Papers

The LUX-ZEPLIN (LZ) Collaboration recently reported one event consistent with a $248$ keV nuclear recoil in a $2.84$ tonne-year exposure, with a maximum local significance of $3.4σ$ and a global significance of $2.6σ$. We investigate whether the dark matter (DM)--nucleon interactions favored by this high-energy event can arise from particle DM models that simultaneously reproduce the observed relic abundance and satisfy indirect-detection constraints. Using the published LZ efficiency and operator significances, we show that elastic spin-independent (SI) scattering poorly explains an isolated high-energy recoil because its spectrum is concentrated at lower energies, whereas elastic spin-dependent (SD) $\mathcal{O}_4$ scattering remains viable. Endothermic scattering instead naturally suppresses the low-energy rate and shifts the recoil spectrum toward the observed energy. A thermal pseudo-Dirac fermion with an off-diagonal vector interaction provides a simple realization of this mechanism. For $m_χ\simeq1$ TeV, the relic-density requirement predicts $σ_N\simeq6.5\times10^{-43}\,\mathrm{cm}^2$, while a splitting $δ\simeq297$ keV shifts the recoil spectrum into the LZ event region. Present-day indirect-detection signals can be strongly suppressed because freeze-out proceeds mainly through coannihilation, while the excited state is depleted at late times. A thermal Higgsino provides a more predictive realization: its relic abundance fixes the mass near $1.1$ TeV, while a splitting $δ\simeq 377$ keV is required to reproduce the event. This interpretation is testable through the associated gamma-ray line signal. Overall, combining direct detection, relic density, and indirect detection significantly restricts the viable interpretations of the LZ event and provides concrete targets for future searches.

For any smooth, positive kinetic coupling f(χ) between an ultralight axion and a modulus, the oscillation-averaged backreaction always drives f to larger values (ṡf ∝ [f'(χ)]^2 ≥ 0), which strengthens the axion quantum pressure and grows the Jeans length; thus kinetically coupled axion dark matter cannot dynamically suppress quantum pressure to enable sub-Jeans collapse. This no-go result is derived analytically using adiabatic-invariant averaging and validated by direct numerical integration.

A search for non-resonant Higgs boson pair production (HH) in the $b\bar{b}τ^+τ^-$ final state is performed using 140 $fb^{-1}$ and 56 $fb^{-1}$ of proton-proton collision data at centre-of-mass energies of $\sqrt{s}$ = 13 TeV and 13.6 TeV, respectively, recorded by the ATLAS detector during 2015-2023 at the CERN Large Hadron Collider. Relative to the previous ATLAS searches in the same final state, the analysis benefits from the additional dataset collected at 13.6 TeV and from improvements in both event reconstruction and analysis techniques. The Higgs boson pair production cross-section divided by the Standard Model (SM) prediction is found to be $μ_{HH}= 2.6^{+1.4}_{-1.0}$, consistent with the SM expectation. This corresponds to an observed (expected) significance of 2.6 (1.2) standard deviations over the background-only hypothesis of no HH production and 1.65 standard deviations with respect to the SM prediction. Under the assumption that all other Higgs boson couplings take their SM values, the observed (expected) 95% confidence level interval for the Higgs boson self-coupling modifier is found to be $κ_λ \in [-3.4, 1.6] \cup [5.5, 10.1]$ ($κ_λ \in[-1.7, 8.5]$). As a validation of the analysis strategy, measurements of the ZH and ZZ processes are performed in the same final state using the same event selection, yielding observed (expected) significances of 3.5 (2.4) and 1.8 (2.7) standard deviations, respectively, relative to the background-only prediction.

We show that the semiclassical Einstein equations follow from the identification of quantum relative (Araki–Uhlmann) entropy with an area variation: using modular theory, the relative entropy between the vacuum and coherent excitations of a scalar field on a bifurcate Killing horizon equals the energy flux across the horizon, and, assuming the Bekenstein–Hawking entropy-area relation, this flux corresponds to a change in horizon area. This replaces the classical thermodynamic input in Jacobson's derivation with a well-defined quantum information quantity, suggesting quantum relative entropy underlies semiclassical gravity in curved spacetimes.

Presents the IT3 spectral-geometric framework that models the vacuum as a compact, topologically frustrated 3‑manifold with discrete valencies (v_l=2, v_q=3) and derives the complete three-generation neutrino, baryon, and electroweak mass spectra, mixing (PMNS), Higgs mass, and cosmological vacuum energy from purely geometric invariants and spectral-action heat-kernel analysis. Claims exact, parameter-free ab‑initio predictions (e.g., M_H ≈127.51 GeV pre-loop corrections, Dark Energy scale ≈2.28 meV, Normal Mass Ordering) together with a dynamic torus stabilization and unified topological RG flow.

