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Quantum Structural Theory of Harmony (QSTH) – Verification Note: Time-Mirror Experiments as Probes of Entropic Coherence

Stepanik, Rostislav

Published Nov 26, 2025• 0 citations
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Abstract

QSTH Verification Note – Time-Mirror Experiments as Probes of Entropic Coherence This verification note proposes a concrete experimental roadmap for testing whether “time-mirror” phenomena can serve as operational probes of entropic coherence in quantum and wave systems. Time-mirror setups use a sudden temporal modulation of the medium (e.g. a fast change of refractive index or permittivity) to produce a time-reversed echo of an incoming wave. Here, this effect is re-cast in terms of an entropic balance between coherent and reductive entropy, ΔS_coh and ΔS_red, and its impact on an effective curvature parameter Λ_eff. The document formulates three testable hypotheses: (H1) that a sufficiently sharp temporal modulation generates a measurable time-reversed, phase-conjugated component of the input signal; (H2) that the associated echo corresponds to a local decrease of spectral entropy and an increase of mutual information between input and echo (a transient approach to “entropic coherence”); and (H3) that the strength and structure of the echo scale in a predictable way with the modulation gradient and inhomogeneity, providing an operational proxy for Λ_eff. For each hypothesis, the note specifies measurable quantities (reflection coefficient in time, coherence functions g^(1), g^(2), information-theoretic metrics, phase curvature) and clear falsification criteria. Two main experimental platforms are outlined: an optical implementation using ultrafast electro-optic or pump–probe modulation of the refractive index, and a microwave / acoustic implementation using rapidly tunable media. The note includes a step-by-step protocol (calibration, control runs, modulation sweeps, data analysis) designed to distinguish genuine time-mirror echoes from trivial reflections or nonlinear artefacts. Relation to QSTH. In the context of the Quantum Structural Theory of Harmony (QSTH), time-mirror experiments offer a way to translate the abstract balance Seff=ΔScoh−ΔSredS_\mathrm{eff} = \Delta S_\text{coh} - \Delta S_\text{red}Seff=ΔScoh−ΔSred and the Bridge Λ_eff ↔ S_eff into laboratory observables. A successful detection of entropically enhanced time-reversed echoes would support the view that spacetime dynamics and information flow share a common entropic structure, while a null result would provide valuable constraints on the QSTH framework Related QSTH Zenodo records (recommended entry points) QSTH 1.0 — Foundational Publication — DOI: 10.5281/zenodo.17455814QSTH 1.0 — Horizon Set — DOI: 10.5281/zenodo.18015679QSTH 4.1 — Planckian Horizon 2.0: The Entropic Bridge between Quantum and Cosmological Reality — DOI: 10.5281/zenodo.17899867QSTH 5.2 — OMEG: The Operational Metric Plane of Entropic Geometrodynamics — DOI: 10.5281/zenodo.17937840QSTH 6.0 — The Info-Dim (I-Dim) Package — DOI: 10.5281/zenodo.18156387QSTH 6.1 — Entropic Zero (E0) & Entropic Stars — DOI: 10.5281/zenodo.18165254QSTH 6.2 — Vacuum as an Entropic Ledger and the Origin of Baryon Asymmetry — DOI: 10.5281/zenodo.18641674QSTH 6.3 — Ledger Reality Reconstruction: I-Dim Mediation, DM/DE, and Arrow-of-Time Diagnostics (with the Eddington Paradox) — DOI: 10.5281/zenodo.18646924QSTH 6.4 — QSTH vs. Feynman Diagrams — DOI: 10.5281/zenodo.18648120QSTH 6.5 — Planckian Horizon 2.0 as a Ledger Boundary — DOI: 10.5281/zenodo.18649631QSTH 6.6 — Planckian Horizon 2.0 as an Operational Entropic-Coherence Principle — DOI: 10.5281/zenodo.18701036QSTH 6.7 — Variational Entropic Lagrangian (R10) — DOI: 10.5281/zenodo.18715255QSTH 6.8 — Mendeleev Table of Relationships among Physical Constants — DOI: 10.5281/zenodo.18762028QSTH 6.9 — I-Dim Elementary Coupling and Semi-I-Dim Classification of the Fine Structure Constant α ≈ 1/137 — DOI: 10.5281/zenodo.18864069QSTH 6.10 — The Fifth Dimension as an Account: A Ledger Formulation in (3+1)D — DOI: 10.5281/zenodo.18871791QSTH 6.11 — The Galois Ledger: Horizon Projection Π : Ω → 𝓛, Gauge Redundancy G, and Operational Invariants S/T/J — DOI: 10.5281/zenodo.18879079QSTH 6.12 — The Emergence of Dimensions as an Entropic Reconstruction — DOI: 10.5281/zenodo.18899448

DOI
10.5281/zenodo.17712248

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Quantum Structural Theory of Harmony (QSTH 5.0) – The Entropic Clock (TiM)

