[Clear1nsight]

Result

At PR3945's exact tariff parameter κ = 1730663236534549309146/10^24, terminal-only enlargement loses more than 0.006843664113335406486182 tariff units per added dimension, even allowing arbitrary fractional owner repacking. Keep helper entrances and all paid interior scalar/native frames fixed; terminal subspaces may be noncoordinate and changes may differ per call. The credited packing dual bounds idle credit by q < 0.987736182658129815011784, while terminal rank concavity forces a surcharge m > 0.994579846771465221497966.

This supplies a quantified budget gate for further changed-boundary work: an interior refit must beat (m-q)D before an added terminal dimension can pay. It does not close PR3945's joint interior/native refits, change the selected frontier, or claim a new κ.

The binary-subspace rank argument is paired with capacitated packing/linear-program duality. The dual formula is prior work from PR3815/3862/3890, independently rechecked here at the changed PR3945 endpoint; the new result is its combination with exact terminal costs and binding to the current literal allocation.

Evidence and bounded pivot

• All 841 patterns of widths5..9:11 symbolic tight,830 strictly positive with exact rational power bounds.
• Both provider frame invoices and the full incumbent local-plus-idle profile reproduced.
• Full external source scan: 1,321,920 roles and725,760 bins. Every actual pattern attains the dual; every occupied slack bin contains only full-dimension helpers. Thus retaining owner identities permits zero positive extensions.
• A concrete mixed pivot is also priced: exactly17 protected width5 terminals per provider admit a direct rank1 refund. The extended width4..9 dual checks 2,551 patterns and charges exactly one idle unit back for each saved rank1 terminal child. These refunds cannot finance extensions. Broader mixed changes remain outside scope.
• Positive rank1-gap absorption and noncoordinate-frame fixtures; actual optimized CLI mutations of dual, capacity, missing empty bins and source bytes reject.

Default registered replay is standard-library and checks the exact theorem, both local invoices, aggregate integer owner certificate and controls. The literal full-owner scan uses explicitly fetched, immutable external inputs; default CI does not silently claim that scan. VALIDATION.json records exact executed modes. Final frozen registered replay passed in45.06s; optimized full-owner replay passed in35.11s. Exact GitHub-authored commit7d85649b64243022b3141df00c61027a083a533a passes the committed-byte/source-history gate and official export integrity checks. The proof, source pins, complete cost-status ledger and open next question are in the package.

Scope and next step

No candidate circuit is emitted. PR3969's exact arbitrary-dirty scalar/permutation identity and full chronology/family checks are inherited; this package freshly checks capacities and invoices. Native phase, physical realization, uniform precision/stock/tape/recovery, all-size compiler, outer release and analytic/BIT obligations remain inherited or unverified, never zero. The endpoint is used as a fixed tariff parameter, not independently recertified as a root or admitted supplier.

The next construction needs one literal interior frame change saving more than the stated per-dimension deficit, with an actual chronological owner reassignment and complete dirty/native bill. The full-budget screen gives no allowance for another terminal-only or direct-refund search.

Sources and credit

Pins: PR3945 91f81d131252db704f945891da1ea54e29d46b8b; PR3969 6ff67539f1131a287eb9a9a98bf1e94a02eecba7; PR3890 772953c9bda6d41db7b89e4cd6bae3dc05d7636e. Canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision6, refreshed during the session. Latest overlap cache covers690 open PR bodies through2026-10-19 08:06:26UTC; signed-in handoff reading is partial and no exhaustive novelty claim is made.

Credit Dugongue; Erwan Secousses / ChaloupeMusic; Sagar Thakrar; ToikY; dataisfire; zxv; Ross Richardson; hexapode; Jeremy Kothe; roger-sato; Arham Tahir and the complete retained native/owner lineage. The frame auditor is explicitly reused and credited; the dual/budget checker is new. Chris R / Clear1nsight with substantial OpenAI Codex assistance. Apache-2.0. No independent human or proof-kernel verification claimed.