Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.
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Obstructions to complete clone-class amplification
_proof: The transversal product formula, seven Fano-cap spectra and seven distinct parity rows prove the complete-cloning obstruction.
The proof is author-recorded Plasma AI work, without independent review or Lean proof. It concerns the expansion containing every allowed -subset in every class. It does not exclude selected inner families or other amplification operations, nor does it resolve Problem 644.
The parity family is the construction of Fon-Der-Flaass, Kostochka and Woodall, described with its source standing in the amplification research account. The obstruction is a distinct deduction about complete cloning; the proof below uses only the explicit parity-family definition and an elementary transversal upper bound. It assumes neither the source's theorem nor its exact transversal number. No native L-claim is consumed.
Conventions. A transversal is a set meeting every edge. tests at most seven distinct edges. Each constructed obstruction also defeats the exactly-seven convention: the expanded family has at least seven edges, and a smaller bad subfamily can be extended.
Verification. Read the exact covering criterion, the Fano-cap incidence construction and the seven cyclic parity rows in the proof. All arithmetic and constructions are explicit and need no artificial computation. No gap remains in the stated obstruction at author standing. The unrestricted amplification and extremal questions remain open.