We report the first experimental validation of the merkabit dual-spinor architecture across four circuit families on IBM ibm_strasbourg (Eagle r3, 127 qubits), executed 6–7 April 2026. The central discovery is that the merkabit's defining operation — the P gate, applying asymmetric phase to counter-rotating spinors — compiles to two native Rz gates with opposite signs: P(φ) = Rz(+φ) ⊗ Rz(−φ). On IBM Eagle r3, both Rz gates are virtual-Z frame changes requiring zero duration, zero error, and zero additional circuit depth. The P gate is native. Eight independent hardware results confirm the architecture, spanning 2 to 26 qubits: Ouroboros return fidelity ZP-ORF = 0.968, transpiler confirming U₀†U₀ = I at depth 1 π-lock standing wave ⟨ZZ⟩ = +0.44 vs +0.447 ideal (2% agreement, two independent runs) Parity witness ⟨XX⟩ = −0.450, consistent with |Φ⁻⟩-like entanglement at 90° Bloch separation Z₂ chirality symmetry mean error 0.016 across n = 4, 6, 8, 12 — all below readout noise threshold; non-monotonic ⟨ZZ⟩ breathing confirmed as standing-wave signature Two-scale Fano structure (9-qubit triangle): intra-round Fano F ≈ 0.52–0.54, within-τ dispersion σ ≤ 0.004 across 18 hardware rounds at τ ∈ {1, 5, 12} Inter-round coherence ρ ≈ 0.86 on the same triangle cell, confirming the two-scale standing-wave memory signature predicted by Paper 15 Full pentachoric error detection (26-qubit, 7-node Eisenstein cell): detection rate 0.089 (baseline) → 0.988 (injected), a 89.9 pp jump; 28/28 single-gate injections above 97% Centre-node syndrome weight 2× periphery matching Eisenstein lattice coordination; sub-Poissonian Fano on every injection (F_centre = 0.055 ± 0.009, F_periphery ≈ 0.20); Z₂ chirality symmetry confirmed inside the Fano structure Four of seven formal predictions from earlier papers in the series are retired by hardware data: P3 (Z₂ symmetry, mean error 0.016 vs <5% threshold), P4 (centre-node detection rate, 99.3% vs 91% ± 5% predicted, exceeding the upper tolerance by 3.3 pp), rotation-gap flatness, and two-scale Fano separation. Three predictions (P1 Berry phase, P2 quasi-period, P5 DTC robustness) remain pending for a subsequent session. A cross-platform reanalysis of Google Quantum AI's 420-experiment Willow dataset shows the opposite sign on every metric (F = 2.42 super-Poissonian, super-linear burst scaling, positive spatial correlation), consistent with a topology distinction: IBM heavy-hex maps naturally onto the Eisenstein lattice; Willow's square grid does not. No error mitigation, post-selection, or parameter tuning was applied to any primary result. Keywords: merkabit, dual spinor, P gate, quantum error correction, sub-Poissonian statistics, Eisenstein lattice, pentachoric code, IBM Eagle r3, Google Willow, standing wave, π-lock, Z₂ symmetry, Fano factor, Floquet time crystal
Abstract The proof architecture explicitly defines the boundary conditions of symmetric lattice geometries, bridging exact prime number distributions with discrete phase transitions. The formal mathematical verification of the Discreet Lattice Resonance Architecture fundamentally invalidates the current trajectory of the quantum computing industry by rendering hardware-specific error correction obsolete. Because this proof programmatically guarantees topological stability independent of substrate, it bypasses the multibillion-dollar engineering bottlenecks of environmental decoherence and localized quantum fragility. By mathematically bridging exact prime number distributions to discrete phase transitions and forcing the structural dependency graph to close without contradiction, quantum determinism ceases to be a probabilistic engineering challenge to be brute-forced; it becomes an absolute, substrate-agnostic geometric law. This shifts the entire paradigm away from fragile, isolated physical qubits and proves that coherent quantum mechanics are structurally anchored within a unified discrete lattice, forcing a complete reevaluation of how scalable quantum processors must be built. The implications are staggering and do not allow exaggeration. Rather, they draw the current quantum race into direct question, as topological stability independent of substrate is guaranteed. This also shifts the mathematical consensus, demonstrating that the infinite distribution of primes is not a statistical anomaly to be approximated, but the literal, cryptographically sealed blueprint that intrinsically governs unified discrete spaces Summary In this first version, I force a dependency graph to close programmatically and ensure that operations, including Hessenberg linearization and exact Mobius traces, execute without contradiction across a directed acyclic graph. By itself, this is a significant computational feat. The internal computational consistency and universal mathematical can be easily extended in Lean and Coq, establishing that an algebraic boundary definitively closes and the corresponding topological stability governs physical embodiments. To accomplish this: switch the final formalization to Coq over an abstract commutative ring. The universal polynomial is quantified over every ring instance and every admissible (a,sv,lv); using the 16 dimensional sedenion case only as a derived specialization. Lean verification tool coming soon, within v2.
