Audio briefing transcript

Exact finite rigidity for Furter's R(3): all windows through n=299

Furter's R three is a rigidity conjecture about polynomial composition. This release proves its first two hundred and ninety-nine instances exactly. The problem is converted into a question about three inverse-series coefficient polynomials. For every window from d equals two through three hundred, the package finds one finite field in which the corresponding weighted-projective zero set is empty, using the same prime on every projective stratum. Properness then transfers that exact finite-field fact to characteristic zero. The result also gives Furter's corresponding length-two Polydegree closure equality for pairs four comma k and k comma four, for k from two through three hundred. It does not prove the universal conjecture. In fact, a new periodic zero-band theorem shows why no single fixed prime can certify every degree by this method. The public package contains the paper, complete frozen scripts and receipts, a fresh-extraction replay receipt, exact structural pilot data, and a machine-readable Universal R three Challenge aimed at future researchers and more capable AI systems. This is an unrefereed candidate with producer-side replay, not specialist review, formal verification, or independent reconstruction. This synthetic-voice briefing is a communication aid, not mathematical evidence.

Voice: OpenAI API synthetic voice (fable).
Published: 14 August 2026.
Permanent record: https://doi.org/10.5281/zenodo.21939362