3229 — Doubled Valuation Energy Is an Exact Local Seam Detector
For every prime and nontrivial finite valuation depth, the direct-minus-dual bordered-chain energy factors as
with (a=p^{-2\operatorname{Re}s}) and (b=p^{2\operatorname{Re}s-2}). Its sign is exactly the sign of (1/2-\operatorname{Re}s), so it vanishes only on the critical seam. The finite Green identity retains both primitive and terminal defects.
The next fourth-tower rung is now singular: derive that a completed theta zero makes the completed doubled energy balance vanish, with primitive, square, seam, and archimedean currents retained.
Durable verification
- Research packet: research/grothendieck/doubled-valuation-energy-is-an-exact-local-seam-detector.md
- Exact checker: research/grothendieck/checkers/check_doubled_valuation_energy_seam_detector.py
- Sequence claim: seqclaim-2ece75a232bec8d15cd83ed8
- Graph event: ev-000000006760-3d2e700c-25da-464c-9120-33ef3c45c0e5