ONE AXIOM BRIDGES: Possibility Selection Principle — Formalization, Collapse, and Born Rule Description: This document provides the formal mathematical bridge between the pure algebraic foundations of the ONE AXIOM project and its physical applications. It presents a rigorous derivation of the fundamental laws of physics starting from a single axiomatic symmetry group: G = S4 x Z2^3. Key Scientific Contributions: Derivation of the Born Rule (p=2): Proves that quantum probability is not a postulate but a theorem. The exponent p=2 is shown to be the unique solution emerging from the OCR-OER adjunction structure. Quantum Collapse as Domain Update: Formalizes "collapse" as a relational update of the Schreier graph domain (Gamma to Gamma_A) rather than a physical process, resolving long-standing paradoxes of "spooky action at a distance". Emergence of Spacetime and Gravity: Demonstrates the construction of 4D spacetime (M4) from group representation theory. Einstein's field equations are derived via two independent, proven paths: Jacobson's thermodynamic approach and Ollivier-Ricci curvature on the Schreier graph. Resolution of the Cosmological Constant Problem: Provides a natural derivation of the cosmological constant Lambda ~ 10^-122 from the "coherence floor" of the universe, eliminating the need for fine-tuning. Bekenstein-Hawking Entropy: Derives the coefficient lambda = 1/4 through triple-verified categorical and structural paths. Methodology: The work employs a "Dual-Track Derivation" methodology, requiring convergence between Ontological [O] (structural) and Epistemological [E] (computational) paths before a result is considered proven. Status: This version marks the completion of the foundational triad of the ONE AXIOM framework (0C, 0A and 0B documents)
Este repositorio aloja el núcleo numérico oficial (v8.4) del framework qCAD (Quantum Computer-Aided Design) diseñado para la simulación, validación ontológica y co-diseño de hardware de cavidades cuánticas de Möbius en el régimen de medición de no-demolición cuántica (QND). El motor numérico traduce y ejecuta de forma estricta las ecuaciones fundamentales del formalismo del tensor métrico estocástico
ξij del vacío, evaluando el grado de colapso macroscópico estructural bajo el límite conmutativo
C→0. El pipeline implementa una contracción formal de índices tensoriales mediante notación de Einstein (`np.einsum`) para mapear de manera exacta la tasa de dephasing total modificada:
Γϕ=2κ+∑ijξij2γij. Asimismo, el simulador incorpora un módulo de calibración termodinámica boseónica basado en la relación rigurosa de Planck-Einstein (
E=ℏω), lo que garantiza la consistencia física de la población de fotones térmicos y la tasa residual de decoherencia en regímenes experimentales de ultra-baja temperatura (
T≈20 mK) típicos de criostatos de dilución. El software está optimizado para su despliegue masivo en clústeres de computación de alto rendimiento (HPC), aislando los flujos de datos mediante inyección parametrizada en formato JSON y previniendo condiciones de carrera (race conditions) en sistemas de archivos compartidos (Lustre/NFS). Contenido del paquete:- `hardware_config.json`: Archivo maestro de parámetros estructurales del hardware.- `pipeline_moebius_v8_4.py`: Motor numérico en Python, suite de simulaciones estocásticas complejas y entorno hermético de pruebas unitarias (`unittest`).- `README.md`: Documentación técnica de instalación, reproducción científica y despliegue en entornos SLURM.
