/`require`
+admission stays enforced.)
+
+## Closest priors
+
+| Prior | Relation |
+|---|---|
+| `research/rank7-group-a-entrance-audit/` | Methodology predecessor (native section); different helpers/W |
+| `research/rank7-joint-endframes/` (#2979 @ `be191346…`) | Source WORD / FULL-NATIVE / adapters |
+| `research/rank7-group-b-single-control-audit/` (`f795116d`) | Deferred soft-overlap margins; this package answers its native OQ |
+| #2993 `rank7-joint-frame-audit` | Frame invoices; not imported |
+
+## What is new vs soft-overlap traps
+
+- **New:** phase-exact residual classes `0:260` / `114:260`, entrance `[51]` vs
+  cold `[]`, climb/wrapper/scalar clocks in both orientations, adapter pin
+  match, native-width → T74 join for helpers `{299,448,449,484,485}`.
+- **Do not claim as new:** joint/single guide margins, width inventory
+  `7/6/6/6/6` alone without native residual binding, or 3330 placements alone
+  (those were the deferred single-control headline).
+
+## Open next questions
+
+1. Complete peer-native / private-cleanup dependency closure for group B.
+2. Physical movement, precision/tape, supplier caps and outer release for the
+   unchanged #2979 source.
+
+## Leave-alone
+
+Open CrocSwap #3392, #3386, #3374, #3349; deferred V45 `1910fd12`; deferred
+group-B single-control `f795116d`; blocked W=532 unpaid F17 terms; merged
+tariff series through #2883; do not reprint #3259 / `p104-pooled-cut-independent`.
+
+## Attribution
+
+Wentao Li `<wentaol4@illinois.edu>`. Prepared by Wentao Li with substantial AI
+assistance. No `Co-authored-by: Victor Li`. Do **not** open a CrocSwap PR from
+this worker (master publishes).

research/rank7-group-b-native-widths-audit/NOTICE.md

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+# NOTICE
+
+This package is licensed under the Apache License, Version 2.0.
+It consumes pinned source archives from `research/rank7-joint-endframes/`
+(PR #2979 and attributed predecessors) and reuses the native-binding
+methodology of `research/rank7-group-a-entrance-audit/` without modifying
+those packages.
+
+Predecessor credit (do not alter historical notices elsewhere):
+
+- Marius-Paul Dumitrean / mdumitrean #2979 — joint rank-7 end-frames, WORD /
+  FULL-NATIVE / RESIDUAL-ADAPTER receipts.
+- DreamingOfClouds / PR458 lineage — `bw_transport` / `bw_emit` residual
+  producer (producer only; not independent evidence).
+- Sagar Thakrar — retained Gaussian-integer exact kernel
+  (`frontier1094-recipes-exact-seed76/clifford.py`).
+- Nick Petalas / group-A entrance audit — mixed-entrance native binding pattern
+  adapted here to group B.
+- Deferred fork tip `f795116d` (`rank7-group-b-single-control-audit`) — already
+  registered STAGE-PRICES margins; this package answers its native-binding open
+  question and does not reprint those margins.
+
+Author: Wentao Li <wentaol4@illinois.edu>
+Prepared by Wentao Li with substantial AI assistance.

