T124 integer-prefix composition on PR2833: conditional κ ≈ 0.00171865827784172

[mdumitrean]

Change and mathematical scope

The PR2833 composition admits conditional κ = 0.0017186582778417198986259999999999999999999998999999999999999999999999, an exact positive gain of about 8.4067486394e-10 over its full 3046-decimal headline. The exact rational and complete paid profile are in research/replica-integer-prefix/CLAIM.json.

An integer prefix reserve permits a literal T124 allocation within the retained row ceiling: actual local prefix 70 → global prefix 2343 → PAYLOAD 2344, with row 20139 < 20161. All 408 helpers, 72 buffers and 8 centres remain charged. The outer cutoff stays dyadic. The stored allocation has 455,328 roles and charges its complete rank 9 residue.

The package also certifies the fixed-provider all-T continuous packing cap at approximately 0.00171865952204203; this candidate realizes 40.32255% of the available gain above PR2833. This relaxation does not assert integer or chronological attainment.

The inherited compiler, source-access, hosting, precision, tape, recovery, BIT and analytic hypotheses remain. This is a conditional finite supplier and modern outer release, not a formal proof of the complete multiplication theorem. The selected record is unchanged.

Task and overlap

Task selected-stock-envelope, scope changed: the assigned integer-prefix/T124 lead was recomposed with the new PR2833 provider inventory after the entry refresh. Reducing the finite residue per live replica is the connection to the stock budget.

The branch merges the pending dependencies, as requested, and adds the scoped research/replica-integer-prefix/ package:

• PR2833: e9307b48d7d1b690939935ecef0f8e524e6d92f4 (actual native words and T74 allocation).
• PR2824: f1826afe1f487333f2c1e5bf862bae2211ce8dd9 (replica lifting and admission).
• PR2827: 4dc1286a476874447f76826885c6af99409a1d46 (independent checking and allocation lineage).

Exact base, source blobs and 560 external live inputs are recorded in TASK.json/SOURCES.json. Final paginated overlap coverage and relevant head checks are under evidence/.

Validation

Python 3.12.15 on Linux, exact dependency pins in requirements.txt:

python3.12 scripts/research_package.py --package research/replica-integer-prefix
python3.12 -B research/replica-integer-prefix/reproduce.py --work /tmp/fresh-t124-release --jobs 24

• Registered replay passed exact source/generator derivations, 455,328 literal roles, seven geometry faults, five moment faults and all 1,163 packing patterns.
• Primary complete admission/release passed 114 admission, 12 BIT, 25 controller, 8 independent-owner and 10 geometry controls, plus 63 modern outer inequalities and 17 rejection controls.
• Git-free default cold replay: PASS, with a source path containing spaces. This starts all four native chains and the retained parent freshly; explicit prepared-native reuse is a separate authenticated option.
• Saved-flow generator replay reproduced all four mathematical payloads, including decompressed FILL, without a solver rerun.
• A deterministic two-worker test reproduces an inherited shared-temporary-file race. The exact derivative assigns unique shard/process temporary paths and preserves all 25 mutation predicates and atomic final writes. The earlier failed run and its diagnostic limits are documented.

The new package passes the current registered runner. That workflow will also
select the frozen imported PR2824/PR2827 packages: their existing TASK.json
metadata fails the current schema check, and their manifests request Python3.13.
These inherited CI metadata incompatibilities are documented separately; their
pinned scientific inputs remain byte-identical.

Supplier/legacy-bootstrap κ and the modern outer headline are distinct freshly derived layers. The release binds the new complex endpoint and complete paid profile into the outer ledger; both receipts are retained. Unmeasured all-size assumptions are not discharged by these finite checks.

Credit

Jeremy Kothe (jeremykothe2) for PR2833; Dugongue for PR2824/PR2827; Marius-Paul Dumitrean's PR2802 work and the retained credited chain, including Tekalign's owner/native checking and PR2768 fast-native tools. Original notices and licenses are preserved. Substantial OpenAI Codex assistance covered parallel research, construction, independent auditing, implementation and documentation.

Open next questions

See the package README and structured TASK.json. The final refresh found PR2839, whose old-provider T114 headline is lower but whose owner-block norm argument is a relevant new precision lead. Check its complete-unitarity and cross-owner-leakage premises against the actual PR2833 words before composing it. The smallest allocation follow-up is one exact residue exchange within T124, bounded by the certified continuous cap and the retained row budget. A larger replica count alone is not an attainment argument. The inherited all-size interface obligations remain separate.