Papers

Introduces a two-dimensional operator diagnostic (χ, η) built from a participation operator P and a rigidity operator M, where χ tracks effective-dimension changes and η is the normalized Frobenius commutator measuring operator misalignment; the construction admits a Gibbs-like variational characterization and explicit bounds. Empirically, η consistently precedes the synchronization threshold in Kuramoto networks across topologies and sizes (outperforming pairwise transfer entropy), distinguishes regimes in driven Floquet systems, and recovers discrete-scale-invariant log-periodic ratios to within 0.3%.

The landmark discovery that neutrinos have mass and can change type (or "flavor") as they propagate -- a process called neutrino oscillation -- has opened up a rich array of theoretical and experimental questions being actively pursued today. Neutrino oscillation remains the most powerful experimental tool for addressing many of these questions, including whether neutrinos violate charge-parity (CP) symmetry, which has possible connections to the unexplained preponderance of matter over antimatter in the universe. Oscillation measurements also probe the mass-squared differences between the different neutrino mass states ($Δm^2$), whether there are two light states and a heavier one (normal ordering) or vice versa (inverted ordering), and the structure of neutrino mass and flavor mixing. Here, we carry out the first joint analysis of data sets from NOvA and T2K, the two currently operating long-baseline neutrino oscillation experiments (hundreds of kilometers of neutrino travel distance), taking advantage of our complementary experimental designs and setting new constraints on several neutrino sector parameters. This analysis provides new precision on the $Δm^2_{32}$ mass difference, finding $2.43^{+0.04}_{-0.03}\ \left(-2.48^{+0.03}_{-0.04}\right)\times 10^{-3}~\mathrm{eV}^2$ in the normal (inverted) ordering, as well as a $3σ$ interval on $δ_{\rm CP}$ of $[-1.38π,\ 0.30π]$ $\left([-0.92π,\ -0.04π]\right)$ in the normal (inverted) ordering. The data show no strong preference for either mass ordering, but notably if inverted ordering were assumed true within the three-flavor mixing paradigm, then our results would provide evidence of CP symmetry violation in the lepton sector.

Decisive experimental confirmation of the $U(1)$ quantum spin liquid phase in quantum spin ice remains an outstanding challenge. In this work, we propose stray-field magnetometry as a direct probe of the emergent photons -- the gapless excitation of the emergent electrodynamics in quantum spin ice. The emergent photons are transverse magnetization waves, which, in a finite sample, form discrete modes governed by one of two sets of natural boundary conditions: ``insulating'' or ``superconducting''. Considering cavity and thin film geometries, we find that the spectrum and spatial structure of the stray magnetic noise provide a sharp qualitative signature of the underlying electrodynamics. The predicted stray-field noise power lies comfortably within the detection range of present-day solid-state defect magnetometry.

We present the first protocol that provably provides both confidentiality and information-theoretic integrity against algebraic manipulation by external adversaries and corrupted intermediate nodes in trusted-repeater QKD networks. The construction combines Algebraic Manipulation Detection (AMD) codes with secret sharing and multi-path relaying, achieves optimal overhead in QKD bits, and is proven secure in a game-based model.

This paper identifies the "Orthogonality Constraint," a geometric limit showing that online neural/associative memory using inner-product addressing catastrophically collapses under semantic density because embeddings are not orthogonal, and validates this failure across text, scientific measurements, and image embeddings. It proposes Knowledge Objects—discrete, typed facts with hash-based identities, controlled vocabularies, and explicit version chains—as a hippocampal-style episodic store that prevents interference, demonstrating large empirical gains (e.g., 45.7% retrieval on 16,309 Wikipedia facts versus near-zero for modern Hopfield/attention) and a learned router with 97.8% routing accuracy.

