Mister-Meeseeks · Oct 14, 2026 · Oct 14, 2026
diff --git a/research/r439-abc-hosted-invoice/README.md b/research/r439-abc-hosted-invoice/README.md
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+# Complete nine-stage hosted invoice for the PR1122 helper-mixing word
+
+**Finite hosted construction replay; no new circuit, supplier selection or κ.**
+The fixed 10,652-ADD word of [PR1122](https://github.com/CrocSwap/integer-mult-bounds/pull/1122)
+passes the unchanged nine-stage emitter and owner auditor with PR589's frozen
+hosting assignment. All **126,432 helper occurrences** are hosted without banks;
+the complete emitted program has **3,911,328 instructions**. Its invoice retains
+the selected bit profile and bit saving. The unrounded prefix and two-level
+bounds use 176 and 390 bits, still charged at 192 and 512 bits.
+
+PR1122 supplied the circuit and native evidence. [PR1194](https://github.com/CrocSwap/integer-mult-bounds/pull/1194)
+supplied the semantic-D substitution argument; [PR1311](https://github.com/CrocSwap/integer-mult-bounds/pull/1311)
+applied it to this changed-A word. Both the composition and bridge packages
+explicitly left the **changed-word hosted emission/audit and invoice** open.
+This package completes that finite handoff, binding those stages to one word.
+It does not supply a new proof of the inherited physical or all-size premises.
+
+## Exact object and complete bill
+
+Base: `0b1cccf86e2f5132ed286a26ef0a681a495740ea`. The candidate is the unmodified
+`research/r439-abc-semantic-bridge/inputs/candidate.json.gz`, inherited from
+PR1122 head `a2551e70fce0cc34348f50f1a94e7cc4c80bbcbf`:
+
+- File SHA256: `2b09a7a3851cdf2a7f19350d1555cf75788d001c9507a37e459cd931881ee066`.
+- Canonical decoded SHA256: `7bbaed96041297cd38e89ff48eb055750cfab36609b9fdbeafcec1b2758c1254`.
+- Emitted instruction SHA256: `8f2239a09b87367ba754a6c0ebd8989e81b295df3628ebf4991d1cab15fabfcf`.
+
+| Quantity | PR589 selected bit word | Fixed PR1122 word |
+| --- | ---: | ---: |
+| Local ADDs, including preparation/restoration | 24,305 | 10,652 |
+| Local MOVE/ADD/COPY/ERASE records | 27,234 | 13,581 |
+| Local COPY / ERASE | 9 / 9 | 9 / 9 |
+| Local rank mass | 5,129 | 5,129 |
+| Nine-stage local invocations | 288 | 288 |
+| Hosted helper occurrences / banks | 126,432 / 0 | 126,432 / 0 |
+| Paid recursive children | 904,896 | 904,896 |
+| Live / physical families | 28,416 / 28,425 | 28,416 / 28,425 |
+| Prefix bits / charge | 177 / 192 | 176 / 192 |
+| Two-level coefficient bits / charge | 393 / 512 | 390 / 512 |
+| Row coefficient | 18,355 | 18,355 |
+
+The baseline column is pinned PR589 evidence, not a new baseline hosted replay.
+All gate savings are PR1122's and its predecessors'. The freshly recounted
+hosted profile is
+`{1:381024, 2:400416, 3:22752, 4:26880, 5:29376, 6:17376, 7:26784, 42:288}`.
+Rank mass is 1,808,352 and deficit is 10,272. The bit saving remains
+`1733427039589844234749 / 10^24`; the next grid point is rejected by exact
+moment enclosures. The selected complex supplier still binds.
+
+[RESULT.json](RESULT.json) retains every integer term of the invoice:
+3,131,712 scalar additions (288 complete local words plus 63,936 bridges),
+2,592 copied-centre episodes, selector, address, compiler, store and precision
+terms. Each episode contains both COPY and ERASE; the inherited `J` term
+also charges their lifecycle work. No virtual replacement D is executed or
+billed. The row, child-size and 192/512-bit guards pass at their full charges.
+
+## Reproduce
+
+Python 3.12, C++17, Boost headers and the exact NumPy/SymPy/SciPy versions in
+[VERIFY.json](VERIFY.json) are required. Set `BOOST_INCLUDE` to the directory
+containing `boost/` if headers are not in `/usr/include`; `CXX` defaults to `c++`.
+From the repository root:
+
+```sh
+python3.12 scripts/research_package.py --package research/r439-abc-hosted-invoice
+```
+
+Expected final lines:
+
+```text
+PASS_R439_ABC_HOSTED_INVOICE ADDs=10652 helpers=126432 banks=0 no_new_kappa
+PASS_REGISTERED_RESEARCH_PACKAGE research/r439-abc-hosted-invoice outcome=completed
+```
+
+The registered command has a 600-second limit. To retain all emitted files,
+native binaries, commands and logs, use a fresh output directory outside the
+checkout:
+
+```sh
+python3.12 -I -B research/r439-abc-hosted-invoice/verify.py --output /tmp/r439-abc-hosted-run
+```
+
+The default replay is read-only with respect to repository files. Existing
+output directories are refused. `--write` explicitly regenerates RESULT.json.
