Exclusion Theorems from Finite Accessibility - Seven Rigorous No-Go Results

Papers I–III derived specific physical structures from three operational axioms: an action gap, finite accessibility, and intersubjective stability. This paper inverts the question: what structures are forbidden? Seven exclusion theorems are proved, showing that large classes of alternative physics are inadmissible under the operational axioms. Each theorem includes explicit assumptions and rigorous mathematical proof. The excluded structures are: 1. **Arbitrarily precise extended synchronisation** — no protocol can certify synchronisation across a domain exceeding the coherence radius R_coh 2. **Higher-than-second-order local dynamics** — via Ostrogradsky instability and certification cost arguments 3. **Non-Born probability assignments** — via the Cauchy functional equation; the Born rule is the unique continuous, non-contextual invariant measure 4. **Non-three-dimensional geometry** — via flux invariance; only d = 3 permits radius-independent total distinguishability 5. **Non-quartic high-frequency dispersion** — via complex analysis of the EFT derivative expansion 6. **Stable relativistic gravitationally-coupled matter** above the accessibility ceiling 7. **Protocol-dependent physical constants** — universality is forced by intersubjective stability The exclusions collectively define an admissibility corridor: the narrow set of physical structures compatible with bounded intersubjective certification. The paper shows that most logically possible alternatives violate the axioms, and that observed physics lies on structural boundaries of the corridor. **This paper is part of the Finite Accessibility series, which reconstructs gravitational geometry, quantum dynamics, gauge structure, cosmological perturbation theory, and the dark sector from a single operational primitive: a finite certification ceiling ω* governing the maximum rate at which physical relations can be maintained across extended domains.** **Introductory papers** - Geometric Limits to Coherent Timekeeping in Extended Reference Frames — https://doi.org/10.5281/zenodo.18824556 - Accessibility Selection Law (ASL) — https://doi.org/10.5281/zenodo.18824649 - Phase Boundary Gravity — https://doi.org/10.5281/zenodo.18824707 **Pillars (numbered I–IV)** - Paper I: Deriving Gravitational Geometry and Schrödinger Dynamics from Finite Accessibility — https://doi.org/10.5281/zenodo.18601600 - Paper II: Deriving Inertia, Motion, and Wave Propagation from Finite Accessibility — https://doi.org/10.5281/zenodo.18625174 - Paper III: Accessible State Spaces, Record Stability, and the Emergence of Quantum Statistics — https://doi.org/10.5281/zenodo.18625192 - Paper IV: Frame Dissolution, the Certification Ceiling, and Observable Deformations — https://doi.org/10.5281/zenodo.18654458 **Extension papers** - Dark Matter from Finite Accessibility — https://doi.org/10.5281/zenodo.18654433 - Dark Energy from Finite Accessibility — https://doi.org/10.5281/zenodo.18654523 - No-Go Theorems and the Admissibility Corridor — https://doi.org/10.5281/zenodo.18654493 - Gauge Structure from Finite Accessibility — https://doi.org/10.5281/zenodo.18928152 - Perturbation Theory from Finite Accessibility — https://doi.org/10.5281/zenodo.18928213 **Experimental paper** - Experimental Probes of Finite Accessibility: GW Dispersion and Vacuum Path Independence — https://doi.org/10.5281/zenodo.18931126 **Keywords:** no-go theorems, admissibility corridor, finite accessibility, exclusion theorems, Born rule uniqueness, spatial dimensionality, Ostrogradsky instability, higher-order dynamics, extended synchronisation, intersubjective stability, certification cost, dispersion constraints, protocol invariance, operational axioms, action gap, quantum gravity constraints