What question did this study set out to answer?

This work aims to provide a new framework connecting geometry and information through the Planckian Horizon as an interface rule.

February 17, 2026Open Access

Quantum Structural Theory of Harmony (QSTH 6.5) – Planckian Horizon 2.0 as a Ledger Boundary: Horizon Ledger Closure, Time-Rate Control, and the "Interstellar Paradox" as an Operational Model

Key Points

This work aims to provide a new framework connecting geometry and information through the Planckian Horizon as an interface rule.
Introduced a pilot parameter to quantify local time-rate response to ledger balance.
Developed a falsifiable audit-ready rule for testing with precise timing and horizon systems.
Used a clean operational reading of time dilation connected to observable facts.
Proposed a linkage between general relativity and ledger-like balance, highlighting the role of coherent information.
Identified potential outcomes where α_interface could equal zero, validating or invalidating the model against gravity principles.

Abstract

QSTH 6. 5 — Planckian Horizon 2. 0 as a Ledger BoundaryHorizon Ledger Closure, Time-Rate Control, and the “Interstellar Paradox” as an Operational Model This release (QSTH 6. 5) is a one-file CORE paper within the operational QSTH 6. x series. It reframes the popular “Interstellar paradox” (extreme gravitational time dilation + the idea of a missing “equation of gravity”) as a real methodological gap: not a mystical formula, but a missing interface rule connecting geometry (GR) with information/entropy closure (what becomes an observable fact). In QSTH terminology, that interface is Planckian Horizon 2. 0 (PH 2. 0 / Φ₁–Φ₂), treated as an effective boundary where coherent, structured information (ΔScoh) is converted into reductive/irreversible entropy (ΔSᵣed) and closed into observational statistics. The key operational object is the ledger balanceB ≡ ΔScoh − ΔSᵣed, and the paper proposes a minimal pilot parameter αᵢnterface that quantifies how strongly the local time-rate (dt/dτ) responds to this balance at the interface. Importantly, QSTH 6. 5 does not claim time travel or violations of causality. It proposes a falsifiable, audit-ready “bridge rule” that can be tested progressively with precision timing, horizon systems, and (where meaningful) laboratory analogs. The model is intentionally lightweight: it aims to produce publishable constraints even under null outcomes. What this release offers researchers (practical value) A clean operational reading of “time dilation + horizon physics” as an accounting/closure problem, not a narrative paradox. A minimal vocabulary and pilot ansatz linking GR baseline time dilation with a ledger-dependent residual: αᵢnterface as an estimable interface-transparency parameter. A compact falsification map: if no correlation exists, αᵢnterface → 0, and the model collapses back to pure GR (negative test). Direct continuity with the QSTH 6. 0–6. 4 operational sequence (ledger closure, I-Dim mediation, demarcation between coherent computation and closed observables). Suggested relations This work is intended as a methodological companion to the operational program, and can be linked in Zenodo metadata as “is supplement to” QSTH 6. 3, and “is related to” QSTH 6. 4 (demarcation layer). Archive note: Foundational releases QSTH 0–QSTH 4. 0 are archived and published on OSF; the operational QSTH 6. x series is released on Zenodo.

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