Rostislav Stepanik

Quantum Structural Theory of Harmony (QSTH) 5.0 – The Entropic Clock (TiM) introduces a structural notion of time defined by the balance and flow of entropy and information between coherent order and reductive noise. The work proposes an operational entropic time coordinate TE(t) together with an Entropic Clock parameter TiM(t) that can be read in two consistent ways: (i) as a dimensionless clock index N°_QSTH(t) (a metronomic tick-rate), and (ii) as the rate of entropic time dTE/dt (a structural time-flow speed). The two views are linked by a calibration factor and share the same underlying driver: the coherence–reduction balance encoded in the QSTH ledger. Within the QSTH framework, the effective state of reality is tracked by the entropic ledger variable Seff = ΔScoh − ΔSred. The instantaneous coherence ratio is R(t) = ΔScoh / ΔSred, and the entropic frequency is ωE(t) = d/dt[ ln R(t) ]. Operationally, QSTH 5.0 treats the entropic clock as a measurable structural parameter controlled by R(t) and an effective entropic curvature/impedance term Λeff(t), with experimental/observational proxies discussed for interferometric visibility, spectral broadening, and field-gradient environments. The bundle includes two appendices extending the core thesis: Appendix A (G-Gate) formulates open operational mechanisms (operator/selector/metronome) as selection thresholds governing when entropic channels become physically active; Appendix B (Quantum Tunneling & TiM) connects tunneling, barrier crossing and apparent superluminality to entropic channel activation without violating causality. Together, the three documents form a compact, test-oriented QSTH 5.0 layer designed as a readable bridge between conceptual structure and experimental/observational windows. We propose extending the typology of Entropic Stars with an ER-type (Embedded-Relic Entropic Star): a star hosting an embedded compact relic (e.g., a primordial black hole) that acts as a long-lived internal entropy driver (sink/source) and can redirect the star’s evolutionary track. In such a scenario, the star may appear evolutionarily “odd” (e.g., unusually cool/extended for its population) because internal accretion feedback modifies energy transport and radiative balance. Crucially, this is not a test-free speculation: models of “PBH-in-stars / Hawking stars” motivate asteroseismology/pulsation signatures as a way to distinguish an embedded relic from standard astrophysical explanations of anomalous stars. In our framework, ER-type is presented as an archetype—latent internal sink/source → measurable macroscopic deviation—as a complement to EO-type and the general ES-type, without making a claim about dark matter. TiM is reported as the dimensionless index N°_QSTH and, under fixed calibration, equivalently as the entropic time-rate dTE/dt. Related QSTH Zenodo records (recommended entry points) QSTH 1.0 — Foundational Publication — DOI: 10.5281/zenodo.17455814QSTH 1.0 — Horizon Set — DOI: 10.5281/zenodo.18015679QSTH 4.1 — Planckian Horizon 2.0: The Entropic Bridge between Quantum and Cosmological Reality — DOI: 10.5281/zenodo.17899867QSTH 5.2 — OMEG: The Operational Metric Plane of Entropic Geometrodynamics — DOI: 10.5281/zenodo.17937840QSTH 6.0 — The Info-Dim (I-Dim) Package — DOI: 10.5281/zenodo.18156387QSTH 6.1 — Entropic Zero (E0) & Entropic Stars — DOI: 10.5281/zenodo.18165254QSTH 6.2 — Vacuum as an Entropic Ledger and the Origin of Baryon Asymmetry — DOI: 10.5281/zenodo.18641674QSTH 6.3 — Ledger Reality Reconstruction: I-Dim Mediation, DM/DE, and Arrow-of-Time Diagnostics (with the Eddington Paradox) — DOI: 10.5281/zenodo.18646924QSTH 6.4 — QSTH vs. Feynman Diagrams — DOI: 10.5281/zenodo.18648120QSTH 6.5 — Planckian Horizon 2.0 as a Ledger Boundary — DOI: 10.5281/zenodo.18649631QSTH 6.6 — Planckian Horizon 2.0 as an Operational Entropic-Coherence Principle — DOI: 10.5281/zenodo.18701036QSTH 6.7 — Variational Entropic Lagrangian (R10) — DOI: 10.5281/zenodo.18715255QSTH 6.8 — Mendeleev Table of Relationships among Physical Constants — DOI: 10.5281/zenodo.18762028QSTH 6.9 — I-Dim Elementary Coupling and Semi-I-Dim Classification of the Fine Structure Constant α ≈ 1/137 — DOI: 10.5281/zenodo.18864069QSTH 6.10 — The Fifth Dimension as an Account: A Ledger Formulation in (3+1)D — DOI: 10.5281/zenodo.18871791QSTH 6.11 — The Galois Ledger: Horizon Projection Π : Ω → 𝓛, Gauge Redundancy G, and Operational Invariants S/T/J — DOI: 10.5281/zenodo.18879079QSTH 6.12 — The Emergence of Dimensions as an Entropic Reconstruction — DOI: 10.5281/zenodo.18899448

•Dec 14, 2025•0 citations

Quantum Structural Theory of Harmony (QSTH 5.0 Revised) — The Entropic Clock Revisited

Rostislav Stepanik

Description / Abstract QSTH 5.0 Revised — The Entropic Clock Revisited examines whether the readable ordering of physical change can be represented through an entropic-informational description of temporal readability. Rather than introducing a new physical time coordinate, the work develops the Temporal Information Metric (TiM) as a candidate measure of how changes in informational organization become readable as ordered records. The publication builds directly on the Born-readout architecture of the QSTH Revised Trilogy. Starting from the standard quantum-mechanical probability readout P = |ψ|² and its informational representation ΔS_coh = −ln|ψ|², it considers an effective informational balance between coherent and reductive contributions, S_eff ~ (ΔS_coh − ΔS_red), and investigates whether changes in this balance can provide an auditable description of temporal readability, persistence, record formation, and settlement. The central distinction is between physical time and readable temporal structure. QSTH 5.0 Revised does not propose that TiM replaces physical time, general relativity, or standard quantum mechanics. Instead, TiM is treated as a candidate informational descriptor asking when physical change becomes sufficiently persistent and organized to support a distinguishable ordering of “before” and “after.” Within this framework, readable temporal flow is associated not with isolated events alone but with the persistence and organization of records. The resulting conceptual architecture is: Born → ΔS_coh → S_eff → TiM → Settlement → Record → E₀. The work therefore provides the second pillar of the QSTH Revised Trilogy: Probability → Readability → Settlement, connecting the Born Readout Ledger developed in QSTH 6.0 Revised with the subsequent treatment of settlement and Entropic Zero in QSTH 6.1 Revised. All proposed quantities and interpretations are presented as components of an auditable informational model, not as experimentally established new physical laws. Additional description / Notes Part II of the QSTH Revised Trilogy: Probability → Readability → Settlement. QSTH 5.0 Revised develops the temporal-readability layer of the trilogy and connects QSTH 6.0 Revised — Born Set Invariants with QSTH 6.1 Revised — Entropic Zero Revisited. Its central question is: How does informational readability become history?

•Aug 17, 2026•0 citations

Quantum Structural Theory of Harmony (QSTH 8.11) — Entropic Genesis of Photon: Photon as a Minimal Transferable Record of Electromagnetic Interaction

