Resonance-cluster analysis for a proposed counterexample to Fried's conjecture
A Lean 4 formalization of the theorem FriedCrossing.fried_counterexample_of_resolvent_inputs, the machine-checked reduction behind a proposed codimension-one failure of Fried's identity ζ(0) = τ_R for acyclic characters on a closed hyperbolic 3-manifold with b₁ = 1. For a simple illustration of the method with figures, see docs/counterexample_intuitive_view.pdf. The Mechanism: Near (g_hyp, ρ_triv), along the conformal family g_τ = e^{−2τb}g_hyp with characters χ_θ, the Ruelle resonances near 0 form two small clusters: a rank-2 cluster in degree 1, encoded by a 2×2 matrix M(θ,τ), and a rank-4…
Comments and reviews
No comments yet.
API
curl /api/v1/records/palomar/PALOMAR-2026-09-17-000006
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-17-000006/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-17-000006/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
-d '{"body": "…", "review": true}'