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2026
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| Online Access: | https://doi.org/10.5281/zenodo.20117997 |
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| author | Stenberg, Selina |
| author_facet | Stenberg, Selina |
| contents | <p> </p> <p>The capstone of the Merkabit Research Series presents a candidate unified theory of physics built on a single algebraic forcing chain with zero free parameters.</p> <p>Starting from the requirement that a self-correcting computational unit exist on the Eisenstein lattice, the chain <strong>R → Z₃ → P₂₄ → E₆ → PSL(2,7)</strong> forces the derivation of fundamental constants — including the fine structure constant α⁻¹ = 137.036 (0.005 ppb vs CODATA 2018), the strong coupling constant α_s = 5/42 (0.02σ), the Weinberg angle sin²θ_W = 3/13 (0.19%), the Higgs vacuum expectation value, Newton's constant, the cosmological constant Λ = 2.876 × 10⁻¹²² (0.2%), the Yang-Mills mass gap Δ = 1/24, and the matter-antimatter baryon-to-photon ratio η_B = 5α⁴/|2T| = 5.91 × 10⁻¹⁰ matching Planck 2018 observation (6.09 ± 0.06) × 10⁻¹⁰ at 3% with zero free parameters — the <strong>Fifth Face of PSL(2,7)</strong>, extending Paper 10's four-faces unification.</p> <p>The architecture's five-gate ouroboros {R, T, S, F, P} is now derived <strong>mechanically from geometric closure</strong> in five steps: the matter triangle (2D face primitive, 3 gates), four triangles closing into a tetrahedron by 3-fold rotation, the counter-tetrahedron under rotation reversal, the dual-tetrahedron toroid where P emerges as the phase between counter-rotating spinors, and the cross-chiral tunnel between toroids where F emerges as the frequency-lock. The architecture is forced to exactly five gates by this closure; the R-locking test confirms it empirically (4-fold and 6-fold variants miss α⁻¹ by 0.15–0.27). The dual pentachoron is <strong>combinatorially over-determined</strong> at multiple counts — 10 tetrahedral cells (the V = 10 of α normalisation), 9 vertices with R-axis merged (the topology-independent 9-entry lookup table of Paper 31, with the (R, R) diagonal as the structurally zero fixed point), 5 single-pentachoron vertices, and 31 = 2⁴ + 2⁴ − 1 binary configurations — providing the architectural backbone for the Standard Model's matter sector.</p> <p>The matter sector B₃₁ exhibits three structurally complete <strong>closure modes</strong> — matter, antimatter, Riemann — that exhaust the obstruction types of the merkabit loop, with the master clock <strong>60 = lcm(h(E₆), h(E₈))</strong> and the 5-fold ouroboros as its 60 → 12 collapse operator. The matter-antimatter rate asymmetry δ_rate = 0.0417 measured in 6-qubit Cirq simulation equals the Yang-Mills mass gap 1/24 to four significant figures.</p> <p>The architecture extends to black hole thermodynamics: the classical singularity is replaced by a T₇₅-saturated core at r_p/r_s = 0.154, the holographic principle emerges as a counting theorem on the discrete Laplace equation, and α⁻¹ is derived a fourth independent way from black hole boundary counting alone.</p> <p>All five pre-registered hardware predictions from Appendix N were confirmed on IBM Eagle r3 and Heron r2 quantum processors within a single week (6–12 April 2026). Three further hardware observables are now pre-registered: Observable 22 (19-qubit Pentachoric Verification Protocol), Observable 25 (9-qubit closure trichotomy on IBM Eagle r3, Heron r2, and Google Willow), and Observable 26 (24-qubit chirality asymmetry on the 24-cell).</p> <p><strong>Executable companion:</strong> <code>github.com/SelinaAliens/genesis_sequence_merkabit</code> — the full genesis pipeline (binary substrate → Standard Model + gravity + black holes, 17 rungs, ~30-second runtime) plus <code>mechanical_genesis_verification.py</code>, the five-step derivation of the gate set itself from pure geometric closure (5/5 PASS, <0.1-second runtime). Every rung is a pass/fail test against a predicted invariant, paired with an explicit falsifier.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20117997 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Merkabit Architecture: A Candidate Unified Theory of Physics, A Zero-Parameter Derivation of the Standard Model, Gravity, Black Hole Thermodynamics, Holography, and the Fine Structure Constant from E₆ Coxeter Geometry and the Discrete Laplace Equation Stenberg, Selina unified theory standard model fine structure constant holographic principle black holes e6 psl (2,7) eisenstein lattice merkabit zero free parameters ibm quantum hardware theoretical physics mckay correspondence coexter number cosmological constant geometry e6 lie algebra <p> </p> <p>The capstone of the Merkabit Research Series presents a candidate unified theory of physics built on a single algebraic forcing chain with zero free parameters.