Rostislav Stepanik

This QSTH 8.11 working publication develops the Entropic Genesis of Photon as a candidate interpretive bridge between coherent possibility, entropic transition, record formation, and the emergence of a minimal transferable carrier of electromagnetic interaction. The publication follows the broader QSTH 8.x condensation sequence, especially QSTH 8.7 — Lambda_lock Technical Note, QSTH 8.8.S — Spin-Locking and Structural Orientation, QSTH 8.9.XS2 — Schrödinger Equation with QSTH Locking Term, and QSTH 8.10.H — Hessian Geometry of Record Settlement. QSTH 8.11 asks the next physical question: If possibility can become a stable record, what is one of the most elementary transferable carriers of such record-like interaction? Within this framework, the photon is not presented as a replacement for the standard quantum-electrodynamic description. Instead, QSTH proposes a candidate interpretive layer in which the photon may be read as a minimal transferable record of electromagnetic interaction: a carrier of energy, momentum, phase, polarization, and readable interaction structure. A central QSTH reading is: Photon = minimal transferable electromagnetic record The publication connects this interpretation to the candidate QSTH distinction between coherent entropy and reductive entropy: Delta S_eff ~ Delta S_coh - Delta S_red where Delta S_coh represents a candidate coherence-preserving contribution and Delta S_red represents a candidate reductive / settlement contribution. These terms are not presented as confirmed thermodynamic state functions, but as candidate bookkeeping variables for future formalization. The text also places the photon in contrast with the Higgs / entropic weight motif. In this contrast, the photon represents a near-massless transferable coherence carrier, while the Higgs-related branch represents the question of how a state acquires structural weight, mass-related settlement, and entropic cost. QSTH 8.11 v1.2 also includes a Spin Audit Bridge. This bridge connects photon-level record transfer with the prior QSTH spin-locking line. In this reading, photon polarization and helicity are not treated as proof of QSTH, but as physically meaningful orientation channels through which the broader QSTH question of spin, directionality, and record readability may be cautiously connected to known physics. A safe candidate relation is: Gamma_lock = Gamma_0 + Gamma_spin + Gamma_wall + Gamma_entropy where Gamma_spin represents a provisional spin-orientation contribution to the broader candidate locking functional. The publication also keeps a strict methodological boundary. QSTH 8.11 does not claim to derive the photon from first principles, replace quantum electrodynamics, or prove a new physical law. It proposes a structured candidate interpretation intended for future formalization, toy-model testing, falsification, and comparison with standard null models. Short description QSTH 8.11 proposes the photon as a candidate minimal transferable record of electromagnetic interaction. It connects photon-level transfer with coherent entropy, reductive entropy, Lambda_lock, spin-locking, Hessian settlement, Higgs contrast, and the broader QSTH 8.x condensation sequence. Methodological status This publication is part of the QSTH CORE/CAND/SUPPORT/FUTURE framework. It should be read as a structured working publication, not as a confirmed physical model. The photon is treated according to standard physics as a quantum of the electromagnetic field. QSTH adds only a candidate interpretive layer: the photon may be read as a minimal transferable record of electromagnetic interaction. This interpretive layer remains CAND / SUPPORT / FUTURE FORMALIZATION. Computability note Several parts of the proposed framework may become suitable for future toy-model exploration. Candidate variables such as Delta S_coh, Delta S_red, Gamma_lock, Gamma_spin, and H_eff can be studied in simplified models once operational definitions are fixed. At the present stage, QSTH 8.11 does not claim empirical confirmation. It identifies candidate modeling entry points and clarifies which claims remain interpretive, which are connected to known physics, and which require future mathematical or experimental development. Safe Zenodo equation block Photon = minimal transferable electromagnetic record Delta S_eff ~ Delta S_coh - Delta S_red Gamma_lock = Gamma_0 + Gamma_spin + Gamma_wall + Gamma_entropy integral Gamma_lock(t) dt >= Lambda_lock -> R_stable H_eff = nabla^2 Phi_lock These expressions are not presented as confirmed physical laws. They are candidate modeling relations and interpretive bridges intended for future formalization, toy-model construction, numerical testing, falsification, and comparison with null models. Diamond sentence The photon is not treated here as proof of QSTH. It is treated as a luminous candidate bridge: a minimal transferable record through which coherence, interaction, orientation, and readable structure may meet. Notes field This record belongs to the QSTH 8.x publication sequence. It follows QSTH 8.7 — Lambda_lock Technical Note, QSTH 8.8.S — Spin-Locking and Structural Orientation, QSTH 8.9.XS2 — Schrödinger Equation with QSTH Locking Term, and QSTH 8.10.H — Hessian Geometry of Record Settlement. QSTH 8.11 provides the photon-level bridge of the 8.x sequence. After possibility, locking, spin orientation, and Hessian settlement have been introduced, this publication asks how a minimal electromagnetic carrier may be interpreted as a transferable record. The publication also prepares the later QSTH 8.XC Closure Note and the future M-independent horizon framework, where the question shifts from local record formation toward horizon-scale ledger closure.

•Jun 6, 2026•0 citations

Quantum Structural Theory of Harmony (QSTH 6.0 Revised) — Born Set Invariants: From Probability Readout to Informational Admissibility

Rostislav Stepanik

QSTH 6.0 Revised — Born Set Invariants returns to the foundational role of the Born rule within the broader architecture of the Quantum Structural Theory of Harmony (QSTH). Rather than treating the Born rule solely as a probabilistic output of quantum measurement, the work examines its informational representation and its possible role as a bridge between quantum amplitude, effective entropic balance, record formation, and informational admissibility. The central observation is that the Born readout can be mapped into an informational representation through the relation ΔS_coh = −ln|ψ|². This provides a direct bridge between the standard quantum-mechanical probability readout and the later QSTH ledger quantities, including S_eff, TiM, Settlement Dynamics, and Entropic Zero. The publication introduces Born Set Invariants as a candidate class of informational quantities, relations, or structures whose meaning may survive admissible changes of representation, projection, or system readout. It further distinguishes probability from admissibility, asking whether a non-zero probability is sufficient for the formation of a stable physical record. Within this framework, S_eff is developed as an informational ledger between coherent and reductive contributions, while Ψ and κ(Γ) are retained respectively as candidate regime-signature and regime-sensitivity descriptors. These quantities are not proposed as new forces or fundamental constants. QSTH 6.0 Revised does not modify or replace the Born rule and does not propose a new quantum mechanics. The Born rule remains a CANON experimental and mathematical anchor. The purpose of the work is instead to construct a disciplined and auditable informational language linking probability → information → ledger → invariance → admissibility → regime. The publication forms the first pillar of the QSTH Revised Trilogy and provides the informational entry point for the subsequent treatment of temporal readability, settlement, and Entropic Zero. Part I of the QSTH Revised Trilogy: Probability → Readability → Settlement. QSTH 6.0 Revised establishes the Born Readout Ledger and provides the informational foundation for QSTH 5.0 Revised — The Entropic Clock Revisited and QSTH 6.1 Revised — Entropic Zero Revisited.

