Paper WR v1.0: Geometric Optics Without Metric — Write Resistance and Photon Paths in Ontological Resolution Theory
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2026
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| author | Kapitanov, Fedor |
| author_facet | Kapitanov, Fedor |
| contents | <p>We introduce <strong>Write Resistance</strong> ℝ = W<sub>eff</sub> / (K<sub>cell</sub> + W<sub>eff</sub>) = 1 − Θ as a fundamental derived quantity in Ontological Resolution Theory (ORT). Write Resistance measures the fraction of a node's computational budget consumed by its information load. It is not a new primitive: it follows directly from the Existence Tax (Theorem Z.5), bilateral gravitational load (Theorem VJ.2), and the throttling axiom (A6) of Canon v31.0.</p> <p>We prove that the photon, as an open-path massless defect paying no Existence Tax, follows the path that minimises total computational cost across the FCC lattice — a discrete analogue of Fermat's principle (Theorem WR.1):</p> <p>γ* = arg min ∑ ℓ / (1 − ℝ<sub>ij</sub>)</p> <p>This gives the carrier an effective refractive index:</p> <p>n<sub>ORT</sub>(<strong>x</strong>) = 1 / Θ = 1 / (1 − ℝ)</p> <p>This resolves <strong>wave-particle duality</strong> without postulates: the photon is a local rewrite operator (particle) whose global path is determined by minimising write resistance (wave). The apparent duality arises because an A0-bounded observer (3% bandwidth) cannot access the back-end FCC graph on which the path selection is computed.</p> <p>We apply Fermat's principle with n<sub>ORT</sub>(r) = 1 + 2M/r to derive <strong>gravitational lensing from first principles</strong>, without a spacetime metric, geodesic equation, or Einstein field equations (Theorem WR.2):</p> <p>δφ<sub>ORT</sub> = 4M/b + (15π/8)(M/b)<sup>2</sup> + O(M<sup>3</sup>/b<sup>3</sup>)</p> <p>The <strong>leading-order term matches General Relativity</strong> exactly, recovering the classical Einstein deflection result. The <strong>next-to-leading-order term is exactly twice the GR prediction</strong>:</p> <p>δφ<sub>GR</sub> = 4M/b + (15π/16)(M/b)<sup>2</sup> + …</p> <p>This factor-of-two difference at O(M<sup>2</sup>/b<sup>2</sup>) is a <strong>falsifiable prediction</strong> of ORT, directly testable by strong-field lensing observations near compact objects. It is the second key falsifiable prediction of ORT in the gravitational sector, alongside the GW-ringdown deviation of 16.7% at r = 4M (Corollary DD.1.1).</p> <p><strong>Observational targets:</strong></p> <ul> <li><strong>Event Horizon Telescope (EHT):</strong> photon ring astrometry around Sgr A* and M87*.</li> <li><strong>GRAVITY/VLTI:</strong> precision tracking of stars in the Galactic Centre.</li> <li><strong>Roman Space Telescope:</strong> microlensing surveys sensitive to second-order corrections.</li> </ul> <p>The paper also shows that the Schwarzschild horizon at r = 2M corresponds to ℝ(2M) = 1/2, not to a coordinate singularity. The limit ℝ → 1 (total write blockage) is prevented by the finite node capacity K<sub>cell</sub> = 133 bits per node (Theorem NS v1.0).</p> <p><strong>Derivation chain:</strong> Existence Tax (Z.5) → Write Resistance ℝ = 1 − Θ → Effective index n<sub>ORT</sub> = 1/Θ → Fermat's principle for γ* → Deflection angle δφ<sub>ORT</sub> → Strong-field lensing prediction.</p> <p>Zero free parameters. No postulated metric. No postulated field equations. Geometric optics emerges from information cost on a discrete FCC graph.</p> <p><strong>Open problems:</strong> anisotropic edge-resolved write resistance (WR-1); quantum interference from discrete path summation without wave function (WR-2); connection between write resistance and the Born rule (WR-3); full strong-field series beyond O(M<sup>2</sup>/b<sup>2</sup>) (WR-4).</p> <p><strong>Canon reference:</strong> Canon v31.0, Sections 2, 8, 10, 12. Theorems Z.5, VJ.2, A6, DD.1, DD.2. Closes: OP-Lensing (full), OP-Duality (partial).