[RichardHoekstra]

Change and mathematical scope

For the frozen complete #5413 caller, reduce the sufficient carrier height in N=2^H by 3.20324× at unchanged conditional κ=.003027288235, from 38569300000000000 to 12040700000000000. Four explicitly weaker savings give a size-saving frontier; κ=.003 has H=1239850102 (31.1 million times smaller than the historical #5413 H).

This is a conditional construction-bound application, not measured runtime, a globally minimal template, a new raw paid profile/root or a selected-frontier update. All 64,260 paid jobs, 10,928 productive fields, component false flags and five framework assumptions remain. Even the smaller carriers are astronomical.

The change evaluates the existing higher-moment theorem's complete alpha^v + 2*gamma^v + 2*delta^v charge directly, including both partial-block tails and target completion, then retunes the logarithmic compiler. The old .97/Bernoulli envelope rejects these choices, so this package makes the changed application explicit rather than claiming the frozen checker already admits them. PROOF.md gives the charge, rational ceiling-grid argument and fresh finite-template/precision application. Three exact precision sites and six named conjunction applications change in scratch; the other 19 source gates are checked AST-identical. All 25 adapted conditions pass for each point.

Task and overlap

Explicitly assigned finite-size work; TASK.json records changed scope from the historical independent-moment card. Arithmetic helper reuse is authenticated and credited, not described as an independent reimplementation. Orientation/source pin: 6cf7a683f447b9f1e2333791907fd92be5009a63; submission parent: de5ec2e7a6074068452f45b1a191b5c72832df4a. All 145 live input files are unchanged between those upstream checkpoints and have exact blob/SHA256 bindings in SOURCES.json. The diff adds only research/pr5413-carrier-frontier/ and preserves frozen packages.

Nearest precedent: #5413's complete caller/application, #5462/#5468's endpoint and gap-parametric work, and zxv's higher-moment-strictification package. #5468 keeps the original tuple; this changes the fully charged tuple and targets finite carrier size at fixed or explicitly weaker saving. A bounded PR title/body search included those predecessors, carrier-related work and the exact new H; it is not an exhaustive novelty proof. The selected construction has advanced separately; no record improvement over its present κ is claimed.

Validation

Linux, CPython 3.12.13, standard library only:

python3.12 -B scripts/research_package.py --package research/pr5413-carrier-frontier --check-only
python3.12 -B scripts/research_package.py --package research/pr5413-carrier-frontier
python3.12 -B scripts/check_research_commit.py --package research/pr5413-carrier-frontier --check-modes

Passed metadata/pins and both registered ordinary and optimized replays. Each first runs the unmodified eight-engine #5413 master, then freshly checks all five funding/precision/conjunction applications and the 54 strict + four functional outer guards. The generalized precision checker also reproduces the entire original precision payload except timing/checker/manifest hashes. Controls reject an unsubstituted application, preceding grid, out-of-domain product, omitted paid job, free completion and invalid higher-moment offset.

Committed-byte/executable-mode preflight passed for 156 files. The committed export passed inventory and all 145 declared-input checks; its optimized direct replay also passed after extraction with no .git and PATH=/nonexistent. Ruff passed for the three new Python files. Ordinary/optimized wrappers compile scientific source with optimize=0. No Lean check, materialized full word, actual Turing-tape run, independent human review or full-history provenance audit is claimed; the source checkpoint is an ancestor, while the local clone is shallow. Hosted CI is separate.

To inspect the generated full written instances and exact source diffs:

python3.12 -I -B research/pr5413-carrier-frontier/verify.py --proof-output /tmp/carrier-frontier-review

Credit

Richard Hoekstra with substantial OpenAI Codex assistance; new material Apache-2.0. Retain Chris R/Clear1nsight's caller, exact arithmetic and precision/conjunction checks; zxv's higher-moment/logarithmic compiler; Jacob Alan Sussman's mixed flow; Cinna Davis's product/helper lineage; Dillon Amburgey's provider; Ali Romman's controller; Cao Yifan's native word; and the cumulative source notices. No proprietary implementation or third-party source is copied into the new package.

Open next questions

See the package's next questions. The immediate useful review is the complete paid-tail argument and six changed conjunction applications against the exact source. Numerical success is not scientific approval. A different compiler geometry with its full ordinary/precision bill remains the larger route toward usable sizes.