[Lyy-iiis]

The two-full border previously needed a missing exact boundary Gaussian or an unpriced extraction. This package gives a smaller, explicitly declared productive domain: L independent X inputs and L−1 independent Y inputs per main pair, all native helper inputs retained, and one owned terminal field. Prefix compression gives an exact noncommutative actual-inverse pair, with no exact boundary provider for this reduced-domain contract.

The local ideal-native invoice is target=L*T−112H17, paid=L*P. Exact rational enclosures show L=66 passes the local C=.0034 screen with margin [5.551473221217, 5.551473223332]; L=65 fails. This is not a new κ or an admitted recursive supplier. A conditional graded endpoint theorem supplies O(e) intermediate height; standard root-only Walsh averaging then extracts the exact Gaussian diagonal using a fixed number of complete executions, without adding repeated-input copies to productive credit.

The remaining gates are explicit: the actual native word must supply coherent shears with all helpers/frames/fresh D factors; a fixed graded whole-job compiler must preserve source/exit/complement ownership and the complete profile; physical/stock/BIT costs remain. An actual inverse by itself does not supply the shear structure. Naive Pascal iteration changes grade populations, so the one-shot invoice is not asserted at every recursive level. The full-domain boundary-provider comparison and scoped counterexamples are kept separate.

Validation: seven bounded standard-library checkers pass directly on CPython 3.14.5 in normal and optimized modes with identical output hashes. Source pins, both-orientation paid census, canonical helper census, metadata-only package validation and committed-byte preflight pass. Independently written subagent checks cover the operator identities, owned-field program, local invoice and precision proof. A full local registered replay correctly stopped at its Python 3.12 version gate; the registered hosted 3.12 replay remains to run. No full native suite, selected cold replay, Lean or Docker run is claimed.

Base: current canonical main f259dabc7d70e0db8d6d36bfda888f008bbfecc1, rechecked before submission; priority revision 7 and selected κ=.00302015 unchanged. Scoped claim/expansion decision: #4611 (comment). Package: research/bounded-lane-border-core. Exact submitted head: e30cfa384f7e48581f9e5a5cb036b1ee7a3b46a9.

Credit: Cao Yifan's round-three native word; Dillon's border/recovery work; Jacob Alan Sussman and the finite-precompiler contributors; retained semantic precision, native/Clifford/helper/outer sources; Yiyang's PR4966 and formal/triangular continuation; Cinna Davis's additive-frame and compensated-pair boundaries. Prepared by Yiyang (@Lyy-iiis) with substantial OpenAI Codex and parallel-agent assistance, Apache-2.0. Separate-agent checking is not independent human or proof-assistant acceptance. No merge or selected-frontier change requested.

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