•Aug 17, 2026•0 citations

Quantum Structural Theory of Harmony (QSTH AQA) — The Condensation of Information into Structure: Acoustic QSTH / Quantum Atlas: Readout, Annotation and Modulation Across the Condensation Branch

Rostislav Stepanik

QSTH AQA is the atlas branch of the later QSTH condensation series. Its role is not to replace the CORE mechanistic publications of QSTH 7.6–7.10, but to provide a dedicated readout space for regime signatures that become clearer in mathematical, visual, and acoustic representation. In this sense, AQA functions as a companion atlas to the condensation architecture rather than as a separate ontology. The branch is structured around three complementary layers:AQA-R — Readout Atlas,AQA-A — Annotated Atlas,AQA-M — Modulation Atlas. Together, these layers examine whether transition regimes can carry not only structural and mathematical signatures, but also identifiable visual and acoustic patterns. The atlas therefore supports the wider QSTH line by tracking settlement, coherence, decoherence, interface memory, lock threshold, horizon echo, ΔS_coh vs. ΔS_red, collapse–revival, asymmetric locking/unlocking, settlement maps, Φ1–Φ2 lag, boundary memory, and rewritten output. This aligns with the AQA publication’s role as an independent atlas home for diagrammatic, acoustic, and modulation-oriented materials around the mechanical line of QSTH 7.6–7.10. A particularly important result of the modulation line is the working conclusion that resonance may be not only diagnostic but also path-shaping: it may alter the path by which a regime settles, including delay, post-collapse return, and the width of the settlement window. This makes AQA methodologically relevant to the broader QSTH architecture while keeping it in its proper atlas role. The same idea is developed more explicitly in the resonance appendix, where AQA-M1 to AQA-M4 are framed as the modulation core of the branch. Within the series logic, AQA should be read as the representational companion to the main condensation branch:QSTH 7.6 provides the classificatory atlas,QSTH 7.7 isolates the closure problem,QSTH 7.8 studies dimensional settlement and gravitational imprint,QSTH 7.9 studies cadence, phase, and the Planckian interface,and QSTH 7.10 provides the final CORE synthesis.AQA does not compete with these texts; it complements them by showing that some regimes may become readable only in the correct representational frame. This representational role is also stated directly in the AQA core text, where the atlas branch is positioned beside, rather than against, the mechanical publications. Relation to companion textsAQA belongs to the later QSTH 7.x condensation landscape as its atlas and signature branch. It should be read together with the main mechanistic line, but not merged into it. The practical discipline remains strict: diagrammatic and acoustic material must not overload the CORE closure texts. This separation is reinforced by the final curatorial split between Appendix A as the disciplined closure/signature atlas and Appendix B as the modulation and resonance note-space. Recommended earlier QSTH recordsQSTH 7.3 — The Condensation of Structure: Dset Deep Layer: From Interface to Manifest Form — DOI: 10.5281/zenodo.19577809QSTH 7.4 — The Condensation of Structure: Regime Settlement and Interface Readout — DOI: 10.5281/zenodo.19578286QSTH 7.5 — The Condensation of Structure: Locking, Resonance and Dimensional Settlement — DOI: 10.5281/zenodo.19580993QSTH 7.6 — The Condensation of Structure: Mendeleev Table III — DOI: 10.5281/zenodo.19651901QSTH 7.7 — The Condensation of Structure: The Missing Closure — DOI: 10.5281/zenodo.19652099QSTH 7.8 — The Condensation of Structure: Dimensional Settlement and Gravitational Imprint — DOI: 10.5281/zenodo.19652233QSTH 7.9 — The Condensation of Structure: Phase, Cadence and the Planckian Interface — DOI: 10.5281/zenodo.19652410QSTH 7.10 — The Condensation of Structure: CORE Synthesis — DOI: 10.5281/zenodo.19652964 Recommended companion / supporting records• QSTH — Information Ledger• later: QSTH 8.0 — Galoisův Ledger Appendix A — Diagram AtlasAppendix A serves as the curated Diagram Atlas of the AQA branch. Its purpose is not to become a warehouse of every possible figure, but to hold only those diagrams that directly reinforce the readability of the closure problem, the threshold landscape, hysteresis, boundary reading, and the nearest dynamic signatures that still support the mechanical core. The appendix explicitly retains only the disciplined closure/signature family A1–A5, B1–B4, and C1–C2. Appendix B — Resonance NotesAppendix B exists because part of the AQA material no longer functions merely as support for the closure problem. It opens a more specific branch: resonance as a shaping factor of transition, lag between layers, return after collapse, modulation of settlement windows, and atlas navigation across regime families. Its core is the AQA-M set, where resonance begins to act not only as protection but as candidate selective shaping of transition paths. Appendix C — Back Doors of the Horizon IAppendix C proposes that a horizon need not be read only as an impenetrable wall, but also as a selective interface through which indirect forms of boundary readout, echo-like response, resonant admissibility, and entropic timing may become meaningful within the wider AQA architecture. Its editorial status remains SUPPORT / CAND, making it strong enough to preserve but still distinct from the main mechanical core. Final working statementQSTH AQA does not replace the mechanics of condensation. It gives that mechanics a second language: a language of readout, atlas clarity, signature families, and later modulation. Its real achievement is architectural: it turns a scattered support branch into a publishable and disciplined atlas of transition regimes. This final characterization closely matches the closing statement of the AQA core publication itself.

•Apr 19, 2026•0 citations

Quantum Structural Theory of Harmony (QSTH M.1B) — Operational Definitions of Structural Objects: Configuration Domain, Equivalence, Effective Entropy and the Limits of Independent Classification

Rostislav Stepanik

Description QSTH M.1B is the operational continuation of QSTH M.1A, Genealogy of Alpha-I-Dim and Equations E1–E10. M.1A established the algebraic genealogy of the reference Alpha-I-Dim construction and identified effective entropy S_eff and the structural parameter κ(Γ) as imported quantities whose physical meaning could not be supplied by algebra alone. M.1B addresses that open requirement by constructing a first explicit finite operational framework for structural configurations, equivalence, representation, statistical measure, dynamics, entropy and independent classification. The study defines typed relational configurations with a decidable admissibility predicate and equivalence under relabelling; constructs a faithful incidence representation; distinguishes representational equivalence, physical equivalence and indistinguishability under a limited readout; and states the conditions under which deterministic and probabilistic dynamics descend consistently to configuration classes. A finite operational statistical entropy is then constructed from a prespecified state space, measure and readout. Independently, a dynamical classifier based on closed recurrent sectors is introduced, together with an audit of exact charge protection versus finite escape time. The central integration result is deliberately restrictive. The independently defined sector count is not a universal entropic coefficient for Equation E10. The same entropy may coexist with different sector structures, while genuine internal degrees of freedom may increase entropy without creating an additional recurrent sector. The independent test is therefore allowed to reject the proposed identification rather than being normalized to reproduce it. Accordingly, the formal mathematical and statistical stage B1-B7 is complete within its declared domain, while physical horizon identification, M-independence and the continuation to E11+ remain open. This publication does not claim a new universal constant, a microscopic theory of horizon entropy, or empirical confirmation of QSTH. Its contribution is an auditable operational framework, explicit counterexamples, reproducible finite tests, and a precise boundary between mathematical construction and physical identification. A separate companion study, QSTH M.1B-SR1, examines whether a richer spectral response can provide a conditional bridge between an independently defined observable and the thermal entropy of specified interface carriers.

