EP4-C documents the results of EP4A — a Lindblad Morse Gradient Test on the 3-qubit XXX Heisenberg spin chain using published ibmq_jakarta hardware parameters (T1=119 μs, T2=113 μs) — and identifies a structural consequence extending to the BCS superconductivity experiment (EP5-BCS). Core findings: (1) The Morse correlation dS = λ · D²_B is confirmed at 14.7× signal-to-noise on the Lindblad analytic trajectory. All thresholds were pre-declared before simulation. Decoherence parameters were taken from published hardware specs, not calibrated to match output. The Heisenberg revival F(|110⟩, U(π)|110⟩) = 1.000000 is verified. (2) The observed drift in λ is explained analytically with 85% accuracy and zero free parameters as a geometric consequence of the trajectory approaching the pure-state boundary ∂D(H) of the density matrix manifold near the revival at t=π. The drift is carried entirely by D_B shrinking as rotating-frame steps become geometrically short near the turning point; dS remains flat (CV=0.175). This is not a post-hoc explanation — the prediction follows from local eigenvalue structure of ρ at each step with no fitting. (3) Two independent aspects of the computation both indicate that the effective gravitational degree of freedom in EFT — f = |∇S|_B — is locally determined on D(H). First: λ(t) is predicted from local quantities only, with no non-local terms entering the drift explanation. Second: the Bures metric singularity near pure states is controlled entirely by the local eigenvalue spectrum of ρ at that point, directly analogous to how spacetime curvature in GR is determined by the local stress-energy tensor. (4) The BCS experiment (EP5-BCS, pending CAN Superconductors disc samples) has the identical geometric structure: the BCS ground state at T=0 is a pure state on ∂D(H). The clean Morse window — where the Pearson correlation between dS and D²_B is predicted to be high (> 0.85) and λ to track the zero-parameter geometric prediction — is 0.2 < T/T_c < 0.8, derived from EFT geometry before any BCS measurement. Boundary drift zones near T=0 and T=T_c are predicted as positive confirmations of the same structure. The document includes: full pre-declared threshold tables, per-step trajectory data, the zero-parameter λ prediction, all figures, reproducible Python code (NumPy/SciPy/Matplotlib only, no Qiskit required, runs in under 30 seconds), and the complete reasoning chain from initial results through geometric diagnosis to the locality finding. Verification chain:- EP4A (this document): Lindblad analytic trajectory — COMPLETE, 14.7× signal- EP4B: IBM hardware tomography at steps 5, 10, 20, 30, 35 — PENDING (script ready)- EP5-BCS: Superconducting disc, CAN Superconductors — PENDING, clean window 0.2 < T/T_c < 0.8 Related work:- EFT standalone: DOI 10.5281/zenodo.18963986- EQ(vT): DOI 10.5281/zenodo.18917317- EP4A (Morse Gradient Test, Lindblad): DOI 10.5281/zenodo.18969071- BCS pre-registration: DOI 10.5281/zenodo.18964362
EP4-C documents the results of EP4A — a Lindblad Morse Gradient Test on the 3-qubit XXX Heisenberg spin chain using published ibmq_jakarta hardware parameters (T1=119 μs, T2=113 μs) — and identifies a structural consequence extending to the BCS superconductivity experiment (EP5-BCS). Core findings: (1) The Morse correlation dS = λ · D²_B is confirmed at 14.7× signal-to-noise on the Lindblad analytic trajectory. All thresholds were pre-declared before simulation. Decoherence parameters were taken from published hardware specs, not calibrated to match output. The Heisenberg revival F(|110⟩, U(π)|110⟩) = 1.000000 is verified. (2) The observed drift in λ is explained analytically with 85% accuracy and zero free parameters as a geometric consequence of the trajectory approaching the pure-state boundary ∂D(H) of the density matrix manifold near the