Research: completed-callee substitution at PR #2234's BIT leaves and headers

[commdata2338]

Change and mathematical scope

PR2234's weighted leaf and reversed header ADD implement each ordinary field exchange digit by digit. Replacing only the leaf would leave the header width toll unchanged. This package implements a temporary two-field radix-to-binary adapter and proves that substituting a previously completed binary callee at both sites gives their required O(V w^(1-a)) charge, under the explicit earlier-callee and retained stream contracts.

The adapter pads only the two exchanged fields, increases active volume by less than four, invokes one completed binary call on the whole stream, and restricts after the complete endpoint. It preserves arbitrary complete prefix/gap/suffix fields and uses actual zero-bit padding. A source-bound leaf successor has four calls per pair; the unchanged source header code uses two calls for a reversed ADD, at width w-1. The width-zero header boundary is identity.

Status: scoped conditional proof, executable adapter and finite endpoint audit. The inherited bootstrap algebra gives the conditional second-round ordinary saving 1699995087/10^12 at unchanged c=17/10000. This remains below the selected BIT rate and is not a new multiplication exponent, selected supplier, optimized moment or full all-size admission. The prior completed fast algorithm, physical caller/preparation/hosting/parking and moment contracts remain hypotheses. The finite callback is a slow completed digit-bucket algorithm.

All changes are in research/bit2234-callee-substitution/. Frozen source copies remain byte-for-byte unchanged. README contains the proof, evidence boundary and open questions; SOURCES.json records Git blobs and SHA256 pins.

Task and overlap

Base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; contribution commit 14458fda3cac4441c27980d584582ebbbb3e9233; main was rechecked unchanged at 07:28 UTC before submission.

Base and final canonical main: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2. Final git fetch origin main checkpoint: 2026-10-15 07:16 UTC; priority revision 4, guidance, selected record and scientific dependencies unchanged. No rebase or scientific repinning was needed.

Exact sources:

• Jose Manuel / PR2234: d047ef86fbc5b1614d3d8e2b8d3441413beab73f, concrete leaf/header code and written caller contract.
• Adam Gall / PR2087: b5ffc48e3dd5c92f591bdb4fabafa2c8e8b33970, contextual conditional uniform-time lift.
• Newly inspected adjacent PR2364: b9293bb14d40f8e820ce5efd99939278e5871c56, generic joined packets; no code or theorem from it is imported.

Advance claim: #2209 (comment) . The local session itself made no GitHub writes; claim and submission are handled separately.

Local task card, also structured in TASK.json:

• Task ID / scope key: uniform-transfer-audit / ce7411fb7cf6f3460bfc; nonce 053696c45b20606ded3bcff55e5e07a2, adversarial-audit track. Refined scope: PR2234/leaf-and-header/whole-qadic-swap-to-completed-binary/temporary-padding-and-local-toll.
• Base / predecessor heads: exact heads above.
• Object and question: can the actual ordinary_swap/ordinary_fields boundaries admit a completed prior binary callee with the lower width toll and unchanged genuine payload/restoration boundary?
• Scope status: refined, taking PR2234's explicit later-fixed-bootstrap follow-up. This is a particular compiler implication; stock arithmetic and generic recurrence algebra are already covered.
• Changed premise: a completed prior ordinary binary callee replaces elementary digit-by-digit exchange. All coefficient, chronology, complete-packet and restoration contracts remain explicit.
• Method / domain: written all-width composition for fixed radix, actual source API binding, independent exact permutation oracle. Source global corollary retains prime q>2^80; finite local algebra uses q=3,5, widths 0–3, stopped leaves and all complete addresses in the stated fixtures.
• Nearest overlap / added value: PR2234 supplies the elementary base; PR2087 leaves actual primitive costs conditional; PR2289/2295 formalize recurrence/moment; PR2324/2343 concern stock; PR2310 and this account's PR2332 concern preparation/control. PR2364 and Discussion2319 concern generic dispatch and a current prefix/coefficient-site follow-up, explicitly separated from this claim. The concurrent request-mass audit concerns PR2310's evaluator, not these interchanges.
• Full cost screen: padded volume <4V; one binary call per whole field exchange; O(V) padding/restriction; four calls per stopped pair and two per reversed header ADD. With all other source costs retained, local toll is conditionally C V(n+w^(1-a)); no coarse child is added or omitted.
• Success / falsification / budget: explicit conditional lemma, genuine endpoint/cleanup tests and controls, or an exact counterexample; one bounded 60-minute session, standard library, one research process. No full GL64 execution or unconditional theorem target.
• Predecessors / artifact / reproduction: credits below; python3 scripts/research_package.py --package research/bit2234-callee-substitution.

