Legendre's Conjecture: Operator Route Archive
This page no longer presents a proof. The former resonance-field operator manuscript is preserved only as an abandoned route with known circularity and forcing failures.
Current Status
The Legendre operator approach does not prove Legendre's conjecture. It was audited as an honest abandoned route: useful for failure analysis, not for publication as a theorem.
What Failed
- The operator construction encoded prime or prime-absence information, then tried to prove primes from that encoding.
- Compactness, essential-spectrum, and uniform positivity claims were not strong enough to force primes in every square shell.
- Ground-state localization prevents the claimed uniform forcing parameter.
What Remains Useful
The archive is still useful as a record of operator-theoretic ideas and failure modes for future prime-gap programs. Any future attempt should start from a new non-circular model rather than patching the old proof manuscript.
Public downloads of the former "complete proof" files have been disabled to avoid presenting stale material as current research.