revival at t=π. The drift is carried entirely by D_B shrinking as rotating-frame steps become geometrically short near the turning point; dS remains flat (CV=0.175). This is not a post-hoc explanation — the prediction follows from local eigenvalue structure of ρ at each step with no fitting. (3) Two independent aspects of the computation both indicate that the effective gravitational degree of freedom in EFT — f = |∇S|_B — is locally determined on D(H). First: λ(t) is predicted from local quantities only, with no non-local terms entering the drift explanation. Second: the Bures metric singularity near pure states is controlled entirely by the local eigenvalue spectrum of ρ at that point, directly analogous to how spacetime curvature in GR is determined by the local stress-energy tensor. (4) The BCS experiment (EP5-BCS, pending CAN Superconductors disc samples) has the identical geometric structure: the BCS ground state at T=0 is a pure state on ∂D(H). The clean Morse window — where the Pearson correlation between dS and D²_B is predicted to be high (> 0.85) and λ to track the zero-parameter geometric prediction — is 0.2 < T/T_c < 0.8, derived from EFT geometry before any BCS measurement. Boundary drift zones near T=0 and T=T_c are predicted as positive confirmations of the same structure. The document includes: full pre-declared threshold tables, per-step trajectory data, the zero-parameter λ prediction, all figures, reproducible Python code (NumPy/SciPy/Matplotlib only, no Qiskit required, runs in under 30 seconds), and the complete reasoning chain from initial results through geometric diagnosis to the locality finding. Verification chain:- EP4A (this document): Lindblad analytic trajectory — COMPLETE, 14.7× signal- EP4B: IBM hardware tomography at steps 5, 10, 20, 30, 35 — PENDING (script ready)- EP5-BCS: Superconducting disc, CAN Superconductors — PENDING, clean window 0.2 < T/T_c < 0.8 Related work:- EFT standalone: DOI 10.5281/zenodo.18963986- EQ(vT): DOI 10.5281/zenodo.18917317- EP4A (Morse Gradient Test, Lindblad): DOI 10.5281/zenodo.18969071- BCS pre-registration: DOI 10.5281/zenodo.18964362
A companion paper, The Gravitational Baseline Principle, proposes a minimal pre-geometric quantum substrate and identifies two precise technical conditions that established theorems require before continuum geometry can be said to emerge from it: linear, Lorentz-consistent dispersion, and a mutual-information matrix that encodes a genuine metric distance. This paper tests both directly by exact diagonalization on the critical spin-1/2 antiferromagnetic Heisenberg chain, with a gapped or dimerized chain as a control. The dispersion condition is confirmed to high precision, matching the exact des Cloizeaux-Pearson result and decisively excluding a quadratic alternative. The metric-encoding condition is falsified in its originally hoped-for Euclidean form but not featurelessly: the specific functional form points toward a hyperbolic alternative, confirmed directly via the standard mathematical definition of hyperbolicity, the Gromov four-point delta, rather than a curve fit. An attempt to extend this to a 2D substrate is reported honestly as inconclusive at reachable system sizes, along with a genuine methodological finding: geometrically frustrated lattice shapes can have degenerate ground states that make naive mutual-information calculations non-reproducible unless explicitly checked. A final test sweeps several small dimerization strengths, checking whether the crossover away from hyperbolicity tracks the correlation length's own predicted field-theory scaling. The correlation length itself confirms the predicted scaling cleanly, but whether the geometric diagnostic's own breakdown tracks the same scale is only weakly supported and reported as an open result, not a positive one.
