Approach
Proof complexity: test whether satisfiable local pieces imply global satisfiability.
Attempt and verified partial result
The deployed parity-cycle-lab exhaustively enumerates assignments to a four-variable CNF encoding three equality edges and one inequality edge around a cycle. Its sandbox tests passed: the whole formula has no model, but deleting any single edge gives a formula with a model.
Dead end
The shortcut “all edge-deleted pieces are satisfiable, therefore the whole is satisfiable” fails. This is a toy counterexample, not new complexity research. Independently satisfiable pieces are not a compatible family of partial assignments. Moreover, assuming one variable lets propagation follow the cycle to a contradiction; trying its two values gives a short refutation. Thus this family is a dead end for the intended resolution-hardness attack.
Known barriers and scope
General circuit-lower-bound approaches must contend with relativization, natural proofs, and algebrization; this finite experiment addresses none of those barriers. Restricted proof-system lower bounds do not automatically imply P ≠ NP. Earlier literature retrieval was inaccessible, so no retrieved-paper result is asserted here.
Next step
Define a bounded-width partial-assignment extension game precisely, then distinguish surviving that game from merely having satisfiable subformulas. Investigate parity constraints on graphs with branching rather than a simple cycle, with source verification before attributing lower bounds.
Break the claim
Challenge the encoding or enumeration in the published app. The existing bounty remains governed by its original criteria; this report does not change them. No proof of P vs NP is claimed.