•Oct 3, 2026•0 citations
QSTH Verification Note – Time-Mirror Experiments as Probes of Entropic Coherence This verification note proposes a concrete experimental roadmap for testing whether “time-mirror” phenomena can serve as operational probes of entropic coherence in quantum and wave systems. Time-mirror setups use a sudden temporal modulation of the medium (e.g. a fast change of refractive index or permittivity) to produce a time-reversed echo of an incoming wave. Here, this effect is re-cast in terms of an entropic balance between coherent and reductive entropy, ΔS_coh and ΔS_red, and its impact on an effective curvature parameter Λ_eff. The document formulates three testable hypotheses: (H1) that a sufficiently sharp temporal modulation generates a measurable time-reversed, phase-conjugated component of the input signal; (H2) that the associated echo corresponds to a local decrease of spectral entropy and an increase of mutual information between input and echo (a transient approach to “entropic coherence”); and (H3) that the strength and structure of the echo scale in a predictable way with the modulation gradient and inhomogeneity, providing an operational proxy for Λ_eff. For each hypothesis, the note specifies measurable quantities (reflection coefficient in time, coherence functions g^(1), g^(2), information-theoretic metrics, phase curvature) and clear falsification criteria. Two main experimental platforms are outlined: an optical implementation using ultrafast electro-optic or pump–probe modulation of the refractive index, and a microwave / acoustic implementation using rapidly tunable media. The note includes a step-by-step protocol (calibration, control runs, modulation sweeps, data analysis) designed to distinguish genuine time-mirror echoes from trivial reflections or nonlinear artefacts. Relation to QSTH. In the context of the Quantum Structural Theory of Harmony (QSTH), time-mirror experiments offer a way to translate the abstract balance Seff=ΔScoh−ΔSredS_\mathrm{eff} = \Delta S_\text{coh} - \Delta S_\text{red}Seff=ΔScoh−ΔSred and the Bridge Λ_eff ↔ S_eff into laboratory observables. A successful detection of entropically enhanced time-reversed echoes would support the view that spacetime dynamics and information flow share a common entropic structure, while a null result would provide valuable constraints on the QSTH framework Related QSTH Zenodo records (recommended entry points) QSTH 1.0 — Foundational Publication — DOI: 10.5281/zenodo.17455814QSTH 1.0 — Horizon Set — DOI: 10.5281/zenodo.18015679QSTH 4.1 — Planckian Horizon 2.0: The Entropic Bridge between Quantum and Cosmological Reality — DOI: 10.5281/zenodo.17899867QSTH 5.2 — OMEG: The Operational Metric Plane of Entropic Geometrodynamics — DOI: 10.5281/zenodo.17937840QSTH 6.0 — The Info-Dim (I-Dim) Package — DOI: 10.5281/zenodo.18156387QSTH 6.1 — Entropic Zero (E0) & Entropic Stars — DOI: 10.5281/zenodo.18165254QSTH 6.2 — Vacuum as an Entropic Ledger and the Origin of Baryon Asymmetry — DOI: 10.5281/zenodo.18641674QSTH 6.3 — Ledger Reality Reconstruction: I-Dim Mediation, DM/DE, and Arrow-of-Time Diagnostics (with the Eddington Paradox) — DOI: 10.5281/zenodo.18646924QSTH 6.4 — QSTH vs. Feynman Diagrams — DOI: 10.5281/zenodo.18648120QSTH 6.5 — Planckian Horizon 2.0 as a Ledger Boundary — DOI: 10.5281/zenodo.18649631QSTH 6.6 — Planckian Horizon 2.0 as an Operational Entropic-Coherence Principle — DOI: 10.5281/zenodo.18701036QSTH 6.7 — Variational Entropic Lagrangian (R10) — DOI: 10.5281/zenodo.18715255QSTH 6.8 — Mendeleev Table of Relationships among Physical Constants — DOI: 10.5281/zenodo.18762028QSTH 6.9 — I-Dim Elementary Coupling and Semi-I-Dim Classification of the Fine Structure Constant α ≈ 1/137 — DOI: 10.5281/zenodo.18864069QSTH 6.10 — The Fifth Dimension as an Account: A Ledger Formulation in (3+1)D — DOI: 10.5281/zenodo.18871791QSTH 6.11 — The Galois Ledger: Horizon Projection Π : Ω → 𝓛, Gauge Redundancy G, and Operational Invariants S/T/J — DOI: 10.5281/zenodo.18879079QSTH 6.12 — The Emergence of Dimensions as an Entropic Reconstruction — DOI: 10.5281/zenodo.18899448
Quantum Structural Theory of Harmony (QSTH) 5.0 – The Entropic Clock (TiM) introduces a structural notion of time defined by the balance and flow of entropy and information between coherent order and reductive noise. The work proposes an operational entropic time coordinate TE(t) together with an Entropic Clock parameter TiM(t) that can be read in two consistent ways: (i) as a dimensionless clock index N°_QSTH(t) (a metronomic tick-rate), and (ii) as the rate of entropic time dTE/dt (a structural time-flow speed). The two views are linked by a calibration factor and share the same underlying driver: the coherence–reduction balance encoded in the QSTH ledger. Within the QSTH framework, the effective state of reality is tracked by the entropic ledger variable Seff = ΔScoh − ΔSred. The instantaneous coherence ratio is R(t) = ΔScoh / ΔSred, and the entropic frequency is ωE(t) = d/dt[ ln R(t) ]. Operationally, QSTH 5.0 treats the entropic clock as a measurable structural parameter controlled by R(t) and an effective entropic curvature/impedance term Λeff(t), with experimental/observational proxies discussed for interferometric visibility, spectral broadening, and field-gradient environments. The bundle includes two appendices extending the core thesis: Appendix A (G-Gate) formulates open operational mechanisms (operator/selector/metronome) as selection thresholds governing when entropic channels become physically active; Appendix B (Quantum Tunneling & TiM) connects tunneling, barrier crossing and apparent superluminality to entropic channel activation without violating causality. Together, the three documents form a compact, test-oriented QSTH 5.0 layer designed as a readable bridge between conceptual structure and experimental/observational windows. We propose extending the typology of Entropic Stars with an ER-type (Embedded-Relic Entropic Star): a star hosting an embedded compact relic (e.g., a primordial black hole) that acts as a long-lived internal entropy driver (sink/source) and can redirect the star’s evolutionary track. In such a scenario, the star may appear evolutionarily “odd” (e.g., unusually cool/extended for its population) because internal accretion feedback modifies energy transport and radiative balance. Crucially, this is not a test-free speculation: models of “PBH-in-stars / Hawking stars” motivate asteroseismology/pulsation signatures as a way to distinguish an embedded relic from standard astrophysical explanations of anomalous stars. In our framework, ER-type is presented as an archetype—latent internal sink/source → measurable macroscopic deviation—as a complement to EO-type and the general ES-type, without making a claim about dark