If gravity is information, then the gravitational potential must be an amount of information written at a boundary — and it must be written in a way that does not depend on what is on the other side. That is the informational form of the equivalence principle: a potential is universal, indifferent to the composition of what it acts on. This paper puts that requirement on a quantum processor and measures it.This is a follow-up to Gravity as Approach to a Rate–Resolution Bound (doi:10.5281/zenodo.21808410), and reports the hardware campaign that paper did not contain. In the parity–entanglement programme a crossing write changes a region's bias by ⟨P⟩ → ⟨P⟩|cos 2θ|, so that the amount of record it fixes, δS₂ = −ln|cos 2θ|, has the bias cancelled out of it: it is independent of the state of the region written on, and under Φ = −c²δS₂ it is the Newtonian potential, with θ = v_esc/2c. That independence, and not the mere existence of a correlation between regions, is what separates a gravitational potential from an arbitrary entanglement flow, and it is directly testable. We test it with an estimator that is decay-free by construction — the ratio R_ij(θ) = ⟨P⟩_i(θ)/⟨P⟩_j(θ) of two states carried through identical circuits, in which any depolarising factor cancels identically — and we test it against a deliberately introduced violation. On ibm_kingston, across fifteen independent measurements in two jobs, the sector-exchange write shows no drift: χ² = 12.77 on 15 degrees of freedom, p = 0.62, largest deviation 2.3σ. In the same jobs, and with the same estimator, a control write that is state-dependent by construction is resolved at p = 1.1×10⁻²⁰, and its drift is reproduced by a closed form with no fitted parameter at χ²/dof = 0.52, the largest predicted effect (16.74%) being recovered as 16.59%. The conserved membrane ⟨Z_A Z_B⟩ supplies a second, independent discriminator, dropping by 0.007 in the signal arm and by 0.071 in the control. We also report a measured correction to Eq. (3) of the parent paper: the identity ⟨P⟩ = Tr ρ_A² = e^−S₂ holds in the Gaussian sector but not in the qubit sector, where Tr ρ_A² = (1+⟨P⟩²)/2, confirmed tomographically to 0.3%. Exact density-matrix propagation shows the estimator cancels depolarising, dephasing, bit-flip and coherent write-angle error to machine precision, so a miscalibrated write can manufacture neither the null nor a violation; amplitude damping is the sole surviving channel, at 0.11γ. Every number is re-derived offline from the deposited counts by the accompanying script. Statements are labelled [P] proved, [K] known, [N] numerical or measured, [F] formal.
Gravity is traditionally understood either as geometric curvature (general relativity) or as an external classical field acting on quantum systems. This paper develops a unified alternative: gravity arises from spatial variation in the temporal coherence window τ(x), the finite interval over which quantum systems can sustain coherent phase relations before collapse. Building on experimental evidence that decoherence rates in laboratory systems obey an empirical κ/τ law, I show that gravitational self-energy constrains coherence time according to τgrav ∝ 1/√(Gρ). Three independent derivations—via a modified Lindblad equation, an effective potential Veff = A/τ, and spectral-overlap analysis—converge on the same dynamical law: a(x) = −∇[1/τ(x)], identifying gravitational acceleration as coherence-gradient descent. In this view, mass is condensed temporal capacity, curvature is the geometric imprint of temporal structure, and falling is the drift of quantum evolution toward regions where coherence collapses most rapidly. I extend this framework to show that gravity is engineerable: any spatially structured decoherence environment producing an artificial coherence profile τart(x) generates a gravitational-like acceleration agen(x) = −κart ∇[1/τart(x)], indistinguishable from natural gravitation insofar as their coherence-gradient profiles match. I provide explicit recipes for realizing such gradients using noise-shaping, optical scattering, dissipative optical lattices, and superconducting cavity engineering, along with quantitative acceleration estimates (10⁻⁷–10⁻³ m/s²) and full experimental protocols for cold atoms, matter-wave interferometry, and superconducting qubits. Finally, the framework offers a microphysical account of gravitational time dilation, predicts non-universal response in highly coherent systems, suggests achievable tabletop tests, and points toward a future τ-field theory capable of reproducing general relativity in the macroscopic limit. The result is a falsifiable, coherence-based foundation for gravitation and the first principled pathway to artificial gravity via engineered temporal coherence.
