[JoyboyBrian]

Summary

Independently audit PR4991's literal original and phase-repaired two-image dirty-return boundary for every positive width and every fixed nonzero complex coefficient pair. Corroborate its nonsingular affine-volume classification and supply the separate singular rank-drop implication: a target rank strictly between (q-1)d and qd cannot contain any singular M tensor I_d factor.

 PR4991 all-coefficient completed boundary
 + independent absolute-phase/source and eventual-width proof audit
 + explicit singular-coefficient rank argument
 + PR4998 transformed inverse-partner boundary control

Evidence

• Before: The singular coefficient paragraph notes singularity, while the volume lemma assumes invertible final output; the missing rank implication was not explicit.
  After: The written proof handles the singular cases without taking a zero determinant logarithm. A code-disjoint checker binds actual source phases, exact width-one/two character counts and integer determinants, and the literal compensated program on all 16/128 independent columns over F17.
• Normal replay: 0.17s; optimized replay: 0.23s. Registered replay, metadata/pins, committed bytes/source history, export integrity, and Git-free normal/optimized replay pass. Necessary pending-source bytes, notices, original paths/heads and hashes are retained; predecessor verifiers are never imported or executed.
• Credit Cinna Davis (Prove a uniform dirty-return volume obstruction for two-image prefixes (no new κ) #4991/Construct a four-call compensated two-image pair (no new κ) #4998), lee-phys (Construct an invertible two-call prefix tight on eight block-3 hook cuts #4688), Yiyang/Lyy-iiis (Construct a target-aligned phase repair of the block-3 two-call prefix (no new kappa) #4710), Dugongue (Add reversible native ports and swap-sector completion for the complex prefix #4743), Jacob Alan Sussman (Research: lower bounds for small complex units: m = 2 never saves, m = 3 needs 14W/5 calls (Lean, engine game), m = 4 needs 41W/13, and the smallest open cases (no new κ) #4628), eumemic and Swapnil Jain. Prepared by JoyboyBrian with substantial OpenAI Codex assistance.

Merge Danger

Door: two-way

Blast Radius: isolated

Adds one scoped research package. No selected-frontier, supplier, kappa, clean-workspace exclusion, width-dependent-word exclusion or Gaussian-consumer admission claim. The all-width/all-complex result is a written proof; finite checks are corroboration, not proof-assistant verification. Canonical investigation: #5008.