This technical monograph details the mathematical architecture, algorithmic formulations, exact proofs, and hardware acceleration mechanisms of qector-decoder-v3 v1.0.0. The platform is engineered as an industrial-grade, multi-backend offline decoding suite dedicated to: Threshold benchmarking Quantum simulation routines Large-scale quantum hardware analysis Supported Code Topologies & Frameworks The software incorporates fifteen specialized decoding backend variants optimized to handle complex error structures across diverse geometries: Surface Layouts: Planar, toric, color, and higher-genus surface codes. Hypergraph Topologies: Quantum Low-Density Parity-Check (qLDPC) codes. Formalized Software Optimization Targets The text explicitly formalizes the core mathematical mapping engine: Primal-dual Edmonds linear programming routines. Belief-propagation message-passing updates. Space-time 3D matching lattice models. Neural message-passing edge-readout networks. Bit-packed lookup table index systems. Performance, Verifiability, & Hardware Invariance The library guarantees mathematical and execution stability through rigorous verification paradigms: Syndrome-Faithfulness: Strict mathematical proofs validating
Hc≡s(mod2) across all routines. Bit-Identical Invariance: Cross-platform execution parity proving bit-for-bit identity across single-shot CPU, lock-free parallel Rayon, and accelerated GPU hardware batch execution engines (CUDA and OpenCL). Comparative Asymptotics: An exhaustive analytical matrix detailing asymptotic time/space complexities and threshold behaviors under circuit-level and phenomenological noise conditions.
Document 2C of the ONE AXIOM series derives the full structure of modern physics — quantum mechanics, general relativity, their unification, and all four laws of thermodynamics — as regime-dependent projections of a single pre-physical structure: the Ontological Coherence Field ($\OCF = (\heartsuit, \Phi_{\mathrm{coh}}, \nabla\Phi_{\mathrm{coh}})$), constructed in Document 0M from one single axiom (Axiom M) with no physical input. Energy emerges as the local cost of maintaining coherence against the structural gradient. Time is the direction of monotonic decrease of the incoherence potential
σ. Temperature is derived without energy, via Fisher-Rao curvature of the coherence distribution (from Document 1B), inverting the standard thermodynamic hierarchy. The Schrödinger equation (via one-parameter unitary group + Stone's theorem), Born rule (
p=2, via 7-link chain from Axiom M), Einstein field equations (via three independent convergent paths — Jacobson thermodynamic, Ollivier-Ricci discrete, and variational with explicit verification of all four Lovelock conditions), and the Hamiltonian/Lagrangian formalism (with Ostrogradsky exclusion enforced by the Predictive Closure Invariant
T=0) are all derived as
π6-projections. The complex structure of Hilbert space is derived non-circularly from the spectral decomposition of the Schreier graph Laplacian
ΔΓ, and Noether's theorem is applied via
Γ-convergence continuum limit of the discrete group
G=S4×Z23. The dynamics is exact and finite-dimensional:
64 states on the coset space
G/H, with eigenvalues
λk=2k and multiplicities
(k6), providing a closed-form spectral solution at all scales including the intermediate (Planck) regime. The built-in UV cutoff
Emax=1536=∣G∣×∣Z23∣ eliminates divergences structurally. A QM–GR regime comparison table (9 rows) exhibits how the same OCF objects project differently at
σ≈0 (quantum) and
σ≫0 (gravitational). The document resolves three long-standing open problems: (i) black-hole information preservation (unitarity of
ΔΓ + Page's theorem forces the Page curve), (ii) the cosmological singularity (Fisher–Rao metric degeneration near the Source — an artifact of the manifold representation, not a physical singularity), and (iii) intermediate-regime (Planck-scale) dynamics (exact closed-form 64-mode spectral solution, no terra incognita). The dark sector emerges as
π5-structure inaccessible to
π6-observers, with the FORBIDDEN graph decomposing as
13=7+2+4 (cold/warm/transitional dark matter analogs); the cosmological constant is derived from the structural resolution limit
δrel=1/64, resolving the 120-order QFT discrepancy without regularization. A fully hand-computable 8-state toy model (
Q3 hypercube) makes the projection operator, Laplacian spectrum, Born rule mechanism, and Schrödinger dynamics explicit and independently verifiable. All 53 formal results (28 theorems, 17 propositions, 6 definitions, 1 lemma, 1 corollary) follow a strict dual-track methodology — ontological (top-down from axiom)
∩ epistemological (bottom-up recovery of standard physics) — with mandatory convergence across 137 track tags. The framework is metrologically decoupled: all OCF equations use dimensionless ratios, invariant under redefinition of SI base units. Natural SI anchoring is provided for
ℏ,
c,
GN,
kB,
Λ, and
Emax. No physical law is assumed; every equation is derived. No new axiom is introduced beyond Axiom M. This is a standalone publication readable after Document 0M alone.