Hypothesis: Log-Harmonic Field Theory (LHFT) Hypothesis: LHFT–to–Standard Model Interface Recovery-First Theorem–Proof Program for GR + SU (3) x SU (2) x U (1) We present a recovery-first mathematical interface between Log-Harmonic Field Theory (LHFT) and baseline physics (General Relativity + the Standard Model). The framework starts from a structural domain with a structural time coordinate, a log-scale coordinate (u = ln (r/r0) ), and an angular sphere, on which the structural fields Df (s, u, Ω) (a dimension/geometry control field) and Ψ (s, u, Ω) (a structural wave field carrying mode content) evolve. An observer-dependent projection ΠO maps this structural description to an effective 4D world (manifold, metric, and effective matter fields). On a declared recovery domain, the induced 4D dynamics take a conservative scalar–tensor effective form with φ: = Df − 3 and a conformal coupling of the effective metric, such that the limit φ → 0 reproduces GR (optionally including a vacuum-energy term) and the Standard Model on curved spacetime. The gauge sector is recovered with GSM = SU (3) c × SU (2) L × U (1) Y, including the Higgs doublet and Yukawa structure, while any LHFT-specific departures are confined to explicitly declared higher-order operators and a preregisterable fixed-template residual channel in log-variables (e. g. , log-harmonic templates with frozen λ and ω0 = 2π/λ). The interface also states the key “attachment constraints” required for full SM consistency: (i) chirality must be realized without mirror duplication in the recovery spectrum, (ii) all chiral gauge anomalies must cancel for the projection-induced representation content, (iii) a future closure theorem is needed to uniquely fix couplings (including α and Yukawas) from structural invariants rather than treating them as inputs, and (iv) Lorentz invariance must be recovered at leading order, with any residual non-differentiability constrained to be extremely small and testable via controlled dispersion/residual searches. The emphasis is auditability: baseline recovery is a strict leading-order requirement, and any beyond-baseline claim is routed into conservative, falsifiable residual tests under explicit null ensembles. If LHFT is presented explicitly as a mathematical construct that requires calibration, then its primary success criterion is internal coherence and recovery of baseline physics, not immediate empirical closure. This staging is standard in theoretical physics: it is a renormalization-group method and modern quantum-gravity program typically begin as mathematical frameworks. In this framing, empirical contact is treated as a calibration step rather than a validation shortcut. Parameters such as lambda are regarded as structural constants to be fixed by calibration, while log-harmonic templates are defined as candidate observables (targets for preregistered searches), not as claims of established detection. Likewise, the projection PiO is introduced as a mathematical map that links structural variables to an effective 4D description; it is not yet an operational measurement device. This removes premature “observer dependence” objections by keeping the discussion at the level of well-defined mappings and recovery requirements. Accordingly, LHFT should be evaluated against the appropriate comparison class: axiomatic field theories, pre-geometric models, and structural effective field theories. Direct competition with precision ΛCDM fitting or full Standard Model parameter derivations is not the initial goal; those belong to later stages once calibration, closure, and explicit recovery theorems are completed. Although the structural layer is field-rich, the recovery-first contract and fixed-template residual program severely restrict effective freedom: leading-order physics is locked to GR+SM, and any beyond-baseline content is audited by preregistered tests under explicit null ensembles.
Christian Baganz (Thu,) studied this question.