Compose P104 private descent reuse with coalesced frames

research/p104-coalesced-private-reuse/README.md

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+# P104 private descent reuse in the coalesced word
+
+The helper-7 reuse from Cinna Davis's [PR2219](https://github.com/CrocSwap/integer-mult-bounds/pull/2219)
+composes with David Arias's cheaper, coalesced word in
+[PR2152](https://github.com/CrocSwap/integer-mult-bounds/pull/2152).
+This checks the previously untested combination and preserves **every original
+public boundary frame and lifetime width**. The combined child profile changes
+by `+H9 - H2 - H7`; its rank mass stays 5894 and its fractional moment decreases
+strictly. The complete inherited owner-window invoice still excludes the
+selected κ. This is a finite forward component, with no new exponent claim.
+
+## What is composed
+
+The predecessor mechanism replaces public helper 7 (register 711) with the
+existing owned copy of query source 133, scaled by −1/2, for pair `(4,57)`.
+All eight actual query terms are already available at the retained B-prefix
+507. The three contact frames are unchanged by coalescing:
+
+| Target | Coefficient | Canonical frame basis | Dimension |
+| --- | ---: | --- | ---: |
+| 159 | −1 | `[2,12,16,33,64,128,261]` | 7 |
+| 203 | 2 | `[2,12,33,80,144,261]` | 6 |
+| 148 | 2 | `[45,82,144]` | 3 |
+
+They form a descending chain from the actual dimension-8 query frame to the
+line `[82]`. The owned path has ranks `[1,1,3,2]`. Its three additions are
+performed before the remaining helpers are seeded and before the B suffix.
+Exact replay checks common charts and the entire resulting scalar map, including
+all 735 independent dirty inputs, all other query terms and all restoration.
+
+PR2219 checks the original `fanout.py` word and leaves the coalesced word open.
+Its patch also retires the unused helper at ZERO. Here the helper retains its
+original FULL exit chart through a **paid rank-9 ZERO→FULL transport**. This
+keeps the exact ordinary-role width vector needed by the inherited owner
+assignment. No freed owner capacity or unproved gather credit is assumed.
+
+The adapter consumes `coalesced.construct()` directly. Every retained scalar
+event is identical to its source event, with its source index recorded; their
+relative order is checked. It deletes 12 helper-related additions and inserts
+three private contacts, retaining the old cleanup and compensation for every
+other helper. Public transports are rebuilt from the actual chronological
+charts. The original 339 chart assignments are never reinterpreted against a
+patched event numbering.
+
+## Complete finite invoice
+
+| Rank | Coalesced public | Composed public | Composed private | Composed total |
+| ---: | ---: | ---: | ---: | ---: |
+| 1 | 2429 | 2427 | 2 | 2429 |
+| 2 | 558 | 556 | 1 | 557 |
+| 3 | 389 | 388 | 1 | 389 |
+| 4 | 112 | 112 | 0 | 112 |
+| 5 | 108 | 108 | 0 | 108 |
+| 6 | 16 | 16 | 0 | 16 |
+| 7 | 6 | 6 | 7 | 13 |
+| 9 | 0 | 1 | 0 | 1 |
+
+The baseline private profile is eight rank-7 paths. The new word has 3625
+transport occurrences, public mass 5838 and private mass 56, eight sequential
+owned copies with peak occupancy one, and 20,947 scalar additions (20,956
+before). All 31 ordinary helper roles retain their original boundary contracts.
+
+For `0 < τ < 1`, the profile difference is strictly favorable because
+`9^τ < 2^τ + 7^τ`. One direct proof divides by `9^τ` and uses
+`x^τ > x` for `x = 2/9, 7/9`. This is a comparison within the retained coverage
+model; it does not admit a supplier.
+
+The exact interval price check uses the retained model `m=73`, `W=832/9`,
+COPY mass 56 and total paid mass 6712 per call. The full ordinary-role packing
+is replayed: 527 roles in each of 144 calls, 75,888 assignments, no owner-family
+aliases or active-data conflicts, and residual idle mass 117,792 globally
+(818 per call). Every boundary width is bound to the composed word.