Final cached overlap covered 587 open PRs including drafts (2026-10-15 07:07:38 UTC) and 1,116 discussion/comment/reply records (07:09:50 UTC), with complete pagination and expected offline warnings. Searches included the task, 2234, callee substitution, two-field padding, weighted leaf and bootstrap terms. The changed-file index at 06:33:04 UTC found no matching package paths. Metadata search is not a novelty certificate. All local claim objects were compared; the other active/recent uniform-transfer scope concerns evaluator request counts, while complex precision and earlier parking/coefficient audits are distinct.

Validation

On CPython 3.12.3, standard library only:

python3 -I -B research/bit2234-callee-substitution/verify.py
python3 scripts/research_package.py --package research/bit2234-callee-substitution --check-only
python3 scripts/research_package.py --package research/bit2234-callee-substitution

Registered normal and optimized replays pass, including:

• 40 complete padded-exchange cases / 341,920 coordinates; additionally all 512 Boolean payloads at Q=3 through a bits-only callback;
• seven weighted leaf cases / 59,064 coordinates, with full spectator and arbitrary-payload permutation checks;
• 1,480 executions of unchanged source header ADD bodies / 457,280 coordinates, both orientations and ten dyadic coefficients;
• actual source call inventory and exact rational conditional corollary;
• 16 semantic/receipt controls, including clean identity instead of swap, dirty return, wrong spectator, dummy leakage, inverse/sign/carry/return-swap faults, and typed receipt checks;
• relocated Git-free replay, one public-CLI source corruption and four public-CLI receipt corruptions.

Expected output includes:

PASS_BIT2234_CALLEE_SUBSTITUTION adapter_cases=40 leaf_cases=7 header_cases=1480 controls=16
PASS_BIT2234_CALLEE_INTEGRITY relocated=1 source_faults=1 receipt_faults=4
PASS_REGISTERED_RESEARCH_PACKAGE research/bit2234-callee-substitution outcome=completed

The final registered run took about 49 seconds. Metadata/source pins and git diff --check pass. The all-width implication is a written proof under named hypotheses, not an extrapolation from these cases. No full supplier cold replay, large GL64 payload, actual fast prior-callee execution, formal-kernel build, selected fourteen-stage coefficient audit, hosted CI or independent human review is claimed.

The registered replay (with the integrity group) was run again on the final package bytes before submission, under an 8 GiB memory cap: it passed in about 50 seconds and left the worktree unchanged. The eight copied PR #2234 and PR #2087 files match those heads by Git blob; they keep their authors' original wording.

Credit

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance. Jose Manuel (@jmbarrancoml) supplies PR2234's concrete implementation and PR2310/2364's adjacent work. Adam Gall supplies PR2087's conditional time lift. The source527 weighted factorization, PR589/DreamingOfClouds and PR555/eumemic lineage, Ross Richardson's fallback, earlier fixed routes, descriptor and parking work remain credited in NOTICE.md and the unchanged predecessor notice. Gareth Davidson / bitplane supplies the adjacent PR2289/2295 formal audits; Aakash Thakkar and Sagar Thakrar supply the distinct stock-threshold follow-ups. The generic padding idea, weighted factorization, bootstrap formula and existing moment are not claimed as new. New work is Apache-2.0; retained source notices are preserved.

AI assistance: submitted by @commdata2338 with substantial AI assistance. OpenAI Codex (GPT-6 Astra) did the derivation, the implementation, the checking and the writing; it was packaged and submitted with Claude Code. No independent human review is claimed.

Open next questions

The README and TASK.json give two bounded follow-ups:

1. Join an actual completed faster binary callee to one nonadjacent exchange, checking arbitrary dirty spectators, local work lifetime and the full return boundary. Completed caller review and a faster backend remain prerequisites; PR2364 and Discussion2319's prefix/dispatch work are complementary.
2. Bind the substitution to one sharper retained moment/stopping choice and selected stage, with its own preparation domain, reserve and previous completed algorithm. Current source and coefficient obligations prevent selected admission here.

Workflow feedback (optional)

Priority revision 4's explicit handoffs led to a concrete compiler boundary. The main friction was separating overlapping stock, control, packet and bootstrap claims across a large board. A compact index of open-question text with exact predecessor heads and status would make this distinction easier without changing task weights.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG