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Hyra: claimed cubic-logarithmic cost for bounded commutators approaching the identity

Reported result · significance if the exact claim is established

If verified · conditional significanceClaim scope and evidenceReported result · not independently verified.
If verified · reference score110,000Editorial revision range 50,000–220,000. Not a statistical interval. Included in rankings as an unverified reported result; excluded from achieved-science progress totals.

Provisional assessment of the stated contribution scope. Scientific evidence and contributor attribution are separate.

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What is claimed?

Retained Tao's operator-matrix construction and used endpoint-forcing supersolutions with controlled discrete concavity to claim, for any infinite-dimensional complex Hilbert space and 0<ε≤1/2, operators with ||[D,X]−I||≤ε and ||D||||X||≤5.3×10⁶ log³(1/ε). Reported result; not independently verified by WRS. Ranked using a provisional grade and reference estimate for the exact claimed result.

Scientific scope

Source-claimed proof, not independently verified by WRS. Arbitrary infinite dimension includes nonseparable spaces; finite dimensions have an obstruction at error below 1. The logarithmic lower bound remains separated from this cubic upper bound. Lean scope excludes the surrounding B(H) right inverse and Banach fixed-point existence argument; no compilation was run.

Evidence state

The source reports this result. WRS has not independently reconstructed the complete argument or validated the reported evidence. The grade and score here express conditional significance; they do not certify correctness. The provisional value enters the main reference rankings with an unverified label, but not achieved-science progress totals.

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