</p> <p>Starting from the requirement that a self-correcting computational unit exist on the Eisenstein lattice, the chain <strong>R → Z₃ → P₂₄ → E₆ → PSL(2,7)</strong> forces the derivation of fundamental constants — including the fine structure constant α⁻¹ = 137.036 (0.005 ppb vs CODATA 2018), the strong coupling constant α_s = 5/42 (0.02σ), the Weinberg angle sin²θ_W = 3/13 (0.19%), the Higgs vacuum expectation value, Newton's constant, the cosmological constant Λ = 2.876 × 10⁻¹²² (0.2%), the Yang-Mills mass gap Δ = 1/24, and the matter-antimatter baryon-to-photon ratio η_B = 5α⁴/|2T| = 5.91 × 10⁻¹⁰ matching Planck 2018 observation (6.09 ± 0.06) × 10⁻¹⁰ at 3% with zero free parameters — the <strong>Fifth Face of PSL(2,7)</strong>, extending Paper 10's four-faces unification.</p> <p>The architecture's five-gate ouroboros {R, T, S, F, P} is now derived <strong>mechanically from geometric closure</strong> in five steps: the matter triangle (2D face primitive, 3 gates), four triangles closing into a tetrahedron by 3-fold rotation, the counter-tetrahedron under rotation reversal, the dual-tetrahedron toroid where P emerges as the phase between counter-rotating spinors, and the cross-chiral tunnel between toroids where F emerges as the frequency-lock. The architecture is forced to exactly five gates by this closure; the R-locking test confirms it empirically (4-fold and 6-fold variants miss α⁻¹ by 0.15–0.27). The dual pentachoron is <strong>combinatorially over-determined</strong> at multiple counts — 10 tetrahedral cells (the V = 10 of α normalisation), 9 vertices with R-axis merged (the topology-independent 9-entry lookup table of Paper 31, with the (R, R) diagonal as the structurally zero fixed point), 5 single-pentachoron vertices, and 31 = 2⁴ + 2⁴ − 1 binary configurations — providing the architectural backbone for the Standard Model's matter sector.</p> <p>The matter sector B₃₁ exhibits three structurally complete <strong>closure modes</strong> — matter, antimatter, Riemann — that exhaust the obstruction types of the merkabit loop, with the master clock <strong>60 = lcm(h(E₆), h(E₈))</strong> and the 5-fold ouroboros as its 60 → 12 collapse operator. The matter-antimatter rate asymmetry δ_rate = 0.0417 measured in 6-qubit Cirq simulation equals the Yang-Mills mass gap 1/24 to four significant figures.</p> <p>The architecture extends to black hole thermodynamics: the classical singularity is replaced by a T₇₅-saturated core at r_p/r_s = 0.154, the holographic principle emerges as a counting theorem on the discrete Laplace equation, and α⁻¹ is derived a fourth independent way from black hole boundary counting alone.</p> <p>All five pre-registered hardware predictions from Appendix N were confirmed on IBM Eagle r3 and Heron r2 quantum processors within a single week (6–12 April 2026). Three further hardware observables are now pre-registered: Observable 22 (19-qubit Pentachoric Verification Protocol), Observable 25 (9-qubit closure trichotomy on IBM Eagle r3, Heron r2, and Google Willow), and Observable 26 (24-qubit chirality asymmetry on the 24-cell).</p> <p><strong>Executable companion:</strong> <code>github.com/SelinaAliens/genesis_sequence_merkabit</code> — the full genesis pipeline (binary substrate → Standard Model + gravity + black holes, 17 rungs, ~30-second runtime) plus <code>mechanical_genesis_verification.py</code>, the five-step derivation of the gate set itself from pure geometric closure (5/5 PASS, <0.1-second runtime). Every rung is a pass/fail test against a predicted invariant, paired with an explicit falsifier.</p> |
| title | The Merkabit Architecture: A Candidate Unified Theory of Physics, A Zero-Parameter Derivation of the Standard Model, Gravity, Black Hole Thermodynamics, Holography, and the Fine Structure Constant from E₆ Coxeter Geometry and the Discrete Laplace Equation |
| topic | unified theory standard model fine structure constant holographic principle black holes e6 psl (2,7) eisenstein lattice merkabit zero free parameters ibm quantum hardware theoretical physics mckay correspondence coexter number cosmological constant geometry e6 lie algebra |
| url | https://doi.org/10.5281/zenodo.20117997 |