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Prove sharp asymmetric tensor-phase recovery (no new κ) - #6330
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Prepared for @CubeJerry with substantial OpenAI Codex assistance. Includes independently challenged root-oracle boundary handling. No new kappa.
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Resolve #5916's asymmetric tensor-square/cube recovery question. For exact unitaries, set a=asin(e2/2), b=asin(e3/2). The sharp one-column error is 2sin(min(a,2b/3)/2) when 3a+2b<pi, and 2sin(pi/3+b/3) otherwise. Scalar unitaries attain both branches, including the jump. Adds exact rational branch decisions and certified algebraic enclosures.
Base: a7638a4.
#5916 source head: f0d87ad.
Unchanged source Git/SHA256 pins: SOURCES.json.
Reproduce (Python 3.12, stdlib):
Expected:
PASS_REGISTERED_RESEARCH_PACKAGE.Executed: 10,201 angular pairs, 101 threshold cases, 160 rational phases and 16 exact matrix pairs (12 noncommuting). Separate Sturm/gcd oracle checks 289 rational budget pairs, 97 jump/one-sided cases and 23 endpoint/common-root cases down to 2^-160. Independent review found and repaired an oracle endpoint-contamination bug; an actual mutation now reproduces that failure. Six registered normal/-O and six read-only Git-free exported checks pass, with source and receipt corruption controls. Fixed exhaustive domains; finite tests corroborate the universal proof.
No new κ. Requires the same exact unitary pair and absolute operator-norm tests. Rounded factors, projective tests, selected-caller integration and all five framework assumptions remain outside the result. Nonunitary and projective counterexamples are explicit. Full-history preflight was not run in the shallow checkout.
By @CubeJerry with substantial OpenAI Codex assistance, separately implemented verification and adversarial review. Credit Nick Petalas (#5916), unpaidmoon (#5837), DLamdata (#5894) and retained lineage. No human/proof-kernel acceptance.
Proof, pins and limitations: https://github.com/CubeJerry/integer-mult-bounds/tree/1990e007746cb0dc28c87e323f1666c6e6012f40/research/asymmetric-tensor-phase
Complete remote Git tree matches the tested contribution.