+
+| Idle model | Baseline κ upper cap | Composed κ upper cap | Composed moment at selected κ |
+| --- | ---: | ---: | ---: |
+| Favorable fractional rank-51 relaxation | 0.00167357279382 | 0.00167393973105 | 0.99999585229209 |
+| Actual inherited owner-window invoice | 0.00165234290426 | 0.00165270058587 | 1.00006553178737 |
+
+The second cap remains **1.1933% below** selected
+`κ = 836330098538459/500000000000000000`. Both complete profiles exclude a
+one-percent gain. These are necessary cost ceilings, not achieved exponents.
+The owner packing remains conditional on inherited windows: no new global
+emitter, data-phase routing, native wrapper, backward supplier, recursive
+precision, reserve bound or all-size multiplication theorem is supplied.
+
+## Reproduce and inspect
+
+From the repository root, Python 3.12 and the standard library:
+
+```sh
+python3.12 scripts/research_package.py --package research/p104-coalesced-private-reuse
+# Direct replay also works without Git:
+python3.12 -I -O -B research/p104-coalesced-private-reuse/verify.py
+```
+
+The registered command recomputes and compares [RESULT.json](RESULT.json).
+It writes only temporary files; `--write-result` explicitly regenerates the
+receipt. It checks all literal transports with the retained exact native
+compiler and independent Gaussian interpreter, including signed Pauli action,
+global phase, 208 intrinsic endpoint adapters and 4096 private-path basis
+columns. Ten additional controls reject a missing contact, wrong coefficient,
+retained dirty compensation, ascending private step, stale source event map,
+omitted public/private charges, retired helper with stale owner widths, wrong
+owner binding and changed predecessor bytes. The native checker also rejects
+a corrupted global phase. This is exact finite verification, not a proof
+assistant verification or independent human review.
+
+The complete registered replay passed on CPython 3.12.3 with assertions
+disabled. CPython 3.14.4 also reproduced the receipt from a Git-free, read-only
+export of ten package files and thirteen declared inputs; a write probe was
+rejected and all 23 exported file hashes remained unchanged.
+
+[SOURCES.json](SOURCES.json) pins main at
+`0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`, PR2152 at
+`05f7aad0f08992ee48ec2dd93e896d9a4567847d`, and the credited PR2219 mechanism
+at `3f913bc17276b68f0c9008a1202b6ce588e77ff6`. The small predecessor archive
+contains ten actually used source/data files plus its unchanged attribution
+README; its exact bytes and each member are pinned. Thirteen external live
+inputs are declared for replay invalidation. Sources are checked before being
+copied into temporary storage; no network, optimizer or patch application is
+needed. [TASK.json](TASK.json) records the original draw, scope and validation.
+
+## Open next questions
+
+Can the composed forward word be realized by a complete native global wrapper
+with these same boundary contracts? Bind the 104 retained ports and complete
+helper widths to actual caller entry/exit wrappers, check their native phases
+and add every charge. This matters because the checked conditional owner
+assignment neither supplies those interfaces nor reaches selected κ. A
+source-bound global emitter, backward orientation and precision/reserve
+contract remain blockers; the structured question is in TASK.json.
+
+## Credit
+
+Prepared by Gareth Davidson / @bitplane with substantial OpenAI Codex
+assistance. No subagents were used. New work is Apache-2.0.
+
+David Arias / DavidAriasC supplied the coalesced 735-register word, exact
+replayer, complete owner packing and pricing adapter in PR2152. Cinna Davis /
+1337isnot1337 supplied the helper-7 private descent reuse in PR2219; that
+mechanism is not new here. `compose.py` and `price.py` adapt the former's
+replay/pricing structure while composing the latter's deliveries. The retained
+archive keeps David's original README and attribution unchanged.
+
+The lineage includes Chafik Boukhalfa's native P104 channel (PR1991), Rohan
+Arun's scalar channel (PR1972) and T16 owner schedule, Adam Gall's chronological
+gather work (PR1940), Josie Elliston and Ali Romman's P104 geometry/decoder
+work, icekylinx's frame-sa504 work, and the selected PR1042/PR1094 lineage.
+Douglas Colkitt supplied the exact ceiling engine. The native compiler and
+interpreter remain unchanged in the repository with their
+[PR1862 notice](../p104-native-channel/notices/PR1862-NOTICE.md) and
+[frame-sa504 notice](../p104-native-channel/notices/FRAME-SA504-NOTICE.md).
+The unchanged T16 source archive retains its jeremykothe2, FanPUYen and earlier
+packing credits. No new numerical enclosure method is claimed.