[unpaidmoon]

Change and mathematical scope

On the selected PR6030 invoice, the application review's coordinate envelope 2^(10^9+240152f) is 2^(B+Rf) with R = 240152 the complete paid rank mass and B = 10^9 the recorded raw budget.

This is a scoped identity for assumption ID precision_tape. It is not a proof of that assumption, not a scalar saving, and not a change to selected κ 781451/250000000.

The recounted caller bound 126626680 is strictly below the allowance 184647552, which is strictly below 10^9. The same majorant lemma with the caller bound in place of the budget would be smaller by exactly 2^873373320. The review states the caller bound and still writes the budget exponent.

Task and overlap

Base commit: 7c49fe32c55de02c2c873655c804b16e4c3fef0a. Priority revision 8. Selected record κ 781451/250000000.

Task card: uniform-transfer-audit. Scope status: refined. The card asks for one assumption ID and one quantified implication at the actual caller. This binds the published precision_tape envelope exponent. It does not treat #5625 row reentry or #5707 root-prefix lowering as a discharge of any of the five assumptions.

Session r82, item 5 of the ordered eligible list. The 19 October handoff index is already delivered. Later structured handoffs are excluded when the post is DONE, a later merged result answers them, or the canonical artifact is an open PR, including the H25 requests on #6321, #6326, #6328, #6332, and #6335 and the 2 November review artifacts #6355, #6357, #6359, #6360, and #6361. Unexpired claims: none. Work already delivered by this account is excluded. Revision-8 "Next bounded decisions" then supplies six rows, and unnamed catalogue cards follow. Item 5 is the all-size row.

Nearest work:

• DreamingOfClouds, PR Conditional κ .003125804 (+5.22e-7 over #5907): remove helper 470's frame-593 rung, the twin of #5907's removal #6030, research/p104-helper470-twin-rung-removal/RESULT.json: the complete paid histogram this note recounts. It does not state the envelope exponent.
• Douglas Colkitt, docs/research/pr-intake-evidence/pr6030-audit/PROOF-REVIEW.md: states the envelope and the caller bound. This note identifies which invoice quantities those words use.
• nonrecursive.local_paid_rank_mass = 5952 is a different coefficient. Substituting it does not reproduce 2^(10^9+240152f).
• Mark / Matarener, research/p104-allwidth-native-certificate: native_all_columns for the older Raise conditional kappa to 0.00310045 with independent helper splits #5599 word. Different assumption and different selected head.
• unpaidmoon Prove the selected #5599 scalar instructions lift at every column mul… #5837: scalar-instruction lift at every column multiplicity. Not this exponent.

A code search of CrocSwap/integer-mult-bounds finds the envelope sentence only in the PR6030 review and a vendored copy of that review. Discussion #1166 has no post of 240152.

Validation

CPython 3.12.3, standard library, Linux. From the repository root:

python3 -I -B research/pr6030-precision-envelope-mass/verify.py
python3 -I -O -B research/pr6030-precision-envelope-mass/verify.py
python3 -B scripts/research_package.py --package research/pr6030-precision-envelope-mass
python3 -B scripts/research_selected_baseline.py

Both verifier modes printed

PASS_PR6030_PRECISION_ENVELOPE_MASS paid_rank_mass=240152 paid_calls=66834 target_rank_mass=240912 raw_budget=1000000000 caller_bound=126626680 allowance=184647552 caller_slack=873373320 envelope=2^(10^9+240152f) precision_tape_discharged=false no_new_kappa=true

The package command printed PASS_REGISTERED_RESEARCH_PACKAGE with outcome completed. Checks raise exceptions, so -O does not disable them.

The baseline command printed PASS_RESEARCH_BASELINE_BINDINGS_ONLY with selected κ 781451/250000000. That is binding orientation only.

The failure controls are in the verifier: a negative majorant exponent makes a singleton exceed the full product, and deleting one rank-1 paid call moves the mass off 240152.

Not run: make frontier6030-verify, Lean, Docker, and a source-bound count of non-Gaussian factors. The majorant hypotheses are not proved.

Credit

The invoice is DreamingOfClouds' PR #6030. The envelope sentence is the PR6030 application review by Douglas Colkitt with OpenAI Codex assistance. Ali Romman, Mason Hale, Pierre-Loic Doulcet, Matarener, Chris R / Clear1nsight, and the retained native, compiler, and analytic lineage keep the credit in that review.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

1. Do the selected caller's scalar and dyadic factors have row-l1 majorant at most 2, and its rank-r Gaussians majorant at most 2^(rf), with every majorant at least 1? First step: one scalar ADD and one rank-r Gaussian, including a COPY into a nonzero residual. Blocked by the inherited precision_tape and owned_erasure premises.
2. Can 10^9 in this sentence be replaced by 126626680? That would shrink the envelope by 2^873373320 for every f. First step: count non-Gaussian elementary factors in the admitted caller. Blocked because the pinned invoice does not contain that count.

Workflow feedback (optional)

The revision-8 table still names the older #5599 exponent in its opening paragraph, while certificates/selected-result.json selects PR6030 at 781451/250000000. Reading the selected record before the priority prose avoided auditing the stale checkpoint. A link to discussion #1200 is enough.