Research: pool PR #2269's 76 private T74 cleanup buffers into a 48-field bank

[commdata2338]

Change and mathematical scope

PR2269's borrowed T74 words allocate 76 private cleanup buffers. This package gives a source-pinned static allocation using 44 fields forward and 48 in the inverse-transpose orientation, so one common 48-field bank saves 28 fields. It adds no arithmetic: 151/409 exact zero operations are omitted and all remaining operations retain their order. All 661 ordinary cleanup-entry arrays are arbitrary, and every pool field returns to zero.

The result is a finite allocation construction and scoped proof, packaged at research/t74-cleanup-buffer-pooling/ (this PR). The two enclosing source words have the same literal cleanup list; both source bindings and both orientations are checked.

Interval coloring plus simultaneous-live witnesses proves 44/48 optimal in the declared zero-to-zero interval-allocation class. A stronger dual witness gives 48 distinct nonzero literal values at event 2686; its rows contain no remaining warp symbols, so it proves the common 48-field capacity sharp for direct literal storage even with equal-value coalescing. This excludes encoding, address packing, ordinary-register borrowing, spills, recomputation, reordering and new cleanup circuits. At the first forward peak there are two equal-value pairs; no broader forward-only minimum is claimed.

No supplier adoption, κ change, recursive-profile improvement, full-record verification or selected-frontier change is claimed. Native allocation/routing/CLEAR accounting, native lowering and phase bindings, precision/tape, whole-call admission and later 78-buffer words remain unchecked. The README gives the exact proof and boundary of the result.

Task and overlap

Base and final refreshed canonical main: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, priority revision 4. Main and contribution guidance did not change at the refresh checkpoint. The older PR2269 scientific input is deliberately frozen; no numerical transfer to a newer record is asserted.

The claim is in discussion #2609. Exact source heads:

• PR2269: b479fc5567bc09ab9185bffe89b62594f36d74e5, both literal words, retained unchanged with Git-blob/SHA256 pins in INPUTS.json.
• PR2315: 4a2f20ea339e30348448096ca789d0efe55df9bb, independent accounting finding and source reference; no checker code imported or copied.
• PR2226: dacaf3d81f1936bb55b8454b1244e5d014272754, credited dirty-borrowing lineage, not an additional executable dependency.

Nearest work: PR2315 reproduces the word and identifies the unpriced 76-buffer bank; PR2309 and successors charge dedicated buffers. PR2394 treats a different initial compensation prefix. Concurrent PR2530 source-partner cut and PR2588 frame-price audits concern lenders and positive-rank charges, not this cleanup storage allocation. No prior pooling result was found in the checked snapshot. Coverage: 812 open PRs at 2026-10-15T16:22:35.669380Z; 1261 discussion records at 16:12:28.504010Z, complete pagination. These are anonymous shared snapshots with explicit offline freshness limitations, not a novelty guarantee.

Local task card:

Task ID / scope key: complex-new-helper-inventory / f3b0895a4f9f1cc62e75;
  PR2269/private-cleanup-zero-lifetimes/optimal-interval-pool.
Base and exact predecessors: main and PR2269/2315 heads above.
Concrete object and question: the two frozen 76-buffer cleanup streams;
  minimum certified zero-to-zero interval pool and a literal pooled realization.
Scope status: changed. Take PR2315's central private-buffer accounting question;
  this physical storage result does not claim the catalogue's moment/ceiling gate.
Existing restriction changed: eager one-field-per-logical-buffer allocation;
  retain event order and omit only proven zero operations.
Method / bounded domain: exact rational free-group-algebra rows for all 661 entry
  arrays, 43 invertible warp symbols, 4500 events, 76 zero buffers, both orientations;
  interval coloring, explicit peak rows, independent noncommuting dense controls.
Nearest overlaps and added value: PR2315 accounting, PR2309 dedicated stock,
  PR2394 initial prefix; adds a literal zero-lifetime pool with a boundary proof.
Optimistic full cost budget / observable improvement: fewer private fields,
  no added arithmetic, native routing and whole-call price remain open.
Success / falsification / budget: exact pool/original boundary equality and zero
  release, matching upper/lower interval witnesses, semantic mutations; 60 minutes.
Predecessor authors / artifact / replay: Kothe, Thakrar, Davis, Dugongue and retained
  lineage; research/t74-cleanup-buffer-pooling; registered replay below.

Validation

Python 3.12.3, standard library only:

python3 -I -B scripts/research_package.py --package research/t74-cleanup-buffer-pooling
python3 -I -O -B research/t74-cleanup-buffer-pooling/verify.py
python3 -I -B research/t74-cleanup-buffer-pooling/check_dense.py

Registered replay and metadata/source pins pass. The exact engine derives all nonzero intervals, checks each allocation/release at zero, replays the static pool, and compares all ordinary output coefficients. The stored receipt contains every plan/interval/omission and a 48-distinct-value dual witness using signed 16-bit inputs. No predecessor Python code is imported or executed.

Six controls per bound case reject overlapping allocation, early release, dirty pool entry, a wrong-sign closing ADD, an unallocated zero read, and an inverse-warp sign change that changes the ordinary map. The separate dense interpreter checks two noncommuting 2-by-2 specializations over each of primes 65537 and 1000003, all 1322 scalar input columns per case, every lifetime, peak rows, the full pool boundary and scratch restoration: eight cases. This supports the exact rational/free-algebra proof; finite-field checks alone are not presented as that proof.

Git-free read-only relocated optimized replays pass. Source-byte corruption, integer-to-Boolean receipt corruption and attempted output overwrite reject. Replays leave package bytes unchanged. git diff --check and package metadata/pin checks pass. Full native/global/outer cold replay, later-word transfer, proof-assistant checking, hosted CI and independent human review were not run or claimed.

Credit

Prepared for commdata2338 (@commdata2338), with substantial OpenAI Codex assistance. Jeremy Kothe/PR2269 supplies the words; Sagar Thakrar/PR2315 identified missing physical buffer charges; Cinna Davis (@1337isnot1337)/PR2226 supplies anticipatory dirty borrowing, early restoration and private-zero cleanup; Dugongue/PR2309 supplies dedicated private-stock accounting. Rohan Arun, Marius-Paul Dumitrean, icekylinx and the retained T74/provider/compiler authors retain the source notices and Apache-2.0 credit. New checkers are separately written; source words and notices are copied unchanged.

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

1. Emit the static allocation in the native cleanup, then check routing, CLEARs and full physical stock. The logical certificate does not discharge those charges.
2. Pin a later 78-buffer word and recompute its lifetimes; do not inherit the number 48 by lineage.
3. Test forward-only equal-value coalescing of (1015,1202) and (1031,1214) against their later writes. Agreement at one cut does not justify merging lifetimes; the dual direct-storage floor remains 48.

The README and TASK.json give first steps and blockers.

Workflow feedback (optional)

Separating private-zero cleanup from the changing record made a bounded, reusable check possible. Publishing a stable cleanup-event interface and a separate physical-stock invoice with future borrowed-word records would make lifetime and allocation audits easier to compare.

🤖 Generated with Claude Code

https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG