Log-Harmonic Field Theory — Partial Readout Principle

Log-Harmonic Field Theory — Partial Readout Principle Title: Partial Readout Principle under LHFT: Projection, Schur Exclusion, Superposition, Quantum Experiments, and the Consequence for S₁L^val Overview This document develops the Partial Readout Principle within Log-Harmonic Field Theory (LHFT). The central idea is that a measurement does not necessarily close all possible quantum branches. Instead, a measurement closes only the projection partition that is actually read by the observer-apparatus coupling. Core statement:A readout closes only the branch distinctions encoded by its projection partition. Interference is suppressed between readout-distinguished blocks, while coherence may remain inside unread or jointly read blocks. In compact notation: Ψ_eff^𝒪 = Σⱼ cⱼ Ψⱼ^𝒪𝒫_𝒪 = {B₁,…,Bₖ}P_𝒫^𝒪(x) = Σ_{B∈𝒫} |Σ_{j∈B} cⱼ ψⱼ(x)|² The document interprets quantum measurement not as universal collapse, but as partition-specific Schur exclusion inside an observer-readable recovery window. Main Contributions Partial Readout Principle: a measurement closes only the projection partition it actually reads. Triple-slit reconstruction: if slit 1 is read while slits 2 and 3 remain unread relative to each other, the result is one single-slit contribution plus a two-slit interference pattern from the unread block. Superposition reinterpretation: superposition is treated as an unclosed branch structure relative to a chosen projection. Schur-exclusion reading: observable branch closure is formulated as projection plus Schur-type exclusion between readout blocks. Quantum experiments under one principle: the framework is applied to Wheeler’s delayed choice, the delayed-choice quantum eraser, the Quantum Cheshire Cat, Bell-type entanglement, Hong–Ou–Mandel interference, the Quantum Zeno effect, Hardy-type branch exclusion, Wigner’s Friend, and Stern–Gerlach spin-axis readout. Consequence for S₁L^val: S₁L^val is not interpreted as an outcome-selecting collapse law, but as the first validity-bearing structural layer from which admissible branch structures, projections, readout partitions, Schur exclusions, and Born-compatible weights must be recovered. LHFT Interpretation LHFT uses the four core categories: structure → state → coupling → projection Observable quantum physics is treated as a projected recovery regime, not as the fundamental layer itself. A quantum branch is therefore not a separate completed reality. It is a possible readout component inside a projection window. The core readout chain is: S₁L^val → K_struct → (Γ_𝒪, Π_𝒪) → 𝒫_𝒪 → K_eff^𝒪 → P_𝒫^𝒪 Here: S₁L^val is the first validity-bearing mathematical access layer. K_struct is the structural operator. Γ_𝒪 is the observer-apparatus coupling. Π_𝒪 is the observer projection. 𝒫_𝒪 is the readout partition. K_eff^𝒪 is the observer-effective recovery operator. Key Formula Pattern A readout partition is written as: 𝒫 = {B₁, B₂, …, Bₖ} Branches inside the same block may remain coherent: i,j ∈ Bₐ ⇒ Iᵢⱼ may remain Branches in different readout blocks are Schur-separated: i ∈ Bₐ, j ∈ B_b, a ≠ b ⇒ Iᵢⱼ → 0 The general probability pattern is: P_𝒫(x) = Σ_{B∈𝒫} |Σ_{j∈B} ψⱼ(x)|² Theorem Target The main theorem target is: S₁L^val ⇒ K_struct ⇒ (Γ_𝒪, Π_𝒪, 𝒫_𝒪) ⇒ 𝒟_QRead^𝒪 = 0 In words: S₁L^val must force the admissible projective quantum readout structure. It must generate branch admissibility, projection windows, readout partitions, compatibility conditions, Schur-exclusion relations, and Born-compatible recovery weights. This remains an open microscopic derivation target. Claim Boundary This document is a recovery-compatible interpretation and theorem-target formulation within LHFT. It does not claim absolute microscopic closure of S_struct. It does not replace standard quantum probabilities. It does not introduce retrocausal signalling, universal collapse, or literal property detachment. The following boundaries are explicitly preserved: Numerical agreement is not treated as derivation. Normal-form closure is not treated as microscopic closure. Observable physics is treated as projected recovery, not as the fundamental layer. Standard quantum mechanics is respected as the empirical recovery map. LHFT adds an interpretive and structural recovery layer, not an unsupported replacement of quantum theory. Suggested Citation Baganz, Christian. Partial Readout Principle under LHFT: Projection, Schur Exclusion, Superposition, Quantum Experiments, and the Consequence for S₁L^val. Log-Harmonic Field Theory (LHFT), 26.06.16 working draft. Licensed under CC BY 4.0.