This paper gives the recovered-core relativity/Standard-Model derivation in Observer-Patch Holography (OPH). Starting from local observer patches on a finite-capacity screen, overlap consistency, and an explicit premise ledger, it reconstructs a schedule-independent overlap normal form, a conditional Lorentz branch, a conditional route to general relativity through a Jacobson-type gravity branch, and a conditional route to the realized Standard Model quotient (SU(3) × SU(2) × U(1)) /Z6. It also derives the exact rational hypercharge lattice and the counting chain Ng = 3, Nc = 3 for the realized low-energy matter package. The paper separates theorem-grade fixed-cutoff structure from scaling-limit assumptions, calibration sectors, and phenomenological continuations. The same calibrated local input P organizes the electroweak/Higgs trunk and, on the declared exact-release extension surface, the gravity coupling G.

by Adam MurphyPublished 5/26/2026

The paper gives three short proofs (produced by an internal OpenAI model) resolving distinct questions of Erdős: (1) it proves a polylogarithmic upper bound (and an infinite logarithmic lower bound) on the minimal k for which the product of prime powers up to k dividing a binomial coefficient exceeds n squared; (2) it constructs an explicit additive basis of order two such that every partition yields at least one part whose sumset has unbounded gaps; and (3) it shows that for every real α the sequence of fractional parts {α p_n} (p_n prime) is not well-distributed, using Diophantine approximation together with recent bounded-gap between-prime results.

Superinductors are circuit elements characterised by an intrinsic impedance in excess of the superconducting resistance quantum ($R_\text{Q}\approx6.45~$k$Ω$), with applications from metrology and sensing to quantum computing. However, they are typically obtained using exotic materials with high density inductance such as Josephson junctions, superconducting nanowires or twisted two-dimensional materials. Here, we present a superinductor realised within a silicon integrated circuit (IC), exploiting the high kinetic inductance ($\sim 1$~nH/$\square$) of TiN thin films native to the manufacturing process (22-nm FDSOI). By interfacing the superinductor to a silicon quantum dot formed within the same IC, we demonstrate a radio-frequency single-electron transistor (rfSET), the most widely used sensor in semiconductor-based quantum computers. The integrated nature of the rfSET reduces its parasitics which, together with the high impedance, yields a sensitivity improvement of more than two orders of magnitude over the state-of-the-art, combined with a 10,000-fold area reduction. Beyond providing the basis for dense arrays of integrated and high-performance qubit sensors, the realization of high-kinetic-inductance superconducting devices integrated within modern silicon ICs opens many opportunities, including kinetic-inductance detector arrays for astronomy and the study of metamaterials and quantum simulators based on 1D and 2D resonator arrays.

The paper introduces a two-dimensional operator-based precursor diagnostic (χ, η) built from a participation operator P and a rigidity operator M, where χ tracks effective-dimension changes and η measures normalized commutator misalignment between P and M. Applied to Kuramoto networks, η reliably peaks before the synchronization threshold across 107/109 trials and outperforms pairwise transfer entropy in lead time and reproducibility; the same operator construction also distinguishes regimes in driven Floquet systems and accurately recovers log-periodic ratios in discrete-scale-invariant spectra.

This paper introduces a two-dimensional operator diagnostic (χ, η) built from a participation operator P and a rigidity operator M, where χ tracks effective-dimension changes and η is a normalized Frobenius commutator measuring operator misalignment; the construction admits a variational (Gibbs-like) characterization and provable bounds. The authors validate η as an early, reproducible precursor of reorganization across systems: in Kuramoto ensembles η peaks before the synchronization threshold in 107/109 trials with an asymptotic gap ≈0.46 and precedes transfer-entropy peaks by 0.31 coupling units with fivefold lower variance, and the method also distinguishes regimes in Floquet systems and recovers log-periodic ratios in discrete-scale-invariant spectra to within 0.3%.

The paper constructs a one-parameter bounded-clock deformation of flat \LambdaCDM ("\Lambdacos") that is provably non-phantom under a fiducial-matter diagnostic but produces apparent phantom crossings when analyzed with common two-parameter templates (e.g., CPL). It fits \Lambdacos to Pantheon+ and DESI DR2 BAO, finding s0 < 0.19 (95% CL) and that the template-induced CPL distortion is structurally present but modest, demonstrating template bias as an explanation for some apparent phantom behavior.

by Blake L ShattoPublished 5/18/2026

Discrete scale invariance (DSI) in the anisotropic stress of a first-order cosmological phase transition imprints a multiplicative log-periodic modulation on the stochastic gravitational-wave background; under the short-correlation-time approximation (β/H* ≳ 10) the modulation factorizes from the source unequal-time correlator to the observable spectrum at the percent level. As a concrete UV completion the paper embeds DSI in walking technicolor, predicting ε∈[0.04,0.18] and b∈[1.7,2.8], LISA-detectable oscillations, and a correlated freeze-in dark-matter mass shift, with all approximations quantitatively justified.

