[zxv]

Local scalar savings can worsen a recursive invoice, and owning helpers removes both paid jobs and productive output credit. Add an exact signed-invoice preflight that compares the complete paid and target histograms before native or compiler replay. It certifies better, equal or worse cost for every concave power tariff when the order is decisive, and reports inconclusive comparisons honestly. The method is classical concave order; the contribution is its reusable interface, explicit accounting contract and source-bound current application.

The current centre-paired helper exchange has a concrete ceiling. Even granting all 144 original exchanges −H1−H8 paid / −H9 targets, its raw crossing is below 0.00302728824994. The 128-exchange bill in #5383/#5387/#5390 has less than 0.00000061348187 raw saving left through this exact lever. Reaching 0.0034 requires a different paid profile, target tradeoff or caller. This is a ceiling on the stated finite invoice family, not a barrier to all ownership or relation methods.

An independent traversal also checks all 3,298 paid events in each source orientation. Under the exact eight backward relations it finds precisely the eight known zero jobs and eight known same-frame proportional snapshots. This corroborates the current investigation in Discussion #5125; it is not a discovery priority claim. The absence result is confined to the retained formal free-word grammar. New native identities, scalar combinations, relations and event graphs remain open.

The preflight distinguishes useful compiler work from recursive-budget gains: #5350's unfiltered H4→2H2 retiming is uniformly worse, while its filtered version preserves the invoice; #5390 usefully improves compiler parameters with the same invoice. The preflight does not dismiss those scalar/compiler contributions. Concurrent #5391 supplies the later trusted receipt/funding join; this earlier arithmetic screen does not duplicate it or fund a candidate from declarations.

Changes:

• Shared standard-library CLI with exact input hashes, separate paid/target deltas, sparse hinge certificates, contract matching and bounded parsing.
• Current-source examples, independent complete invoice reconstruction and directed rational proof of the 144-slot ceiling, including a global nonfunding interval cover.
• Independent fixed-eight formal-row census, explicit reopening conditions, contributor credit and a short contribution guide.

Validation:

• Ten CLI tests, including 625 exhaustive signed small profiles, pass normally and under -O on CPython 3.12.8 and 3.14.5.
• Registered source-bound package replay passes normal and optimized modes. Budget/census controls reject wrong relation/sign/source action and invented inventory, and demonstrate that omitting target debits falsely funds 0.0034.
• Two additional Codex agents reviewed the proof, interval arithmetic, source reconstruction and scope without finding a blocker.
• Committed-byte checks and the official export/integrity checks pass; an optimized read-only Git-free export replay passes.
• The optional full-history check is unavailable because the checkout is shallow. Direct base ancestry passes. All consumed scientific exports are local; no pending foreign Git object is required for replay.

Limits: histogram declarations do not establish circuit legality or catch omitted source charges; raw order does not establish supplier admission or a compiler endpoint. Full physical phase/tape/precision execution, the selected cold replay and inherited analytic foundations were not rerun. No selected record or research allocation changes.

Credit Cao Yifan (@intqwq), Ali Romman (@aliromman), @Dugongue, Chris R (@Clear1nsight), @ahrazzle, @mightyOil and the retained native/controller/compiler/analytic lineage. Prepared for @zxv with substantial OpenAI Codex GPT-6.1 Sol assistance, including explicitly authorized subagents. Apache-2.0.

Reproduce:

python3.12 -B tests/test_compare_recursive_invoices.py
python3.12 -B scripts/research_package.py --package research/owned-relation-exhaustion