Log-Harmonic Field Theory (LHFT) - Trace-Readout Theory

"Only the present physical state of an observer, apparatus, or record system is directly accessible. The past is not accessed as the event itself, but through present records: retarded light signals, detector marks, memory states, correlations, interference patterns, fossil traces, or cosmological radiation. The future is not a completed event waiting ahead. It is the set of dynamically admissible continuations compatible with the present state, the interaction, the boundary conditions, and the relevant constraints. In LHFT language, a measurement does not include a finished answer from the outset. It stabilizes a readout by excluding alternatives from the foreground. Modes that are not required for the chosen question are not destroyed; they become background or complement degrees of freedom and may still affect the foreground through effective dynamics." Trace-Code, Model Decoding, Exclusion, Schur Complement, and Defect-Controlled Reconstruction Author Christian Baganz (1969, Potsdam/Germany) Framework Log-Harmonic Field Theory (LHFT) Document type Theoretical framework / ontological decoding module / defect-controlled recovery subtheory Version 26.06.23 — Working draft License Creative Commons Attribution 4.0 International (CC BY 4.0) Status Strictly curated LHFT subtheory / Framework formulated / Candidate Schur-coding mechanism / Defect architecture formulated / Microscopic derivation open Overview This publication introduces LHFT Trace-Readout Theory as a strictly bounded module within Log-Harmonic Field Theory (LHFT). It formulates physical knowledge as model-based decoding of present trace-code. The central thesis is that the present is not directly possessed as reality itself. Rather, the present is treated as a trace-state in which past coupling, exclusion, and readout history are encoded. Scientific models act as decoders: they reconstruct past histories from present traces and project constrained spaces of possible future readouts. P≤tphys → R≤tO → P̂≤tO → P̂>tO Here P≤tphys denotes the physical past history, R≤tO denotes present trace-code available to observer or apparatus O, P̂≤tO denotes the reconstructed past, and P̂>tO denotes the constrained space of possible future readouts. Core Principles The framework is organized around six core principles: Principle Meaning Status Trace-Code Principle The present contains encoded past coupling, exclusion, and readout history. Definition Model-as-Decoder Principle Scientific models decode present trace-states into reconstructed histories and possible future readouts. Definition Time-as-Encoding Principle Time is treated as the ordered encoding of past readout history into the present trace-state. Candidate LHFT ontology Exclusion-Readout Principle Readout arises by exclusion, not by primitive positive inclusion. Definition / Candidate LHFT principle Schur-as-Coding Candidate The Schur complement is proposed as the candidate normal form of exclusion-based coding. Candidate Defect-Control Principle A readout closes only when its defect vanishes or is controlled small inside a specified recovery window. Definition Main Demonstration: The Double-Slit Experiment The double-slit experiment is used as the central demonstration of Trace-Readout Theory. The document separates three different readout claims: Detector hit: closed as a localized trace. Which-path partition: not closed without path detection. Interference pattern: closed statistically as an ensemble trace. The key interpretation is: The interference pattern is a macroscopic statistical trace of microscopic non-which-path closure. In compact closure form: Closed(xᵢ) = 1, Closed(L|R) = 0, Closed(pattern) = 1 Thus, the interference pattern is not treated as a path trace. It is treated as a trace that the slit region was not read as an exclusive left-or-right path partition. Schur Complement as Candidate Coding Mechanism The publication introduces the Schur complement as a candidate mathematical normal form for exclusion-based coding: Kvis = A − B† C⁻¹ B In this reading, the visible readout is not simply the directly visible block A. It is a residue of an excluded complement C, including hidden backreaction through the coupling block B. The visible readout is a residue of exclusion with hidden backreaction. This is treated as a candidate normal-form mechanism, not as a completed microscopic derivation. Defect Architecture The theory is organized by explicit defect gates. The minimal master defect is: DTRTO = DtraceO + DdecodeO + DexclusionO + DSchurO + DreadoutO + DpredictionO + DtranslationO A defect-zero statement is always read as projective recovery closure inside a specified observer window, not as absolute closure of the full structural layer. DXO = 0 ⇒ X is closed inside the stated observer window. Scientific Boundary This document does not claim: a complete derivation of quantum mechanics, a complete derivation of the Born rule, microscopic necessity of the Schur complement, observer-created reality, reality as mere information, a fully prewritten future, or absolute closure of the full structural layer. The main theorem target remains open: S1L ⇒ DTRTO = 0 This means that the deeper LHFT structural action boundary should eventually derive the trace-code, exclusion, Schur, readout, prediction, and translation closures in an admissible observer window. In the present document, this implication is a theorem target, not a completed proof. Contents Scope, Trace-Code, and Models as Decoders Time, Past, Future, and Prediction Exclusion and Schur Coding Incompatible Readouts and Trace Accessibility Double-Slit Demonstration Defect Architecture, Final Status, and Open Proof Obligations An additional appendix lists the required non-LHFT reference sources for quantum foundations, uncertainty, complementarity, decoherence, quantum eraser experiments, Schur complement mathematics, forensic trace reasoning, measurement uncertainty, and model-based inference. Keywords Log-Harmonic Field Theory; LHFT; Trace-Readout Theory; trace-code; model decoding; exclusion; Schur complement; defect principle; quantum measurement; double-slit experiment; which-path information; interference; decoherence; complementarity; scientific reconstruction; observer-relative recovery; projective recovery closure. Suggested Citation Baganz, Christian. “LHFT Trace-Readout Theory: Trace-Code, Model Decoding, Exclusion, Schur Complement, and Defect-Controlled Reconstruction.” Log-Harmonic Field Theory (LHFT), 26.06.23 working draft. Licensed under CC BY 4.0.