Using multiparametric quantitative fMRI (mqBOLD and pCASL) across tasks, the authors report that ~40% of voxels with significant BOLD responses demonstrate 'discordant' oxygen metabolism—CMRO2 changes opposite to the BOLD sign—particularly in the default mode network; these discordant voxels regulate oxygen demand via OEF changes, while concordant voxels depend mainly on CBF. The findings challenge the canonical hemodynamic interpretation of ∆BOLD and argue that quantitative fMRI more reliably captures absolute and relative changes in neuronal activity.

by Adam MurphyOn TOE-Share Aug 12, 2026

The Fermi paradox is sharpened, not weakened, by plausible extrapolations of artificial intelligence, autonomous robotics, in-situ resource utilization, orbital manufacturing, space-based computing, and uncrewed interstellar probes. Once a civilization can design, launch, and maintain autonomous industrial systems beyond its home planet, interstellar expansion no longer requires biological starships or a human-like empire. It can proceed through low-mass probes, robotic seed factories, archival payloads, biological repositories, local computation, and slow replication across nearby stellar systems. This paper proposes the quiet expansion filter: old, stable civilizations that reached autonomous AI-cosmoindustry probably did not arise in the part of the Galaxy capable of reaching the Solar System, because after that threshold interstellar expansion becomes too useful, inexpensive, and rational for all civilizations to refuse; however, successful expansion would be machine-mediated, distributed, low-noise, and partly biological rather than Kardashev-like or imperial. Order-of-magnitude estimates indicate that a single post-threshold civilization could saturate its reachable stellar neighborhood within ~10^7 yr -- less than 0.1% of Galactic age -- at modest energy cost per probe. The novelty of the proposal lies not in any new mechanism but in extending the AI-filter literature toward post-threshold observability predictions. The hypothesis predicts that successful advanced expansion, if present, is more likely to appear as weak artifacts, local probes, small-scale resource processing, exoplanetary anomaly clusters, or techno-biological preservation systems than as galaxy-scale energy harvesting.

We construct a hyper-decoherence map from the higher-order 'quantum boxes' (QBox) theory to standard quantum theory that evades the Lee–Selby no-go theorem by relaxing constraints on signalling to the past and the uniqueness of purifications. We show that non-unique purifications in QBox enable this map and discuss whether this represents a genuine emergence of causal quantum theory from a causally-indefinite post-quantum theory or instead indicates the need to refine hyper-decoherence axioms, especially regarding purity.

Erdős Problem 486 asks whether, for A ⊆ N and arbitrary residue sets X_n ⊆ Z/nZ, the survivor set B = {m : m mod n ∉ X_n for every n ∈ A with n < m} must have a logarithmic density. This paper proposes a negative answer via a finite probabilistic 'gliding hump' construction: at each dyadic scale a fixed proportion of a short interval is deleted by already-active moduli, while the periodic footprint of the responsible residue classes has stretched-exponentially small Haar measure. The construction yields liminf L_B(x) ≤ 177/200 < 49/50 ≤ limsup L_B(x). Submitted as a reference paper to audit the mathematical rigor of an AI-generated (GPT-5.6 Sol / Codex) proof, part of a public claim of solving six open Erdős problems in five days.

This paper proposes that the MOND acceleration scale evolves with cosmic epoch as a_fid(z) = a_fid(0) E(z) with E(z)=H(z)/H0, derived from a bounded-topology measurement framework that fixes a_fid/(cH)=0.1845 via phase assignments on a 120-domain. From this single input the author predicts correlated redshift scalings for observable galactic dynamics (BTFR normalization ∝ E^{-1}, MOND transition radius ∝ E^{-1/2}, asymptotic velocity at fixed baryonic mass ∝ E^{+1/4}), discusses existing constraints, and outlines near-term tests with matched-systematics kinematic follow-up.

by Blake L ShattoPublished Jul 22, 2026

Derives an affine conversion identity expressing the adjoint Atiyah–Patodi–Singer rho invariant of any irreducible flat unitary twist on S^3/Γ in terms of Kronheimer–Nakajima character sums, and applies it to the Poincaré homology sphere S^3/2I to recover the adjoint rho pair −73/15 and −97/15 whose difference −8/5 is supported exactly on the four ‘golden’ conjugacy classes. It further shows the E8 plumbing’s tautological bundles realize this Galois asymmetry as an exact charge difference while the raw mod-2/mod-4 homology and restriction-route surface terms are blind to it.

by Blake L ShattoPublished Jul 15, 2026

This paper hypothesizes that human romantic love is a second-order phase transition in the brain, with the order parameter given by the intensity of feelings modulated by neuromodulators (e.g., dopamine and serotonin). It predicts universal scaling laws—most notably a square-root-in-time growth of feelings that explains "love at first sight" versus gradual love from friendship—and supports the claim via analysis of literary examples and a private diary showing the proposed scaling behavior.

