Research: Exact scalar tables

research/current-scalar-flat-tables/.gitignore

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+__pycache__/
+*.pyc

research/current-scalar-flat-tables/DEPENDENCIES.json

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+{
+  "schema_version": 1,
+  "files": [
+    {
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "ab239cb6ee884e7a900dd9101c34448077fad0b0",
+      "original_path": "research/compiled-owned-bank-lifecycle/machine.py",
+      "local_path": "vendor/lifecycle/machine.py",
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+    {
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "ab239cb6ee884e7a900dd9101c34448077fad0b0",
+      "original_path": "research/compiled-owned-bank-lifecycle/source_ir.py",
+      "local_path": "vendor/lifecycle/source_ir.py",
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+    },
+    {
+      "repository": "CrocSwap/integer-mult-bounds",
+      "commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+      "original_path": "research/delimited-continuation-stack/stack.py",
+      "local_path": "vendor/stack.py",
+      "git_blob": "a5d6753b901901a5b2d1a4dd72134e53af70c666",
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+    }
+  ]
+}

research/current-scalar-flat-tables/PR-DESCRIPTION.md

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+## Result
+
+**No new κ.** This package gives actual fixed finite ADD/SCALE transition
+tables for the current three-bit coded lifecycle ABI. They execute through
+the unchanged published `execute_table` and `Controller.primitive`, with no
+runtime numerical callback or decoded length. The all-width theorem accepts
+exactly the common-grid outputs that fit the original signed word, stages the
+entire field before target writes, preserves borrowed sources, returns heads
+and physically erases its two work tapes on success.
+
+This supplies one concrete missing scalar-provider implication in the current
+compiler/owned-lifecycle composition. It covers 366,842 original ADD/SCALE
+occurrences in the exact 642,410-event selected caller, using 42 tables with
+58,544 rows. It does not discharge the five assumptions as a whole or improve
+the selected conditional κ = 0.003125804.
+
+## Why this is new
+
+CrocSwap/integer-mult-bounds#3098 already executes inherited scalar recipes on
+aligned sequential packets and leaves their actual caller/owner binding open.
+This package binds the current exact source tokens and ordered owners to
+tables accepted by the newer coded lifecycle, with complete copying, head
+return, backing and erasure costs. It also removes recipe-specific temporary
+headroom requirements: four-bit SCALE(-1/2) accepts -8 → +4, and ADD(2) accepts
+(-7,+7) → +7, without storing either overflowing intermediate word.
+
+The 31-coefficient/denominator-16 census is credited to
+CrocSwap/integer-mult-bounds#6928 and is not claimed anew. The general fixed
+rational theorem does not prove the unfinished-context grid condition of
+CrocSwap/integer-mult-bounds#6932 or CrocSwap/integer-mult-bounds#6934.
+
+## Exact sources
+
+- Canonical base: `7c49fe32c55de02c2c873655c804b16e4c3fef0a`.
+- Selected local word from CrocSwap/integer-mult-bounds#6030 and the original
+  productive controller, pinned by Git blob and SHA256 in `SOURCES.json`.
+- Unchanged [published lifecycle machine and source compiler](https://github.com/CubeJerry/integer-mult-bounds/tree/ab239cb6ee884e7a900dd9101c34448077fad0b0/research/compiled-owned-bank-lifecycle),
+  pinned in `DEPENDENCIES.json` at
+  `ab239cb6ee884e7a900dd9101c34448077fad0b0`.
+- Unchanged CrocSwap/integer-mult-bounds#5356 physical continuation source.
+
+## Verification
+
+```sh
+python3 -B scripts/research_package.py --package research/current-scalar-flat-tables
+```
+
+The manifest registers eight bounded normal/optimized checks, with exact
+committed receipts. The physical oracle covers all 10,870 width-1-through-4
+signed cases for the actual table catalogue, wider complete fields through
+width 129, and 400 additional rational cases. A real unchanged-controller
+fixture executes the complete initial scalar block at source events 1..9895
+on 799 coded fields, totaling 41,088,794 physical cell actions, and compares
+every endpoint to a separate exact Fraction interpretation.
+
+Twenty-five controls detect arithmetic, shape, source, alias and erasure
+failures, including mutants of the final-carry sign and sign extension. An
+independent lead AI mathematical audit derived the terminal equation and
+checked a separate 14,260-case integer-digit/Fraction domain. It is described
+separately from physical executor tests in `VERIFICATION.md`. The all-size
+proof is in `PROOF.md`; finite tests do not establish it alone.
+
+## Limits and next obligations
+
+Successful execution requires aligned complete operands on the same grid and
+the stated final signed range. Source owner maps and original lifecycle
+contracts remain premises. Arithmetic rejection preserves public contents but
+can leave heads advanced and work occupied; no physical rollback is claimed.
+
+The positive complete scalar bill is `O_q(V+D+Q)`, with two used work tapes and
+current backing at most `2V+3+O(1)`; retained erased history remains counted.
+This does not certify the complete old numerical allowance. Native maps,
+row/recursive services, whole-caller precision/error returns, global ownership
+and analytic recovery remain open composition obligations.
+
+## Credit and assistance
+
+Prepared for **@CubeJerry**, with substantial OpenAI assistance in mathematics,
+implementation, source analysis and checking. Prior credit is preserved for
+Jose Manuel/jmbarrancoml (CrocSwap/integer-mult-bounds#3098), Nick Petalas
+(CrocSwap/integer-mult-bounds#3078 and CrocSwap/integer-mult-bounds#3090),
+Sagar Thakrar (CrocSwap/integer-mult-bounds#696), James Chang
+(CrocSwap/integer-mult-bounds#1869), the encoded arithmetic of
+CrocSwap/integer-mult-bounds#3091, Ali Romman's productive caller/continuation
+work, DreamingOfClouds' selected word, Mark/Matarener's occurrence sources,
+and the retained native/compiler/lifecycle lineage. The geometry and precision
+work in CrocSwap/integer-mult-bounds#6878, CrocSwap/integer-mult-bounds#6900 and
+CrocSwap/integer-mult-bounds#6901 retains its scope and credit. Separate AI
+review is not independent human or proof-kernel admission.