ESTABLISHED
Uniform locality
The analytic first arrow
Uniform interaction norms, not profiniteness, give parameter-independent Lieb-Robinson bounds. Thermodynamic dynamics also require a uniform vanishing tail.
Research corpus / six documents
One program, six exact interfaces
Each paper isolates one obligation in the passage from local interaction data to a proposed invertible condensed phase spectrum.
ESTABLISHED
Condensed observables
Positivity, C*-norms, and descent
Section algebras preserve fiberwise positivity and the supremum C*-norm while separating analytic structure from bare condensed algebra.
PROPOSED
Thermodynamic gaps
Witnesses, images, and stability
A quantitative gap witness is data; the qualitative uniformly gapped locus is its propositional image, conditional on analytic input.
OPEN
Microscopic → effective
Three maps, not one equivalence
Functional calculus gives a controlled free-fermion map to K-theory, while scaling, classification, and inverse realization remain distinct.
OPEN
Physical realizability
From abstract class to lattice witness
Kitaev, BDI, and AKLT models verify concrete low-dimensional rows without claiming every bordism or homotopy class is realizable.
PROPOSED
Phase spectrum program
Conditional assembly and claim-status ledger
The synthesis keeps the five-stage program precise: solid analytic inputs, conditional categorical assembly, and no unproved spectrum comparison.