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

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

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 (ΔS_coh) is converted into reductive/irreversible entropy (ΔS_red) and closed into observational statistics. The key operational object is the ledger balance
B ≡ ΔS_coh − ΔS_red,
and the paper proposes a minimal pilot parameter α_interface 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: α_interface as an estimable interface-transparency parameter.

• A compact falsification map: if no correlation exists, α_interface → 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.

Related QSTH Zenodo records (recommended entry points)

QSTH 1.0 — Foundational Publication — DOI: 10.5281/zenodo.17455814
QSTH 1.0 — Horizon Set — DOI: 10.5281/zenodo.18015679
QSTH 4.1 — Planckian Horizon 2.0: The Entropic Bridge between Quantum and Cosmological Reality — DOI: 10.5281/zenodo.17899867
QSTH 5.2 — OMEG: The Operational Metric Plane of Entropic Geometrodynamics — DOI: 10.5281/zenodo.17937840
QSTH 6.0 — The Info-Dim (I-Dim) Package — DOI: 10.5281/zenodo.18156387
QSTH 6.1 — Entropic Zero (E0) & Entropic Stars — DOI: 10.5281/zenodo.18165254
QSTH 6.2 — Vacuum as an Entropic Ledger and the Origin of Baryon Asymmetry — DOI: 10.5281/zenodo.18641674
QSTH 6.3 — Ledger Reality Reconstruction: I-Dim Mediation, DM/DE, and Arrow-of-Time Diagnostics (with the Eddington Paradox) — DOI: 10.5281/zenodo.18646924
QSTH 6.4 — QSTH vs. Feynman Diagrams — DOI: 10.5281/zenodo.18648120
QSTH 6.5 — Planckian Horizon 2.0 as a Ledger Boundary — DOI: 10.5281/zenodo.18649631
QSTH 6.6 — Planckian Horizon 2.0 as an Operational Entropic-Coherence Principle — DOI: 10.5281/zenodo.18701036
QSTH 6.7 — Variational Entropic Lagrangian (R10) — DOI: 10.5281/zenodo.18715255
QSTH 6.8 — Mendeleev Table of Relationships among Physical Constants — DOI: 10.5281/zenodo.18762028
QSTH 6.9 — I-Dim Elementary Coupling and Semi-I-Dim Classification of the Fine Structure Constant α ≈ 1/137 — DOI: 10.5281/zenodo.18864069
QSTH 6.10 — The Fifth Dimension as an Account: A Ledger Formulation in (3+1)D — DOI: 10.5281/zenodo.18871791
QSTH 6.11 — The Galois Ledger: Horizon Projection Π : Ω → 𝓛, Gauge Redundancy G, and Operational Invariants S/T/J — DOI: 10.5281/zenodo.18879079
QSTH 6.12 — The Emergence of Dimensions as an Entropic Reconstruction — DOI: 10.5281/zenodo.18899448