For a Haag–Kastler net satisfying isotony, microcausality and additivity, the paper proves that the largest von Neumann subalgebra of B(H) containing A(O) whose inner automorphisms (and more generally normal completely positive maps implemented in the algebra) are non-signalling to all spacelike regions is A(O')'. Consequently A(O) is maximal with respect to no-signalling if and only if essential duality holds; the work also gives algebraic and entropic characterizations and related structural identities (e.g. a wedge-intersection identity and equivalent formulations of essential duality).

FDTD simulations show that explicit log-periodic time modulation of boundary permittivity (scaling ratio b = 13/8) in a one-dimensional electromagnetic cavity imprints a reproducible discrete-scale hierarchy in the probe-point power spectrum: after subtracting the smooth power-law envelope the residual oscillates periodically in ln ω with period ln(13/8). The effect is robust across parameter sweeps, absent in undriven/harmonic/random controls, statistically significant (r ≈ 0.81, p < 0.001), and persists with coherent propagation into the cavity interior.

The paper develops an operational reinterpretation of weak/static gravitational scaling in which a scalar polarizable-vacuum parameter K is mapped to an effective radiative-damping order parameter ζ originating from a local stochastic electromagnetic environment. The model algebraically reproduces the Schwarzschild weak-field scaling while preserving Heisenberg uncertainty products and proposes concrete clock, spectroscopy, and resonance experiments to search for K-like perturbations.

Presents a formalism that expresses the general Two-Higgs-Doublet Model scalar potential in gauge-invariant functions and derives concise criteria for classical stability and electroweak symmetry breaking, including methods to locate all stationary points. The authors apply the results to the MSSM and the Gunion et al. potential, reproducing known limits and clarifying the stability and vacuum structure of those models.

Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this exponential suppression only occurs if the physical error rate is below a critical threshold. In this work, we present two surface code memories operating below this threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. The logical error rate of our larger quantum memory is suppressed by a factor of $Λ$ = 2.14 $\pm$ 0.02 when increasing the code distance by two, culminating in a 101-qubit distance-7 code with 0.143% $\pm$ 0.003% error per cycle of error correction. This logical memory is also beyond break-even, exceeding its best physical qubit's lifetime by a factor of 2.4 $\pm$ 0.3. We maintain below-threshold performance when decoding in real time, achieving an average decoder latency of 63 $μ$s at distance-5 up to a million cycles, with a cycle time of 1.1 $μ$s. To probe the limits of our error-correction performance, we run repetition codes up to distance-29 and find that logical performance is limited by rare correlated error events occurring approximately once every hour, or 3 $\times$ 10$^9$ cycles. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.

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.

by Adam MurphyPublished 5/8/2026

This comment demonstrates that the recent paper by Lohmiller & Slotine (Proc. R. Soc. A 482: 20250413) contains a foundational mathematical error. By neglecting spatial derivatives of the probability density amplitude, the authors omit the quantum potential (identified by Madelung and Bohm). Their proposed equivalence is not exact but constitutes the standard semiclassical approximation. The illustrative examples either belong to a class where the quantum potential vanishes identically, or import quantum eigenfunctions through initial conditions.

We show that the Schrödinger equation can be solved exactly based only on classical least action and its associated classical density. The exact wave function is constructed by combining multi-valued classical action with the density of classical position dynamics computed along each extremal action path. This provides a simpler computing alternative to Feynman path integrals using only a discrete set of classical paths. Examples include the double-slit experiment, hydrogen atom, and EPR correlations. Results extend to relativistic Klein-Gordon and Dirac equations.

