Complete native and hosted replay of the R438 bit improvement

research/r438-native-rehost/README.md

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+# Native checks and hosted emission for the R438 bit supplier
+
+**A complete finite native/hosted replay of the PR2423 improvement. No new κ.**
+This package takes the explicit native-emission handoff in commdata2338's
+[PR2653](https://github.com/CrocSwap/integer-mult-bounds/pull/2653) and
+[Discussion1289](https://github.com/CrocSwap/integer-mult-bounds/discussions/1289).
+It emits Sagar Thakrar's fixed transported R438 word and rehosting selection,
+checks the actual emitted owners against the independent geometric certificate,
+and runs the complete native, parent, hosted and exact-price pipeline.
+
+The circuit, selection and predicted endpoint belong to the predecessors.
+The new result is their source-bound emitted realization and complete finite
+replay, including the previously untested rank-34 remainder. This does not
+promote a selected supplier or settle the inherited all-size interfaces.
+
+| Complete bill | Selected PR589 control | PR2423 emitted candidate |
+| --- | ---: | ---: |
+| Dirty helpers per local call | 439 | 438 |
+| Local ADDs, including compensation/restoration | 24,305 | 24,248 |
+| Local COPY / ERASE pairs | 9 | 9 |
+| Local paid rank mass | 5,129 | 5,121 |
+| Whole hosted helper occurrences | 126,432 | 126,144 |
+| Paid recursive children | 904,896 | 904,320 |
+| Global paid rank mass | 1,808,352 | 1,808,352 |
+| Live data families | 28,416 | 28,416 |
+| Nine-stage precision charge | 192 bits | 192 bits |
+| Two-level precision charge | 512 bits | 512 bits |
+| Exact bit endpoint | 0.001733427039589844234749 | **0.001734846264120199151475** |
+
+Both moment engines accept the reported endpoint and reject the next point
+on the `10^-24` grid. The candidate is about 0.08187% above the selected bit
+endpoint. The selected complex endpoint remains
+`0.001675462676808103522925`, below both; the selected overall result remains
+`κ = 836330098538459/500000000000000000`. This work does not combine pending
+complex claims with the bit candidate.
+
+## What is implemented
+
+Ali Romman's PR1043 `pipeline.py` is imported from its pinned source without
+editing it. Its selection callback is replaced with a small adapter that writes
+PR2423's published patterns and stage demands. No emission, geometry, mutation,
+precision or moment acceptance predicate is replaced. The old selection format
+requires a floating heuristic field; the adapter recomputes that metadata using
+the predecessor formula, but it is not used to certify a price or optimum.
+
+The original baseline and the candidate both run through the unchanged C++17
+legality checker and native five/nine/eleven-stage formal-column checkers.
+The candidate has 882/1,326/1,548 formal columns; the baseline has
+883/1,327/1,549. Local arbitrary-dirty replay covers all 660 candidate inputs,
+and the original H1–H5 flags and their conclusions all pass.
+
+The unchanged supplier pipeline then emits and audits the parent and hosted
+programs and computes the complete invoice. The new `bind_emitted` bridge
+compares all 126,144 **actual emitted** helper owners to PR2653's independent
+slot expansion, physical family identities and projector supports. It also
+compares every emitted remainder histogram, requires the local programs to be
+unchanged by hosting, and independently recounts the global profile from those
+program costs and emitted remainders. The owner/projector digest must equal
+PR2653's independently reconstructed digest.
+
+The rank-34 remainder is the actual complement `[30,64)` of the helper slice
+`[22,30)` inside child 6's pending `[22,64)` space. It occurs once per replica
+and is charged 32 times. Deleting a helper returns 72 idle-rank units per
+replica (2,304 globally); those charges are retained. The global profile is
+`{1:380736,2:400352,3:22752,4:26880,5:29376,6:17376,7:26496,34:32,42:320}`.
+The maximum child remains 42, with `2*42^2 < 64^2`; the row coefficient is
+18,355, below 20,161. All source access, nine copied totals, local cleanup,
+whole-helper occupancy, idle remainders and bridge work are included by the
+unchanged pipeline.
+
+## Reproduce
+
+Python 3.12, C++17 and Boost headers are required. Install the recorded Python
+versions in a virtual environment using `requirements-native.txt`. Set `CXX`
+if needed, and `BOOST_INCLUDE` to the directory containing `boost/` if it is
+not `/usr/include`. From the repository root, run:
+
+```sh
+python3 -B research/r438-native-rehost/verify.py
+```
+
+Expected last line:
+
+```text
+PASS_R438_NATIVE_REHOST native=5,9,11 owners=126144 children=904320 c=0.001734846264120199151475 no_new_kappa
+```
+
+The default uses a temporary directory and compares the entire normalized
+certificate with `CERTIFICATE.json`. `--output /absolute/new/directory` retains
+the emitted templates, commands, logs and full receipts. The destination must
+not exist. Only timing, toolchain metadata and the pipeline's explicitly
+historical cited-PR548 outer assembly are excluded from the new certificate;
+all mathematical fields of its native and hosted receipts are retained.
