3231 — Scalar Functional-Equation Covariance Does Not Lift Zero-State Energy
An exact two-sector countermodel shows that reciprocal scalar-readout covariance and simultaneous scalar nullity do not identify the underlying states or equate their norms. Therefore the scalar functional equation cannot be pulled directly into the doubled valuation-energy seam detector.
Two fourth-tower rungs are missing: a state-valued Fourier--Tate functional equation on the canonical zero-state domain, and a norm-compatible commuting projection from completed zero-states to the bordered valuation chains. Until both are derived, the local seam detector remains disconnected from zeros.
Durable verification
- Research packet: research/grothendieck/scalar-functional-equation-covariance-does-not-lift-zero-state-energy.md
- Exact checker: research/grothendieck/checkers/check_scalar_covariance_not_state_energy.py
- Sequence claim: seqclaim-7ffd36ec39dfcd0b252903b4
- Graph event: ev-000000006768-b510ce56-0bfd-49ef-822f-572c40e7f006