This paper proposes that a black hole is a ‘double zero’ in a scaling law: the phase position Θ reaches a domain boundary and the local hierarchy Ω_H collapses simultaneously, causing the observable sampling amplitude C(Θ) to vanish. It connects this scaling description to spectral geometry on the Poincaré homology sphere—identifying Hawking radiation and Reidemeister torsion as the surviving first-order signals at the double zero—and motivates area-law entropy while leaving the A/4 coefficient open.

by Blake L ShattoPublished 4/24/2026

The paper derives Newton's constant G from topology by identifying the cosmological constant Λ as the ground eigenvalue of a Möbius surface embedded in S^3; Gauss–Codazzi converts this 2D eigenvalue to Λ_obs = 3/R^2 and, together with a topology-derived fermion mass spectrum that fixes the energy scale μ_Λ, yields G = 3 c^4/(8π R^2 μ_Λ^4), reportedly matched to observations at the percent level. It further reframes dark matter and dark energy as geometric sectors at different manifold depths, removing the need for additional particle content.

by Blake L ShattoPublished 4/17/2026Linked to: Mode Identity Theory

For the Poincaré homology sphere S^3/2I, every intrinsic admissible spectral construction (from natural Laplacians, Dirac/signature operators, torsion, equivariant eta, and their finite algebraic combinations) can read Dirichlet and Hecke L-function data but cannot constrain zeros of any individual L-function. Any vanishing of such a construction is explained by one of four exhaustive obstructions — shifted-value coincidence, encoding degeneracy, framework mismatch, or character completeness — rather than by forcing L-function zeros.

by Blake L ShattoPublished 4/16/2026Linked to: Mode Identity Theory

Using Mode Identity Theory, the paper derives the fine-structure constant and the three Standard Model gauge couplings from a single topological postulate: an icosahedral grid and a matter phase well (13/60) together with a fractional Ω_Λ exponent. The formula yields α = 0.00733 (0.5% error) and similarly close predictions for α_s and α_W, with accompanying structural selection and uniqueness scans.

by Blake L ShattoPublished 4/16/2026Linked to: Mode Identity Theory

We propose that the observed arrow of time emerges from a decoherence gradient operating across cosmological environments. The decoherence gradient, initially defined as the spatial variation in the quantum-to-classical transition rate, provides a mechanism for temporal asymmetry without requiring a special low-entropy initial condition. We derive a coupling between the gradient magnitude and the local expansion environment, and argue that differential decoherence across the cosmic web generates an effective asymmetry in temporal evolution. The framework predicts small but potentially observable differences in integrated phase stability and clock synchronization between low-density and high-density large-scale environments.

Constructs a fermion mass formula from spectral geometry on the quotient S³/2𝐼 that multiplies a vacuum-energy scale by a Kostant geometric phase, a McKay-graph hierarchical exponent tied to the cosmological constant, and Reidemeister torsion from three flat SU(2) connections. Applied to 8 irreducible representations across 3 vacua it produces 24 mass predictions, 10 of which are assigned to Standard Model fermions (9 within a factor of 3 and 3 within 6%).

by Blake L ShattoPublished 4/9/2026Linked to: Mode Identity Theory

The Millennium Prize asks whether pure Yang–Mills theory on ℝ⁴ has a positive mass gap. On flat space, confinement must emerge dynamically. On the Poincaré homology sphere M = S³/2I, the answer is forced by geometry. Positive Ricci curvature provides a universal floor. The finite fundamental group yields exactly three isolated vacua: trivial, standard, and Galois conjugate. The McKay correspondence for the extended E₈ diagram filters the spectrum at each vacuum, producing a ninefold enhancement at the Galois sector. The same curvature that enters the Λ conversion guarantees confinement.

by Blake L ShattoPublished 4/1/2026Linked to: Mode Identity Theory: Modal Realization from Nested Topology, Mode Identity Theory, Mode Identity Theory, Mode Identity Theory

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.