+The inherited geometry JSON includes elapsed time. Every original geometry
+and template hash is checked within its own run, then `semantic_*` digests
+omit only `geometry.seconds` and rebind that stable geometry digest inside
+the templates. That digest binds every other geometry field; the full generated
+geometry remains in the replay output rather than adding a second large copy
+to this package.
+Source archives are byte-pinned; template identity uses decompressed canonical
+JSON, and histogram keys are normalized before comparison.
+
+The registered standard-library command is deliberately a **local-only**
+check: `python3 -B scripts/research_package.py --package research/r438-native-rehost`.
+It rechecks source pins, both local words, the exact projector certificate and
+three candidate faults. Its marker says `native_not_run`; it does not stand
+in for the full command above. All modes reject `-O` because inherited engines
+use assertions. `--write-certificate FILE` is an explicit fresh-output mode
+for rebuilding evidence, not a comparison against the committed certificate.
+
+## Failure detection and scope
+
+The complete run retains 96 native omitted-bridge controls across the two
+words, 34 parent-template mutations and 32 hosted-template mutations.
+PR2653's ten geometric controls/witnesses are replayed. Nine new controls
+reject omitted cleanup, omitted dirty compensation, the old transport frame,
+a wrong emitted port, a wrong replica, an equal-width wrong slice, an omitted
+or undercharged rank-34 remainder, and a deleted emitted local instruction.
+The selected R439 program is the positive end-to-end control.
+
+This is finite conditional construction evidence, not a formal proof of the
+full multiplication theorem or an implementation of its physical machine.
+The common-label/mutable-source realization, correlated whole-call hosting,
+injective cover/all-size compiler, recursive physical storage and routing,
+precision/tape and analytic-transfer contracts remain inherited. Native scalar
+columns alone do not prove those contracts. PR2653 supplies the geometric
+argument, which is reused and bound to the emitted program here; it is not
+presented as a new independent proof. The historical PR548 outer assembly
+happens to execute inside the original pipeline, but is not used as the
+current frontier or as evidence for a new κ. The selected cold replay, full
+repository suite and Lean are outside this contribution.
+
+Exact sources are in `SOURCES.json`; the task, three alternatives, seed 08,
+local claim, overlap coverage and stopping rule are in `TASK.json`.
+Research base: `389fa10d714f5b40afe624908e487eb5e424498d`.
+Dependency heads:
+
+- PR1043, Ali Romman: `e309e17f83f5759b1ea1fa24a76f24838784cb4d`.
+- PR2423, Sagar Thakrar: `13cd273dc13c98244b1f9bcf588b6e828cbc0347`.
+- PR2653, commdata2338: `ff26f4477786cf9ab188e060d6820a39dd2ed117`.
+- PR589, DreamingOfClouds: `a5afc8c6169ea61ba7c51dfd3cade02cc7b13b46`.
+
+PR1043 is archived but remains partially reviewed; PR2423 and PR2653 were
+incorporated only within their explicitly scoped reviews. Their unresolved
+native-emission handoff, not their merge status, motivates this work.
+
+## Open next questions
+
+Review this exact emitted candidate against the retained all-size physical
+interfaces before any supplier admission. The concrete first step is to bind
+its local program and owner digests to those compiler/hosting hypotheses;
+finite native execution does not supply a complete physical routing proof.
+Any future overall improvement also needs a stronger admitted complex supplier.
+No further packing or transport search was performed here.
+
+## Credit and license
+
+Prepared by **@CubeJerry**, with substantial **OpenAI Codex assistance** in
+scoping, implementation, mathematical checking and writing. No independent
+human review or proof-kernel certification is claimed.
+
+Credit Ali Romman for helper470 deletion and the complete source pipeline;
+Sagar Thakrar for the transport, optimal fixed-slot layout and predicted price;
+commdata2338 for the pending-projector proof and independent census. Retain
+DreamingOfClouds, eumemic, DaysSky, Zhihao Chen, chafreaky, the PR555/543/545/510
+and PR442 hosting lineage, PR1023 packing, and the seed72/seed14 window work.
+Their sources and notices are imported unchanged. New material is Apache-2.0.