Operational theorem package: R′ (resolution), T′ (common-mode invariance), C′ (sub-bin curvature irrelevance), D′ (near-null registrar trivialization), H′ (horizon implementability) This record contains the final manuscript and supporting materials for a strictly operational analysis of quantum measurement in spacetime. Following the introduction of Quantum Measurement Timeline Framework (QMTF), in which a measurement is defined as a POVM statement on a declared spacetime target frameD* = R* × T* at finite resolution (Δx, Δt). An event is the realization of a single POVM effect E_U on one spacetime bin U; all dynamical relations among alternatives—including gravitational influence—belong to pre-event evolution. Within this orthodox setting, we prove a five-part operational theorem package: R′ (resolution). Finite operational resolution is derived, not assumed, from the metrological chain quantum Fisher information → Bures/Fidelity → total variation distance, yielding explicit Δx_min and Δt_min at any discrimination threshold ε_disc. T′ (common-mode invariance). Uniform time dilation or global phases are probability-irrelevant for any POVM; only differential phases can affect outcome statistics. C′ (sub-bin curvature irrelevance). Curvature variations confined below the declared resolution cannot change single-bin event probabilities beyond ε_disc. After Hadamard-controlled spatial and temporal smearing, such effects are common-mode or strictly sub-threshold. D′ (near-null registrar trivialization). With finite information rate, the boundTVD ≤ √(F / 8) · τ implies that no nontrivial discrimination is possible as the registrar’s proper-time budget τ → 0. H′ (horizon implementability). An exterior laboratory cannot implement POVM effects localized strictly in the interior algebra of a black-hole spacetime; interior bins have zero operational support for exterior observers. Together, these results close “gravity at the event” in the single-run semiclassical domain: gravity can only shape pre-event phases and support via proper time and cannot appear as an event-internal degree of freedom at any finite operational resolution. Each theorem is stated with explicit inequalities and clean falsifiers (sub-resolution curvature tests, near-null discrimination limits, and exterior-only interior implementability), ensuring refutability. The framework uses no assumptions beyond standard quantum mechanics (POVMs and instruments) and general relativity (proper time and locality) and is consistent with interferometric observations such as COW neutron interferometry and Kasevich–Chu atom interferometers, where gravity appears exclusively through differential pre-event phases. Keywords: POVM measurement; operational quantum measurement; quantum Fisher information; distinguishability bounds; Unruh–DeWitt detector; Hadamard states; proper time; semiclassical quantum mechanics and general relativity; algebraic quantum field theory; interferometry, QMTF. Author: R. Necsanu ORCID: 0009‑0009‑1281‑9180 Reference record (QMTF): Necsanu (2026), Zenodo 10.5281/zenodo.18262158
β = 2√2 as a Geometric Fixed Point: From Quantum Correlations to Galactic Dynamics Overview This work addresses a foundational question in quantum mechanics: Why does nature permit quantum entanglement up to the Tsirelson bound (β = 2√2), but no further? We demonstrate that β = 2√2 emerges as a geometric fixed point from three scale-independent interface constraints, requiring no reference to quantum postulates such as Hilbert spaces or superposition. This geometric derivation suggests that quantum correlations may reflect deeper structural necessities rather than being fundamental axioms. Key Results 1. Geometric Derivation (Theorem 3.5) Under three interface constraints—binary freezing (G1), interface separability (G2), and minimal-distortion lock-in (G3)—we prove that the maximal admissible CHSH correlator is uniquely: β = 2√2 ≈ 2.828 This is derived from Clifford algebra structure at a pre-quantum interface layer, without invoking quantum mechanics. 2. Experimental Validation Reanalyzing CHSH inequality measurements on IBM Quantum hardware (ibm_kyiv, 127-qubit processor), we obtain: S = 2.797 ± 0.012 This represents 69σ agreement with the geometric prediction, confirming that the interface constraints are physically realized. 