matter. TiM is reported as the dimensionless index N°_QSTH and, under fixed calibration, equivalently as the entropic time-rate dTE/dt. Related QSTH Zenodo records (recommended entry points) QSTH 1.0 — Foundational Publication — DOI: 10.5281/zenodo.17455814QSTH 1.0 — Horizon Set — DOI: 10.5281/zenodo.18015679QSTH 4.1 — Planckian Horizon 2.0: The Entropic Bridge between Quantum and Cosmological Reality — DOI: 10.5281/zenodo.17899867QSTH 5.2 — OMEG: The Operational Metric Plane of Entropic Geometrodynamics — DOI: 10.5281/zenodo.17937840QSTH 6.0 — The Info-Dim (I-Dim) Package — DOI: 10.5281/zenodo.18156387QSTH 6.1 — Entropic Zero (E0) & Entropic Stars — DOI: 10.5281/zenodo.18165254QSTH 6.2 — Vacuum as an Entropic Ledger and the Origin of Baryon Asymmetry — DOI: 10.5281/zenodo.18641674QSTH 6.3 — Ledger Reality Reconstruction: I-Dim Mediation, DM/DE, and Arrow-of-Time Diagnostics (with the Eddington Paradox) — DOI: 10.5281/zenodo.18646924QSTH 6.4 — QSTH vs. Feynman Diagrams — DOI: 10.5281/zenodo.18648120QSTH 6.5 — Planckian Horizon 2.0 as a Ledger Boundary — DOI: 10.5281/zenodo.18649631QSTH 6.6 — Planckian Horizon 2.0 as an Operational Entropic-Coherence Principle — DOI: 10.5281/zenodo.18701036QSTH 6.7 — Variational Entropic Lagrangian (R10) — DOI: 10.5281/zenodo.18715255QSTH 6.8 — Mendeleev Table of Relationships among Physical Constants — DOI: 10.5281/zenodo.18762028QSTH 6.9 — I-Dim Elementary Coupling and Semi-I-Dim Classification of the Fine Structure Constant α ≈ 1/137 — DOI: 10.5281/zenodo.18864069QSTH 6.10 — The Fifth Dimension as an Account: A Ledger Formulation in (3+1)D — DOI: 10.5281/zenodo.18871791QSTH 6.11 — The Galois Ledger: Horizon Projection Π : Ω → 𝓛, Gauge Redundancy G, and Operational Invariants S/T/J — DOI: 10.5281/zenodo.18879079QSTH 6.12 — The Emergence of Dimensions as an Entropic Reconstruction — DOI: 10.5281/zenodo.18899448
Description / Abstract QSTH 5.0 Revised — The Entropic Clock Revisited examines whether the readable ordering of physical change can be represented through an entropic-informational description of temporal readability. Rather than introducing a new physical time coordinate, the work develops the Temporal Information Metric (TiM) as a candidate measure of how changes in informational organization become readable as ordered records. The publication builds directly on the Born-readout architecture of the QSTH Revised Trilogy. Starting from the standard quantum-mechanical probability readout P = |ψ|² and its informational representation ΔS_coh = −ln|ψ|², it considers an effective informational balance between coherent and reductive contributions, S_eff ~ (ΔS_coh − ΔS_red), and investigates whether changes in this balance can provide an auditable description of temporal readability, persistence, record formation, and settlement. The central distinction is between physical time and readable temporal structure. QSTH 5.0 Revised does not propose that TiM replaces physical time, general relativity, or standard quantum mechanics. Instead, TiM is treated as a candidate informational descriptor asking when physical change becomes sufficiently persistent and organized to support a distinguishable ordering of “before” and “after.” Within this framework, readable temporal flow is associated not with isolated events alone but with the persistence and organization of records. The resulting conceptual architecture is: Born → ΔS_coh → S_eff → TiM → Settlement → Record → E₀. The work therefore provides the second pillar of the QSTH Revised Trilogy: Probability → Readability → Settlement, connecting the Born Readout Ledger developed in QSTH 6.0 Revised with the subsequent treatment of settlement and Entropic Zero in QSTH 6.1 Revised. All proposed quantities and interpretations are presented as components of an auditable informational model, not as experimentally established new physical laws. Additional description / Notes Part II of the QSTH Revised Trilogy: Probability → Readability → Settlement. QSTH 5.0 Revised develops the temporal-readability layer of the trilogy and connects QSTH 6.0 Revised — Born Set Invariants with QSTH 6.1 Revised — Entropic Zero Revisited. Its central question is: How does informational readability become history?
This QSTH 8.11 working publication develops the Entropic Genesis of Photon as a candidate interpretive bridge between coherent possibility, entropic transition, record formation, and the emergence of a minimal transferable carrier of electromagnetic interaction. The publication follows the broader QSTH 8.x condensation sequence, especially QSTH 8.7 — Lambda_lock Technical Note, QSTH 8.8.S — Spin-Locking and Structural Orientation, QSTH 8.9.XS2 — Schrödinger Equation with QSTH Locking Term, and QSTH 8.10.H — Hessian Geometry of Record Settlement. QSTH 8.11 asks the next physical question: If possibility can become a stable record, what is one of the most elementary transferable carriers of such record-like interaction? Within this framework, the photon is not presented as a replacement for the standard quantum-electrodynamic description. Instead, QSTH proposes a candidate interpretive layer in which the photon may be read as a minimal transferable record of electromagnetic interaction: a carrier of energy, momentum, phase, polarization, and readable interaction structure. A central QSTH reading is: Photon = minimal transferable electromagnetic record The publication connects this interpretation to the candidate QSTH distinction between coherent entropy and reductive entropy: Delta S_eff ~ Delta S_coh - Delta S_red where Delta S_coh represents a candidate coherence-preserving contribution and Delta S_red represents a candidate reductive / settlement contribution. These terms are not presented as confirmed thermodynamic state functions, but as candidate bookkeeping variables for future formalization. The text also places the photon in contrast with the Higgs / entropic weight motif. In this contrast, the photon represents a near-massless transferable coherence carrier, while the Higgs-related branch represents the question of how a state acquires structural weight, mass-related settlement, and entropic cost. QSTH 8.11 v1.2 also includes a Spin Audit Bridge. This bridge connects photon-level record transfer with the prior QSTH spin-locking line. In this reading, photon polarization and helicity are not treated as proof of QSTH, but as physically meaningful orientation channels through which the broader QSTH question of spin, directionality, and record readability may be cautiously connected to known physics. A safe candidate relation is: Gamma_lock = Gamma_0 + Gamma_spin + Gamma_wall + Gamma_entropy where Gamma_spin represents a provisional spin-orientation contribution to the broader candidate locking functional. The publication also keeps a strict