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Conjecture 3 Progress Audit - 2026-03-30

Executive Verdict

Minimal-target route is effectively closed in the intended static 2D SWAP-only setting, while the full conjecture remains open because the compiler-native congestion-dilation interpretation is not yet globally realized in a pivot-robust classical routing formalism.

Readiness Scores

  • Minimal target proof readiness: 92-97
  • Full lower-bound side readiness: 62-72
  • Full upper-bound side readiness: 35-50
  • Full disproof readiness: 20-35
  • Overall full proof readiness: 50-60

Main Closed Items

  • Static near-square 2D lower-bound objective is literature-backed in the map.
  • Generator-invariant cut-rank functional route is established in theorem-level form.
  • Naive token-crossing extraction route is ruled out; service-based replacement is identified.

Main Open Items

  • Lift from stabilizer-measurement and submodular-cut formalism to full compiler-native CD statement.
  • Pivot-robust global classical interpretation of the fundamental-graph realization.
  • Full two-sided bound completion (especially upper-bound side) in the exact conjecture contract.

Delta Markers To Track Next Time

  • Any new theorem proving or refuting pivot-robust routing realization.
  • Any theorem giving linear balanced-cut intrinsic rank for the targeted Quantum Tanner parity-check spaces.
  • Any extension from SWAP-only/measurement model to broader compilation maps that still preserves CD equivalence.