adam-murphy

A nonlinear negative-excursion statistic on the band-limited explicit-formula field of the Riemann zeros shows a strong coherence excess that blind two-engine tests attribute entirely to GUE/CUE spectral rigidity. Intervention experiments on the prime field are explained by comb geometry plus Gaussian dilution. The surviving finite-height residual is resolved by bandwidth tomography into a variance deficit −2Λ/(λ²ℓ²) below the Heisenberg scale (Λ = 1.57314…) and a discrete recovery at λ = 1 + log(q/p)/ℓ; Bogomolny's published pair-correlation formula reproduces the measured curve at three heights to ~0.2% with no free parameters. A fourth-cumulant residual with a sign change near λ ≈ 1.1 remains open.

A sketch of a scale‑invariant mathematical framework that defines a dimensionless coherence order parameter φ∈[0,1], models competing entanglement and decoherence attractions via simple potentials, and argues that degrees of freedom and agency peak in the transition zone; the framework maps physical and cognitive phenomena (from particles to civilizations) to positions, inertia, and trajectories on this coherence landscape and connects alignment to trajectory dynamics.

Defines a dimensionless diagnostic Y ≡ ln(Tc/θ_glue) − ln(vF*) and, from a curated dataset of 16 superconductors, shows that Y cleanly separates spin-fluctuation (SF) and phonon-mediated (PH) materials (Mann–Whitney p = 0.0005), with SF materials clustering near Y ≈ 0 and PH materials near Y ≈ −3.4. Within SF materials Y exhibits a positive trend with ln(ξ/a), indicating that larger Cooper-pair extent relative to the lattice correlates with higher coupling efficiency, and the finding is robust to θ_glue and vF provenance uncertainties.

The paper presents a resolution of the laboratory–cosmology neutrino mass tension using the Quantum Harmonia (QH) framework, introducing empirically driven scale-dependent mass running; a Bayesian MCMC fit simultaneously matches KATRIN (m_beta ≈ 0.250 eV) and Planck+DESI (Σm_ν ≈ 0.053 eV) and finds a scaling exponent β = 1.023 (+0.069/−0.051), significantly deviating from the naive β = 0.5 and yielding falsifiable predictions for upcoming experiments.

This paper extends the Quantum Harmonia (QH) framework, augmented by Unified Temporal Gravity (UTG), to quantum biology, proposing Lindblad-shielded microtubule entanglement and cryptochrome radical-pair coherence as mechanisms underlying 40‑Hz cortical oscillations and avian magnetoreception. Analytic Lindblad modelling, neural-network quantum-state simulations, and a Bayesian stack of eight biological datasets predict microtubule coherence of 0.1–1 ms and cryptochrome lifetimes of 1–10 μs (aggregate Z = 4.8σ), arguing a sub‑unity scale-coupling exponent δ ≈ 0.4615 substantially attenuates decoherence.

This position paper hypothesizes that entanglement is the primitive of reality and that the structural similarity between physical unification and AI alignment implies many alignment failures are ontological inaccuracies—agents optimizing against a model of separateness rather than a coherently coupled reality. It introduces minimal formal notions (gate-perception, gate-action, ticks) grounded in the double-slit experiment to argue that a unified physical framework would change what counts as rational action and thus materially alter alignment failure modes.

This work introduces the Quantum-Classical Advantage Boundary (QCAB) framework, a parameterized analytical model for determining when hybrid QPU-GPU systems outperform classical quantum simulation methods. The framework defines a Quantum Utility Ratio across five physical parameters and establishes scaling laws for the transition to quantum computational dominance.

A large-scale empirical study of the Birch and Swinnerton-Dyer (BSD) conjecture using 1.9 million elliptic curves from Cremona's database, revealing anomalous Tate-Shafarevich groups and establishing a power-law distribution with exponent α ≈ 2. The work provides numerical verification of BSD identities for rank-0 curves and identifies systematic patterns in Sha group sizes across unprecedented dataset scales.

We present a unified toroidal-cavity model for black hole vibrational resonances that simultaneously satisfies observational constraints from intermediate-mass black holes and gravitational-wave ringdown events. Through dual-constraint optimization of QNM-inspired parameters, our model achieves excellent agreement across six orders of magnitude in mass, reproducing IMBH compatibility factors within ±33% and exactly matching the 510 Hz fundamental overtone of GW150914.

We present a novel resolution to the S₈ tension using Quantum Harmonic Effective Field (QHEF) theory with a two-stage quantum-to-classical transition mechanism. Our framework features an early-time coherence phase (z > 6000) with strong quantum effects, followed by a late-time classical regime. Using Bayesian analysis of Planck CMB, BAO, growth factor, and black hole shadow data, we demonstrate excellent agreement with observations while resolving the S₈ tension through scale-dependent modifications to the effective Newton constant.

We investigate computational methods for identifying elliptic curves with anomalously large Tate-Shafarevich groups ($|Ш| ≫ 1$) among rank-0 curves over $ℚ$. After documenting and correcting circular reasoning in AI-assisted analysis, we find that the BSD geometric factor $α_{BSD}(E) = Ω_E^+ · ∏_p c_p(E) / |E(ℚ)_{tors}|^2$ achieves 99.5% precision at 98.4% recall for detecting $|Ш| > 1$ curves. We additionally report a power-law tail distribution for $|Ш|$ across 1.9 million curves with exponent $α̂ = 2.02 ± 0.07$, placing the distribution at the convergence threshold for $𝔼[|Ш|]$.