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Prove the uniform all-term Dn root-code cost floor - #2719
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For every n >= 4 and coefficient field of characteristic other than two, proves that the full dense D_n root-code Gram decoder has minimum algebraic rank cost n(n-1), allowing arbitrary finite term counts and arbitrary factors within the root code. Every optimum uses exactly n nonzero terms. This retires larger overcomplete searches inside this precise family; it makes no physical supplier or kappa claim.
The new step is the uniform support-deficiency classification and the odd-dimensional one-extra argument: at most two unmatched-axis cheap terms can coexist. DreamingOfClouds retains priority for the D4/D5/D6 all-term floors, deficiency method and overcomplete coupling lemma in PR2228/2277. Aaron Wang's PR2518 generator and screens are source-pinned. Prior PR2659 treats only a fixed-coordinate one-extra family.
Validation: registered Python 3.12 replay passes 583,115 actual support pairs, 366 exact factorizations over Q/F3/F5, seven semantic controls, an independent edge-mask checker with 1,482 rectangles and 208,348 cheap-triple attempts, and optimized Git-free/source/typed-receipt/overwrite controls. Two separate agent proof reviews found no actionable issue. No Lean, native circuit, selected cold replay or hosted CI claim.
Scope, proof, reproduction commands, obligation ledger, exact source pins, overlap limitations and Open next questions are in research/dn-unrestricted-root-code-floor/README.md. Claim: #2277 (comment). Started from canonical main 6bd33bc; final canonical checkpoint c3c94c2 has unchanged guidance and selected record.
Prepared for ywz65 with substantial OpenAI Codex assistance; predecessor attribution is retained.