methodological boundary. QSTH 8.11 does not claim to derive the photon from first principles, replace quantum electrodynamics, or prove a new physical law. It proposes a structured candidate interpretation intended for future formalization, toy-model testing, falsification, and comparison with standard null models. Short description QSTH 8.11 proposes the photon as a candidate minimal transferable record of electromagnetic interaction. It connects photon-level transfer with coherent entropy, reductive entropy, Lambda_lock, spin-locking, Hessian settlement, Higgs contrast, and the broader QSTH 8.x condensation sequence. Methodological status This publication is part of the QSTH CORE/CAND/SUPPORT/FUTURE framework. It should be read as a structured working publication, not as a confirmed physical model. The photon is treated according to standard physics as a quantum of the electromagnetic field. QSTH adds only a candidate interpretive layer: the photon may be read as a minimal transferable record of electromagnetic interaction. This interpretive layer remains CAND / SUPPORT / FUTURE FORMALIZATION. Computability note Several parts of the proposed framework may become suitable for future toy-model exploration. Candidate variables such as Delta S_coh, Delta S_red, Gamma_lock, Gamma_spin, and H_eff can be studied in simplified models once operational definitions are fixed. At the present stage, QSTH 8.11 does not claim empirical confirmation. It identifies candidate modeling entry points and clarifies which claims remain interpretive, which are connected to known physics, and which require future mathematical or experimental development. Safe Zenodo equation block Photon = minimal transferable electromagnetic record Delta S_eff ~ Delta S_coh - Delta S_red Gamma_lock = Gamma_0 + Gamma_spin + Gamma_wall + Gamma_entropy integral Gamma_lock(t) dt >= Lambda_lock -> R_stable H_eff = nabla^2 Phi_lock These expressions are not presented as confirmed physical laws. They are candidate modeling relations and interpretive bridges intended for future formalization, toy-model construction, numerical testing, falsification, and comparison with null models. Diamond sentence The photon is not treated here as proof of QSTH. It is treated as a luminous candidate bridge: a minimal transferable record through which coherence, interaction, orientation, and readable structure may meet. Notes field This record belongs to the QSTH 8.x publication sequence. It follows QSTH 8.7 — Lambda_lock Technical Note, QSTH 8.8.S — Spin-Locking and Structural Orientation, QSTH 8.9.XS2 — Schrödinger Equation with QSTH Locking Term, and QSTH 8.10.H — Hessian Geometry of Record Settlement. QSTH 8.11 provides the photon-level bridge of the 8.x sequence. After possibility, locking, spin orientation, and Hessian settlement have been introduced, this publication asks how a minimal electromagnetic carrier may be interpreted as a transferable record. The publication also prepares the later QSTH 8.XC Closure Note and the future M-independent horizon framework, where the question shifts from local record formation toward horizon-scale ledger closure.
QSTH 6.0 Revised — Born Set Invariants returns to the foundational role of the Born rule within the broader architecture of the Quantum Structural Theory of Harmony (QSTH). Rather than treating the Born rule solely as a probabilistic output of quantum measurement, the work examines its informational representation and its possible role as a bridge between quantum amplitude, effective entropic balance, record formation, and informational admissibility. The central observation is that the Born readout can be mapped into an informational representation through the relation ΔS_coh = −ln|ψ|². This provides a direct bridge between the standard quantum-mechanical probability readout and the later QSTH ledger quantities, including S_eff, TiM, Settlement Dynamics, and Entropic Zero. The publication introduces Born Set Invariants as a candidate class of informational quantities, relations, or structures whose meaning may survive admissible changes of representation, projection, or system readout. It further distinguishes probability from admissibility, asking whether a non-zero probability is sufficient for the formation of a stable physical record. Within this framework, S_eff is developed as an informational ledger between coherent and reductive contributions, while Ψ and κ(Γ) are retained respectively as candidate regime-signature and regime-sensitivity descriptors. These quantities are not proposed as new forces or fundamental constants. QSTH 6.0 Revised does not modify or replace the Born rule and does not propose a new quantum mechanics. The Born rule remains a CANON experimental and mathematical anchor. The purpose of the work is instead to construct a disciplined and auditable informational language linking probability → information → ledger → invariance → admissibility → regime. The publication forms the first pillar of the QSTH Revised Trilogy and provides the informational entry point for the subsequent treatment of temporal readability, settlement, and Entropic Zero. Part I of the QSTH Revised Trilogy: Probability → Readability → Settlement. QSTH 6.0 Revised establishes the Born Readout Ledger and provides the informational foundation for QSTH 5.0 Revised — The Entropic Clock Revisited and QSTH 6.1 Revised — Entropic Zero Revisited.
QSTH AQA is the atlas branch of the later QSTH condensation series. Its role is not to replace the CORE mechanistic publications of QSTH 7.6–7.10, but to provide a dedicated readout space for regime signatures that become clearer in mathematical, visual, and acoustic representation. In this sense, AQA functions as a companion atlas to the condensation architecture rather than as a separate ontology. The branch is structured around three complementary layers:AQA-R — Readout Atlas,AQA-A — Annotated Atlas,AQA-M — Modulation Atlas. Together, these layers examine whether transition regimes can carry not only structural and mathematical signatures, but also identifiable visual and acoustic patterns. The atlas therefore supports the wider QSTH line by tracking settlement, coherence, decoherence, interface memory, lock threshold, horizon echo, ΔS_coh vs. ΔS_red, collapse–revival, asymmetric locking/unlocking, settlement maps, Φ1–Φ2 lag, boundary memory, and rewritten output. This aligns with the AQA publication’s role as an independent atlas home for diagrammatic, acoustic, and modulation-oriented materials around the mechanical line of QSTH 7.6–7.10. A particularly important result of the modulation line is the working conclusion that resonance may be not only diagnostic but also path-shaping: it may alter the path by which a regime settles, including delay, post-collapse return, and the