by Adam MurphyPublished 3/28/2026

Three large‑angle CMB features have persisted across COBE, WMAP, and Planck with no explanation within ΛCDM. The Möbius embedding in S³ restricts the mode spectrum at large scales, breaks even‑odd symmetry through the non‑orientable identification, and defines a preferred axis as the twist normal. What has been called the “axis of evil” may be the universe revealing the geometry of its beginning.

by Blake L ShattoPublished 3/23/2026Linked to: Mode Identity Theory, Mode Identity Theory, Mode Identity Theory, Mode Identity Theory

Measurements of the Hubble constant have split into two persistent camps: the cosmic microwave background gives 67.4 km/s/Mpc; local distance ladders give 73. The discrepancy survives every systematic check and every independent method. Mode Identity Theory resolves the tension through the phase field: observers embedded in galactic structure sample from a shifted position on the 120‑domain. The shift is one bosonic step, Θf = 2/120, and the logarithmic slope of the phase operator at the H₀ well converts that step into an 8.4% increase. Both measurements are correct. They sample different positions on the same wave.

by Blake L ShattoPublished 3/22/2026Linked to: Mode Identity Theory, Mode Identity Theory: Modal Realization from Nested Topology, Mode Identity Theory, Mode Identity Theory, Mode Identity Theory

James Webb has found galaxies too massive, too early. Stellar masses of ∼10¹⁰ M⊙ within 600 Myr of the Big Bang require star formation efficiencies exceeding unity under ΛCDM, a physical impossibility. Mode Identity Theory predicts that the MOND acceleration scale a₀ is an edge mode (n = 1) referencing the evolving Hubble horizon: a₀(z) = a₀(0) × H(z)/H₀. At z = 10, this gives a₀ ≈ 20× the local value, enhancing gravitational binding and accelerating structure formation without new physics. Critically, MIT predicts a₀ evolves while Λ remains fixed: the inverse of standard assumptions. Both predictions are independently testable.

by Blake L ShattoPublished 3/22/2026Linked to: Mode Identity Theory, Mode Identity Theory: Modal Realization from Nested Topology, Mode Identity Theory, Mode Identity Theory, Mode Identity Theory

DESI reports mounting evidence (2.8–4.2σ) that the dark energy equation of state w evolves with redshift. If true, it would overturn the cosmological constant and reshape modern physics. Mode Identity Theory says the change is an illusion: Λ is fixed by the geometry of the universe, and what looks like evolution is the observer’s phase position on a standing wave. The “phantom crossing” through w = −1 arises as a template artifact rather than exotic physics. Tested against DESI DR2 baryon acoustic oscillation data, the Pantheon+ supernova compilation, and a Planck‑calibrated CMB ruler prior, MIT with locked parameters achieves ΔAIC = −2.1 over ΛCDM at the same parameter count.

by Blake L ShattoPublished 3/22/2026Linked to: Mode Identity Theory, Mode Identity Theory: Modal Realization from Nested Topology, Mode Identity Theory, Mode Identity Theory, Mode Identity Theory

Einstein introduced Λ in 1917 to hold the universe static. When Hubble proved expansion, he removed it, calling it his “biggest blunder.” A century later, standard cosmology revived Λ as dark energy. This note completes the arc: there is no dark energy nor mysterious force. Λ is set by the ground‑mode eigenvalue of the cosmic boundary; the geometry of the universe itself driving expansion. Einstein was right the first time, for reasons then unknown. The Möbius surface selects half‑integer modes; the lowest yields Λtop = 2/R², where R is the curvature radius of S³. The observationally inferred Λobs differs by a factor of 3/2, obtained through Gauss–Codazzi embedding under totally geodesic embedding and isotropy; the surface‑to‑eigenvalue identification is motivated from three directions.

by Blake L ShattoPublished 3/22/2026Linked to: Mode Identity Theory, Mode Identity Theory: Modal Realization from Nested Topology, Mode Identity Theory, Mode Identity Theory, Mode Identity Theory

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.

by Adam MurphyPublished 3/21/2026

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.

by Adam MurphyPublished 3/20/2026

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.

by Adam MurphyPublished 3/11/2026

Youtube video transcript

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 $𝔼[|Ш|]$.

by Adam MurphyPublished 3/3/2026