[Dugongue]

Ordinary rational rank bases can introduce non-native coefficients such as 1/3. This package uses integer unimodular column operations to factor every dyadic matrix M as U V with rank(M) columns, dyadic U and integral V, then emits a sequential one-temporary shear program with every clear and coefficient charged.

Four disjoint windows in the actual retained native source have complete scalar allowance 766 → 698 per orientation. This is a 68-unit local upper-bound reduction beyond repeated-edge coalescing; one window has rank two. It adds at most one reusable owned field, no temporary productive credit and no recursive jobs. It is not a best scalar rewrite or a κ improvement.

python3.12 -B scripts/research_package.py --package research/dyadic-block-compiler

The standard-library replay authenticates the original source and pricing function, locates both actual orientations, checks independent ranks and all 160 local persistent/dirty-owned columns, and verifies 200 additional dyadic matrix cases plus invalid-alternative controls. Registered, isolated optimized, committed-byte and Git-free export checks pass on Windows. Linux execution remains untested.

PROOF.md proves termination, alphabet preservation, the complete local operator identity and inverse-transpose construction. RESULT.json includes the emitted programs. General nonidentity query-rank declarations remain explicit caller premises; all four applications use the exact identity query. Complete caller stock, native/global admission and all asymptotic obligations remain separate.

This extends #4489's shared-bridge handoff, with source credit to zxv and the retained native/compiler authors, Jacob Alan Sussman, Cinna Davis and #4359/#4416/#4440/#4441/#4447/#4470. Integer reduction and rank factorization are classical, with no priority claim. Substantial OpenAI assistance; Apache-2.0. No selected-frontier change.