3. Scale Invariance We prove that β = 2√2 remains invariant under coarse-graining maps, predicting its manifestation across: Quantum scale (10⁻¹⁵ m): CHSH correlations ✓ Confirmed Atomic scale (10⁻¹⁰ m): Mode coupling (Predicted) Galactic scale (10²⁰ m): Radial acceleration relation ✓ Derived Cosmological scale (10²⁶ m): CMB parity (Predicted) 4. Astrophysical Prediction Without fitting to galaxy data, we derive a radial acceleration response function Φ_β that: Reproduces the Newtonian limit with 0.037 dex precision Exhibits systematic deviations from empirical exponential forms Provides a falsifiable prediction through functional form differences (algebraic √ vs exponential) Methodology Theoretical Framework: Clifford geometric algebra, interface geometry, coarse-graining theory Experimental Validation: IBM Quantum Experience (GHZ states, CHSH inequality) Astrophysical Analysis: SPARC database comparison (limited validation) Statistical Significance: 69σ for quantum confirmation Significance This work proposes a paradigm shift from asking "what are the laws?" to asking "why these laws?" The derivation suggests: Quantum bounds as geometry: The Tsirelson bound may reflect geometric necessities rather than quantum axioms Cross-scale universality: Diverse phenomena (quantum correlations, galaxy dynamics) may probe the same underlying interface structure Falsifiable framework: Predicted functional forms enable empirical tests at multiple scales Data and Code Availability This deposit includes: Full manuscript (18 pages, peer-review submission format) All figures (8 publication-quality images) Experimental data documentation (IBM Quantum CHSH measurements) Analysis code (Python scripts for figure generation) Complete documentation (README, citation metadata, license) All materials are released under CC BY 4.0 license for maximum reproducibility and reuse. Publication Status Submitted to: Foundations of Physics (February 2026) Version History: v1.0: Initial deposit (February 2, 2026) v2.0: Author affiliation standardized (same day update) Limitations and Future Work Acknowledged limitations: Galactic-scale predictions require comprehensive SPARC dataset analysis (planned companion paper) Atomic-scale predictions await experimental verification Cosmological predictions require CMB higher-point function analysis Planned extensions: Full statistical analysis of 153 SPARC galaxies Detailed CMB selection rule derivation Experimental proposals for atomic-scale tests Contact Author: Takayuki TakagiORCID: 0009-0003-5188-2314Email: lemissio@gmail.comLocation: Higashimatsuyama, Saitama, Japan For questions about the theoretical framework, experimental validation, or collaboration opportunities, please contact via email. Citation If you use this work, please cite: @misc{takagi2026beta, title={β = 2√2 as a Geometric Fixed Point: From Quantum Correlations to Galactic Dynamics}, author={Takagi, Takayuki}, year={2026}, publisher={Zenodo}, doi={10.5281/zenodo.18454720}, url={https://doi.org/10.5281/zenodo.18454720}, note={Submitted to Foundations of Physics} } Keywords: Tsirelson bound, geometric fixed point, interface geometry, quantum foundations, Bell inequalities, CHSH inequality, radial acceleration relation, dark matter, galactic dynamics, scale invariance, Clifford algebra License: Creative Commons Attribution 4.0 International (CC BY 4.0) *This work was conducted independently with no institutional funding or conflicts of interest.*
EP4 is the fourth experimental entry point of the EQ(vT) theory (Time as a Vector Field, DOI: 10.5281/zenodo.18917317). EQ(vT) predicts that the density matrix of any decohering quantum system evolves along a Bures–Morse gradient flow with attractor ρ → I/d (the maximum-entropy state). This deposit formalizes the EP4 test against real IBM quantum hardware data. Data source: IBM Open Science Prize 2021 (qiskit-community/open-science-prize-2021). System: 3-qubit XXX Heisenberg spin chain on ibmq_jakarta (qubits 1, 3, 5), initial state |110⟩, ISL-optimised Trotterisation (35 steps, t = π). Full quantum state tomography: 27 Pauli bases, 16192 shots/circuit, 8 repetitions. Methodology: Density matrices reconstructed from raw hardware data using an ignis-free pipeline (calibration matrix inversion + linear Pauli inversion + PSD projection). The test operates in the rotating frame, isolating the decoherent component by removing accumulated unitary evolution at each Trotter step. This is the correct and necessary frame for testing a decoherence model. Data provenance: Step 35 (t = π) uses the density matrix reconstructed directly from real ibmq_jakarta hardware. Steps 1–34 use an analytic T₁/T₂ decoherence model calibrated to ibmq_jakarta hardware parameters (T₁ = 120 μs, T₂ = 90 μs, gate time 15 ns/step). Model purity at step 35 agrees with hardware to <1%. Full per-step hardware tomography is a limitation noted in §5.2 of the formalization document. Results: Three test statistics all pass. T1 (best-fit Morse residual): median 0.0037 vs noise floor 0.011, ratio 0.33× — well below the 5× conventional significance threshold. T3 (monotone approach to I/8): Bures distance decreasing. S4 (scalar Morse ratio dS/|∇S|²_Bures): constant at 0.005 ± CV~0.005 across all 34 usable Trotter steps, confirming the gradient flow structure independently of any fitting procedure. Contents: EP4_MorseTest_Formalization.docx (formal write-up), MorseTest_IBM_v4.py (full implementation), MorseTest_IBM_v4.png (results figure). Related: EQ(vT) theory (DOI: 10.5281/zenodo.18917317) · EFT Standalone (DOI: 10.5281/zenodo.18963986) Michael Adis · ETN Invest AB · Södertälje · 2026