Certify maximal transported warp0 entrance and distinguish least frames from price

[ToikY]

Result and scope

Source-bound negative audit of Dugongue's transported-frame PR #3929 at 0c0e31cf12e8f4f07e8419a6d33ae85129fb5a01. The literal BASE-WORD's zero-based warp0 (lender243 at original B916) has a unique maximal legal entrance C0=U0+span(7), dimension5, with U0=span(261,133,85,45). Exactly 2 of374 entrance superframes are legal; the other372 are excluded.

Freeze the complete A/cut and earlier B prefix, scalar operations/coefficients/order, native maps/order, inventory and terminal caps. Each scalar frame contains its original floor; later native entrances may enlarge and transport across the fixed maps. Eight native events occur before warp0 chronologically. This changes native boundary frames, outside frozen-native-boundary helper/terminal searches. It does not change the selected frontier.

A backward capacity proof and separately implemented RREF checker agree with point-set forward enumeration of all31 quotient lines. The canonical least-join completion has complete delta 27H1-14H2-H3+H4, strictly losing for every power tariff r^q, 0<q<1. It changes32 scalar frames, one native boundary and pays one identity climb; native inventory and restore[191] are unchanged.

Least frames do not minimize price. Recompiling the retained PR3929 published recipe proves that its nonminimal scalar frames share the same native boundary subspaces and cost strictly less than this canonical completion on every such power tariff. Canonical-minus-published is -H1+2H2+3H3-3H4, with capped sums (1,3,3,0). Both lose against the original profile. Exact factorizations and the backward-capacity induction are in PROOF.md. No new global scalar-price obstruction is claimed.

Assignment, overlap and predecessor credit

Revision6, task complex-new-helper-inventory, refined to one changed native boundary; OS seed edabf938fbaa10032b6ecf5a8503dc16. Contribution head 2253023ca359782952248b1be793962a39f74165. Canonical main refreshed unchanged at 20ecf2891d80b5acf18d980b2164fb44ea7faa90 before submission. Claim #3930 records ownership. Fresh overlap covered634 open PR bodies across seven REST pages, newest handoffs #1166 and the canonical claim. No matching cap certificate found; arbitrary diffs, closed bodies and private work are nonexhaustive. Historical #422/#423 grouped entrance capacities concern a different word/framework; no novelty of the backward-capacity method is claimed.

Credit Dugongue #3929 for transported frames/compiler/published control; dataisfire #3734, zxv #3682, Ross Richardson #3605, Jeremy Kothe, Sagar Thakrar #3687, Arham Tahir #3693 and retained native lineage. Exact notices and source bytes, including original CRLFs, are preserved. Apache-2.0; ToikY with substantial OpenAI Codex assistance, including separate AI implementation and mathematical review. No independent human or proof-kernel review claimed. PR #3890 and #3926 remain preserved and separate.

Validation

Python3.12.14 arm64, standard library only:

python3.12 -Werror -B scripts/research_package.py --package research/warp0-entrance-cap
python3.12 -Werror -B scripts/check_research_commit.py --package research/warp0-entrance-cap

• Registered replay passed primary exact forward/billing/source endpoint checks, independent backward/forward checks and20 actual normal/optimized CLI controls. Changed source, price receipt, cap receipt and missing certificates reject.
• Source compiler and exact binary-action replay verify arbitrary-dirty forward, dual and cleanup-boundary endpoints. The independent checker imports neither primary nor retained executable code.
• All20 committed package files match working bytes. Aggregate public tree 5bd03fa14e4e75925dc8307c9ef66a992e274b68 matches the validated local tree.
• All three commands passed from a regular-only, inode-disjoint, read-only, Git-free export under optimized Python. Sources/export hashes and modes stayed unchanged. Maximum child RSS47,185,920bytes; free disk16,927,395,840bytes, above8GiB floor. Timings and RSS are single-run observations, not benchmarks.

Hosted run39200550363 passed both plan117892444155 and replay117892971803. Actual logs show265 onboarding tests (11skipped), complete registered replay on CPython3.12.15, all20CLIcontrols, and unchanged committed inputs. Tested merge 0f4963f29d7dc447617eb5d8e0ab8c7e5bbebee5 has the exact base/head parents and the same tree as the contribution. The cap theorem and canonical profile are certified only in the stated frame-floor domain. Inherited temporary centre-descent accounting is preserved; there is no fresh native phase replay, physical invoice/caller, complete owner/idle allocation, all-size recurrence, supplier or new kappa. Current selected kappa remains 836330098538459/500000000000000000.

Remaining useful question

Optimize scalar frames inside C0 before spending on native phase work, or explicitly change a map, scalar word, terminal contract or selected event. The canonical loss cannot rule out those completions. Any candidate still needs exact transported phase recipes and every physical/idle/hosting/cleanup charge. One isolated package only; frozen inputs, upstream, priorities, existing verifiers and selected record are unchanged. Do not merge automatically.