Before a Theory of Everything: What Fundamental Reconstructions Are Not Allowed to Assume
Lucién Hardy · arXiv (Cornell University) · 2001
Reconstruction programmes ask whether familiar physical structures—for example time, factorization, quantum theory, or spacetime—can be derived from more modest premises. A derivation may be mathematically correct yet support a stronger headline than those premises warrant. Four recurring failures are that the target is an artifact of representation, is already present in an uncredited law or auxiliary input, follows from a construction too vacuous to discriminate it, or is never connected to the advertised observables and physical regime. This article develops a claim-relative audit that keeps exact mathematics separate from evidence-dependent scientific judgment. It freezes the claim and the experimentally protected interface, tests reversible re-encodings, records a provenance bill of materials, checks law–state noncircularity and anti-tuning, and requires an explicit physical-recovery bridge. Missing required evidence blocks a pass. In the finite class studied here, the same operational interface can be reversibly repackaged from many displayed factors into one: raw declared factor counts are therefore not representation invariants, and the corresponding minimum over admitted presentations is one, while an indecomposable role count requires additional justified factorization structure. Further bounded examples treat naturality, fixed points, hidden time, interventions, and quantum recovery. A worked audit of the Chiribella–D’Ariano–Perinotti reconstruction accepts its exact finite-dimensional conditional theorem while separating that result from claims of unique ontology, empirical inevitability, quantum field theory, spacetime, or gravity. The paper is neither a Theory of Everything nor a universal decision procedure; it specifies what a reconstruction must expose before receiving the inferential credit it claims.