</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20026941 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Paper WR v1.0: Geometric Optics Without Metric — Write Resistance and Photon Paths in Ontological Resolution Theory Kapitanov, Fedor <p>We introduce <strong>Write Resistance</strong> ℝ = W<sub>eff</sub> / (K<sub>cell</sub> + W<sub>eff</sub>) = 1 − Θ as a fundamental derived quantity in Ontological Resolution Theory (ORT). Write Resistance measures the fraction of a node's computational budget consumed by its information load. It is not a new primitive: it follows directly from the Existence Tax (Theorem Z.5), bilateral gravitational load (Theorem VJ.2), and the throttling axiom (A6) of Canon v31.0.</p> <p>We prove that the photon, as an open-path massless defect paying no Existence Tax, follows the path that minimises total computational cost across the FCC lattice — a discrete analogue of Fermat's principle (Theorem WR.1):</p> <p>γ* = arg min ∑ ℓ / (1 − ℝ<sub>ij</sub>)</p> <p>This gives the carrier an effective refractive index:</p> <p>n<sub>ORT</sub>(<strong>x</strong>) = 1 / Θ = 1 / (1 − ℝ)</p> <p>This resolves <strong>wave-particle duality</strong> without postulates: the photon is a local rewrite operator (particle) whose global path is determined by minimising write resistance (wave). The apparent duality arises because an A0-bounded observer (3% bandwidth) cannot access the back-end FCC graph on which the path selection is computed.</p> <p>We apply Fermat's principle with n<sub>ORT</sub>(r) = 1 + 2M/r to derive <strong>gravitational lensing from first principles</strong>, without a spacetime metric, geodesic equation, or Einstein field equations (Theorem WR.2):</p> <p>δφ<sub>ORT</sub> = 4M/b + (15π/8)(M/b)<sup>2</sup> + O(M<sup>3</sup>/b<sup>3</sup>)</p> <p>The <strong>leading-order term matches General Relativity</strong> exactly, recovering the classical Einstein deflection result. The <strong>next-to-leading-order term is exactly twice the GR prediction</strong>:</p> <p>δφ<sub>GR</sub> = 4M/b + (15π/16)(M/b)<sup>2</sup> + …</p> <p>This factor-of-two difference at O(M<sup>2</sup>/b<sup>2</sup>) is a <strong>falsifiable prediction</strong> of ORT, directly testable by strong-field lensing observations near compact objects. It is the second key falsifiable prediction of ORT in the gravitational sector, alongside the GW-ringdown deviation of 16.7% at r = 4M (Corollary DD.1.1).</p> <p><strong>Observational targets:</strong></p> <ul> <li><strong>Event Horizon Telescope (EHT):</strong> photon ring astrometry around Sgr A* and M87*.</li> <li><strong>GRAVITY/VLTI:</strong> precision tracking of stars in the Galactic Centre.</li> <li><strong>Roman Space Telescope:</strong> microlensing surveys sensitive to second-order corrections.</li> </ul> <p>The paper also shows that the Schwarzschild horizon at r = 2M corresponds to ℝ(2M) = 1/2, not to a coordinate singularity. The limit ℝ → 1 (total write blockage) is prevented by the finite node capacity K<sub>cell</sub> = 133 bits per node (Theorem NS v1.0).</p> <p><strong>Derivation chain:</strong> Existence Tax (Z.5) → Write Resistance ℝ = 1 − Θ → Effective index n<sub>ORT</sub> = 1/Θ → Fermat's principle for γ* → Deflection angle δφ<sub>ORT</sub> → Strong-field lensing prediction.</p> <p>Zero free parameters. No postulated metric. No postulated field equations. Geometric optics emerges from information cost on a discrete FCC graph.</p> <p><strong>Open problems:</strong> anisotropic edge-resolved write resistance (WR-1); quantum interference from discrete path summation without wave function (WR-2); connection between write resistance and the Born rule (WR-3); full strong-field series beyond O(M<sup>2</sup>/b<sup>2</sup>) (WR-4).</p> <p><strong>Canon reference:</strong> Canon v31.0, Sections 2, 8, 10, 12. Theorems Z.5, VJ.2, A6, DD.1, DD.2. Closes: OP-Lensing (full), OP-Duality (partial).</p> |
| title | Paper WR v1.0: Geometric Optics Without Metric — Write Resistance and Photon Paths in Ontological Resolution Theory |
| url | https://doi.org/10.5281/zenodo.20026941 |