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

Abstract

“What remains after exclusion is not absolute truth, but the non-excluded readout within a given coupling, projection, and question.” — LHFT, Exclusion Readout Principle The present readout is the only directly accessible physical state. The past is reconstructed from trace-code encoded in that present readout. The future is the admissible continuation space constrained by the present readout. In LHFT, a readout is the stabilized foreground form that remains after coupling, projection, and exclusion; non-required modes are excluded into the complement/background sector, where they remain structurally effective through Schur-complement backaction. full system: H = H_foreground ⊕ H_background H_background is not absent from reality. It is excluded from the explicit foreground representation of the current readout, but its influence remains effective through Schur-complement backaction. effective readout: K_eff = A - B† C⁻¹ B Since every perception is a reconstruction of what has already occurred, we always require a model to decode the present trace of the past and to constrain the dynamically admissible continuations of the future. 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.