width of the settlement window. This makes AQA methodologically relevant to the broader QSTH architecture while keeping it in its proper atlas role. The same idea is developed more explicitly in the resonance appendix, where AQA-M1 to AQA-M4 are framed as the modulation core of the branch. Within the series logic, AQA should be read as the representational companion to the main condensation branch:QSTH 7.6 provides the classificatory atlas,QSTH 7.7 isolates the closure problem,QSTH 7.8 studies dimensional settlement and gravitational imprint,QSTH 7.9 studies cadence, phase, and the Planckian interface,and QSTH 7.10 provides the final CORE synthesis.AQA does not compete with these texts; it complements them by showing that some regimes may become readable only in the correct representational frame. This representational role is also stated directly in the AQA core text, where the atlas branch is positioned beside, rather than against, the mechanical publications. Relation to companion textsAQA belongs to the later QSTH 7.x condensation landscape as its atlas and signature branch. It should be read together with the main mechanistic line, but not merged into it. The practical discipline remains strict: diagrammatic and acoustic material must not overload the CORE closure texts. This separation is reinforced by the final curatorial split between Appendix A as the disciplined closure/signature atlas and Appendix B as the modulation and resonance note-space. Recommended earlier QSTH recordsQSTH 7.3 — The Condensation of Structure: Dset Deep Layer: From Interface to Manifest Form — DOI: 10.5281/zenodo.19577809QSTH 7.4 — The Condensation of Structure: Regime Settlement and Interface Readout — DOI: 10.5281/zenodo.19578286QSTH 7.5 — The Condensation of Structure: Locking, Resonance and Dimensional Settlement — DOI: 10.5281/zenodo.19580993QSTH 7.6 — The Condensation of Structure: Mendeleev Table III — DOI: 10.5281/zenodo.19651901QSTH 7.7 — The Condensation of Structure: The Missing Closure — DOI: 10.5281/zenodo.19652099QSTH 7.8 — The Condensation of Structure: Dimensional Settlement and Gravitational Imprint — DOI: 10.5281/zenodo.19652233QSTH 7.9 — The Condensation of Structure: Phase, Cadence and the Planckian Interface — DOI: 10.5281/zenodo.19652410QSTH 7.10 — The Condensation of Structure: CORE Synthesis — DOI: 10.5281/zenodo.19652964 Recommended companion / supporting records• QSTH — Information Ledger• later: QSTH 8.0 — Galoisův Ledger Appendix A — Diagram AtlasAppendix A serves as the curated Diagram Atlas of the AQA branch. Its purpose is not to become a warehouse of every possible figure, but to hold only those diagrams that directly reinforce the readability of the closure problem, the threshold landscape, hysteresis, boundary reading, and the nearest dynamic signatures that still support the mechanical core. The appendix explicitly retains only the disciplined closure/signature family A1–A5, B1–B4, and C1–C2. Appendix B — Resonance NotesAppendix B exists because part of the AQA material no longer functions merely as support for the closure problem. It opens a more specific branch: resonance as a shaping factor of transition, lag between layers, return after collapse, modulation of settlement windows, and atlas navigation across regime families. Its core is the AQA-M set, where resonance begins to act not only as protection but as candidate selective shaping of transition paths. Appendix C — Back Doors of the Horizon IAppendix C proposes that a horizon need not be read only as an impenetrable wall, but also as a selective interface through which indirect forms of boundary readout, echo-like response, resonant admissibility, and entropic timing may become meaningful within the wider AQA architecture. Its editorial status remains SUPPORT / CAND, making it strong enough to preserve but still distinct from the main mechanical core. Final working statementQSTH AQA does not replace the mechanics of condensation. It gives that mechanics a second language: a language of readout, atlas clarity, signature families, and later modulation. Its real achievement is architectural: it turns a scattered support branch into a publishable and disciplined atlas of transition regimes. This final characterization closely matches the closing statement of the AQA core publication itself.
Description QSTH M.1B is the operational continuation of QSTH M.1A, Genealogy of Alpha-I-Dim and Equations E1–E10. M.1A established the algebraic genealogy of the reference Alpha-I-Dim construction and identified effective entropy S_eff and the structural parameter κ(Γ) as imported quantities whose physical meaning could not be supplied by algebra alone. M.1B addresses that open requirement by constructing a first explicit finite operational framework for structural configurations, equivalence, representation, statistical measure, dynamics, entropy and independent classification. The study defines typed relational configurations with a decidable admissibility predicate and equivalence under relabelling; constructs a faithful incidence representation; distinguishes representational equivalence, physical equivalence and indistinguishability under a limited readout; and states the conditions under which deterministic and probabilistic dynamics descend consistently to configuration classes. A finite operational statistical entropy is then constructed from a prespecified state space, measure and readout. Independently, a dynamical classifier based on closed recurrent sectors is introduced, together with an audit of exact charge protection versus finite escape time. The central integration result is deliberately restrictive. The independently defined sector count is not a universal entropic coefficient for Equation E10. The same entropy may coexist with different sector structures, while genuine internal degrees of freedom may increase entropy without creating an additional recurrent sector. The independent test is therefore allowed to reject the proposed identification rather than being normalized to reproduce it. Accordingly, the formal mathematical and statistical stage B1-B7 is complete within its declared domain, while physical horizon identification, M-independence and the continuation to E11+ remain open. This publication does not claim a new universal constant, a microscopic theory of horizon entropy, or empirical confirmation of QSTH. Its contribution is an auditable operational framework, explicit counterexamples, reproducible finite tests, and a precise boundary between mathematical construction and physical identification. A separate companion study, QSTH M.1B-SR1, examines whether a richer spectral response can provide a conditional bridge between an independently defined observable and the thermal entropy of specified interface carriers.