+All checks in the wrapper remain enabled under `-O`; inherited scripts run
+in separate interpreters with assertions enabled.
+
+## What is checked
+
+1. The unchanged PR1311 verifier checks the full arbitrary-dirty D boundary,
+   raw J/V/K blocks, original-D chronological splice, geometry, endpoints and
+   its nine semantic controls. Literal H2 and K syntax still reject the actual
+   helper-mixing word; their predicates are not weakened.
+2. The unchanged exporter, native legality checker and native 5/9-stage
+   programs replay the actual candidate, with 883 and 1,327 formal columns.
+   Local positive bounds are F=15,223 and B=3,910,388, using 92 bits below the
+   104-bit cap. Six and eighteen omitted-bridge controls reject.
+3. The inherited geometry and exact string parameterizers run afresh.
+   PR589's fixed selection is read directly; no optimizer is invoked.
+   The parent checks 4,839 independent unbanked scalar columns and rejects
+   seventeen template mutations. The hosted auditor independently reconstructs
+   ownership, windows, full instruction digest and paid profile, rejecting
+   sixteen ownership/template mutations.
+4. `invoice.py` expands the inherited bit invoice into inspectable integer
+   terms. It also executes every statement of the unchanged adapted PR510
+   bit-invoice prelude, through its `res` assignment, and compares the exact
+   coefficient, two-level bound, scalar/selector counts and moment brackets.
+   The subsequent historical complex/outer assembly loop is outside this task.
+   This is a port-consistency check, not an independent mathematical method.
+5. Seven additional controls reject mixed word/record receipts, an understated
+   profile, prefix or COPY charge, a missing bridge control, and a stale
+   hosted-parent binding. These mutate the actual output files at the collector
+   boundary and restore them after each check.
+
+The inherited geometry receipt contains elapsed time. Only that nonmathematical
+field is normalized to zero **before** downstream hashing, so the final
+certificate is reproducible. Every downstream producer and auditor consumes
+and binds those same bytes. No geometry assertion or mathematical field changes.
+
+[SOURCES.json](SOURCES.json) pins the complete 53-file input/context closure
+to the base, Git blobs and SHA256. Runtime Python read inventories and native
+compiler dependency files reject undeclared repository dependencies. Compiler,
+Boost and third-party Python libraries remain trusted environment dependencies;
+they are not vendored or claimed as independently verified. Catalogue and
+selected-record pins are historical provenance, so later selections do not
+silently retarget this experiment.
+
+## Scope and inherited obligations
+
+This is a finite, source-bound emitted-template and invoice result. It is not
+an enumeration of the astronomical cover, a proof-assistant theorem, a new
+all-size compiler, or unconditional admission of the supplier. It retains the
+common-frame/label interpretation, mutable-source realization, chronological
+substitution, whole-call correlated-helper hosting, precision/tape, exact
+recovery and analytic-transfer premises of the cited chain. Maintainer
+acceptance of the replacement semantic interface remains separate. No current
+outer assembly or eleven-stage hosting replay is claimed. The selected record,
+upstream files and all predecessor packages are unchanged.
+
+## Open next questions
+
+Should this exact word be admitted as a maintained supplier under semantic D?
+The next step is a review of PR1194/PR1311 together with this bound hosted
+receipt, followed by the repository's supplier-admission process if accepted.
+The blockers are acceptance of the replacement interface and inherited
+physical/all-size premises, not a missing finite nine-stage invoice. The paid
+profile is unchanged, so this package gives no exponent-based reason to change
+the selected frontier. [TASK.json](TASK.json) records the same handoff.
+
+## Coordination and credit
+
+Assignment seed **1**, bit supplier; card `bit-helper-contract`, refined to the
+existing word's complete hosted bill. [Discussion1796](https://github.com/CrocSwap/integer-mult-bounds/discussions/1796)
+records the claim. Three candidate scopes and the overlap check are in TASK.json.
+Source-supported batch deletion (active Discussion1785), the already covered
+3x4/4x4 feedback censuses (PR1557/1706), and PR1782's different copy-sharing
+word were not repeated.
+
+Prepared for **Matthieu Pascal (@mtpsl)** with substantial **OpenAI Codex
+assistance** in implementation, checking and writing. Apache-2.0; no independent
+human review claimed. Credit Gareth Davidson/PR1122 for the composed word and
+native work; Arham Tahir/PR1311 and woklerx/PR1194 for the semantic bridge;
+Sagar Thakrar/PR1062, Sricharan Vagvala/PR967, Aaron Wang/PR1015 and Ross
+Richardson/PR923 for its circuit lineage; DreamingOfClouds/PR589/510 and
+eumemic/PR555/543 for the supplier and parameterization; DaysSky, chafreaky,
+Zhihao Chen, Dylan Crow and the retained exporter/native/hosting/moment
+contributors. Their OpenAI/Anthropic assistance disclosures and source notices
+are retained in the unchanged dependencies.