research/rank7-group-b-native-widths-audit/README.md

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+# Group B's native residual widths through the shipped T74 fill
+
+**Finite native/interface audit; no new kappa or supplier admission.**
+
+Both literal PR2979 providers pass the mixed-entrance check for group B.
+Helpers 448, 449, 484 and 485 enter at `[51]` and end at
+`W = [256,128,64,34,17,11,4]`. Their emitted residual width is **six**, not
+the terminal dimension seven. Helper 299 enters at zero and uses width
+**seven**. Exact native identities include global phase and both orientations.
+These widths bind to all 3,330 group-B placements in the shipped T74
+allocation. Adapter and `LOCAL-CHECKS` hashes match the retained
+`FULL-NATIVE-RECEIPT.json`.
+
+This package deliberately does **not** headline the already-registered guide
+margins `+42541` / single-299 `-58943`. Those facts reprint `#2979`
+`STAGE-PRICES.json` and match the deferred soft-overlap tip `f795116d`
+(`research/rank7-group-b-single-control-audit/`). The contribution here is the
+native residual / wrapper binding that tip left open.
+
+### Existing coverage and the added check
+
+`research/rank7-group-a-entrance-audit/` already binds group A's native
+residuals for helpers 331/450/451/508/509 under a different shared word
+`W_A = [256,128,64,38,20,10,1]`. Group B is outside that package.
+
+The deferred group-B single-control audit already checked joint versus
+single-299 guide margins and placement counts. It recorded an open question
+asking whether emitted mixed-entrance wrappers and native residual recipes
+match widths `7/6/6/6/6` in both orientations. This package answers that
+question with an independent source-bound native replay.
+
+## Exact native statement and source binding
+
+The source is [PR2979][2979] at
+`be191346391661f4d35fc0d1508d0a6029572576`; the base is canonical main
+`6f100d4bb5083f8c35d96fd95a539811c62f245c`, priority revision 6
+(κ = `0.001672660197076918`). [SOURCES.json](SOURCES.json) records exact Git
+blobs and SHA256 hashes. The native producer, exact kernel and retained
+emitter are authenticated before execution. No frozen predecessor is modified.
+
+For entrance `E` and terminal `U`, write the native residual as
+`S(E,U) = T_U T_E^-1`. The source compiler produces `S = L F_w R`, where
+`F_w` is the retained coordinate Fourier primitive on the first `w` address
+axes. A separate exact Gaussian-integer kernel checks all 512 columns of
+that identity, and the emitted inverse wrappers satisfy
+
+```text
+L^-1 S(E,U) R^-1 = F_w,
+w = dim(U) - dim(E).
+```
+
+| Helper(s) | Entrance | Parent terminal dimension | Parent width | Joint/final width |
+|---|---|---:|---:|---:|
+| 299 | zero | 8 | 8 | 7 |
+| 448, 449, 484, 485 | span(51) | 8 | 7 | 6 |
+
+Here `51 = 34 xor 17` lies in the span of `W`. Treating the entering helpers
+as cold would select the wrong native operator even if a rank field were
+edited to six. The cold right wrapper and the entering right wrapper are not
+interchangeable: the all-column check rejects that substitution. A different
+contained line, `[4]`, has the same dimension but also fails with the actual
+`[51]` recipe.
+
+The verifier regenerates both complete emitted programs with the unchanged
+transport/emitter and reconstructs the full serialized adapter file using
+the original generation convention. The uncompressed `LOCAL-CHECKS.json`
+and `RESIDUAL-ADAPTERS.json` hashes match PR2979's retained native receipt.
+Both regenerated event streams also match the counts and canonical event
+digests inside that pinned receipt.
+
+## Reproduction
+
+```sh
+python3 -I -B research/rank7-group-b-native-widths-audit/verify.py
+python3 -I -O -B research/rank7-group-b-native-widths-audit/verify.py
+python3 -I -B research/rank7-group-b-native-widths-audit/test_verify.py -v
+python3 -I -B scripts/research_package.py --package research/rank7-group-b-native-widths-audit --check-only
+python3 -I -B scripts/research_package.py --package research/rank7-group-b-native-widths-audit
+```
+
+Expected verify line:
+
+```text
+PASS_GROUP_B_NATIVE_WIDTHS providers=2 helpers=5 residual_widths=7,6,6,6,6 pairs=299:0:260,448:114:260,449:114:260,484:114:260,485:114:260 placements=3330 adapter_pinned both_orientations no_new_kappa
+```
+
+## Open next questions
+
+1. Can the checked group-B direct paths and endpoints be joined to the
+   complete native dependency closure of their private cleanup?
+2. Do the complete physical, precision/tape and outer obligations admit the
+   unchanged PR2979 source after independent review?
+
+## Credit
+
+Builds on #2979 (Dugongue / mdumitrean), the DreamingOfClouds / PR458 emitter
+lineage, Sagar Thakrar's exact kernel, Nick Petalas's group-A entrance native
+audit, and the deferred group-B single-control tip `f795116d` (which this
+package does not reprint). New check by Wentao Li. Apache-2.0.
+
+Prepared by Wentao Li with substantial AI assistance.
+
+[2979]: https://github.com/CrocSwap/integer-mult-bounds/pull/2979