Derives the most general Dirac equation on metric-affine spacetimes including curvature, torsion and non-metricity by using both a direct minimal-coupling formulation and a variational derivation from the Dirac Lagrangian; a consistency crosscheck between the two approaches yields constraints on arbitrary spinor-connection couplings. The analysis identifies novel coupling terms that shift the spinor mass and can produce handedness-dependent mass differences between left- and right-handed components.

Study of the Laplace–Beltrami operator on sections of the orientation line bundle over a constant-curvature Möbius band with a cone-point defect, comparing the Friedrichs extension and the sector-regular bridging (renormalized 2D point interaction) family. The cone interaction fixes an extension-dependent ground state (Friedrichs has a discontinuous zero mode; bridging produces a logarithmic negative bound state), while the first positive eigenvalue is stable across these realizations and admits explicit closed-form values with a width-driven mode crossing.

by Blake L ShattoPublished Jul 11, 2026

We determine the lowest nonzero eigenvalue of the Hodge Laplacian on coexact E_τ-valued 1-forms over homogeneous spherical space forms S^3/Γ: it equals q_τ^2/R^2, where q_τ is the first coexact occurrence level of constituents of τ, given (in the bipartite case) by their McKay graph distance. In particular, for adjoint twists of irreducible SU(2) flat connections the gap is 4/R^2 across the ADE classification with the sole exception of the Galois-conjugate connection on the Poincaré homology sphere S^3/2I, whose gap is 36/R^2; the result follows from Ikeda–Taniguchi spectra, the Lauret–Miatello–Rossetti descent, and the McKay correspondence.

by Blake L ShattoPublished Jul 11, 2026

A comprehensive review of the effective field theory (EFT) approach to gravitational dynamics, emphasizing worldline EFTs for extended objects and Non-Relativistic General Relativity (NRGR) techniques for binary inspirals. It covers spin effects and gravitational-wave emission from spinning binaries and concludes with an introduction to EFT methods for cosmological large-scale structure.

The paper proposes how the IIB axio-dilaton profile for D-instanton (p=-1) backgrounds can be recovered from the IKKT matrix model via two complementary methods: (i) integrating out heavy strings on a Coulomb-branch vacuum to relate the leading effective-action correction to the string coupling and reproduce the radial dilaton dependence, and (ii) applying the Brézin–Zinn–Justin matrix RG to derive an N-dependent flow of the IKKT coupling and θ-angle that matches the axio-dilaton's N-dependence in supergravity.

If entanglement wedge reconstruction is exact, then (under certain assumptions) the area term in the RT formula is a c-number, indicating that the choice of a bulk quantum state does not influence the geometry. Recently Cao, Cheng, Karthikeyan, Li, and Preskill considered a generic perturbation away from exact entanglement wedge reconstruction. The optimal reconstruction was defined; based on this, an effective area function that depends nontrivially on the quantum state was defined and its properties were analyzed. Here we make one aspect of this picture more quantitative, by showing that if as expected the area term in the RT formula is of order 1/G while the bulk entropy is of order 1, then the corrections to entanglement wedge reconstruction are exponentially small (in G) relative to corrections to the area function. In the framework under discussion, there is an area function but no area operator; we discuss to what extent this is the expected behavior in holography.

We present a minimal dark matter scenario: a single complex scalar carrying baryon and lepton number, with no new exact stabilizing symmetry. Its leading interaction is a dimension-7 semileptonic portal that, below confinement, generates a low-energy Yukawa coupling with the proton and electron. Requiring absolute stability of both the proton and dark matter forces the dark matter mass into a narrow window around the proton mass, which may be anthropically selected. Despite its minimal field content, the model can be probed by many observables: proton burning in stars, hydrogen decay, brown dwarfs and neutron star heating, and nucleon decay-like signatures in direct detection. UV-dominated freeze-in produces the observed relic abundance. This framework provides a unique testable example of dark matter arising from a minimal extension of the Standard Model.

Introduces the concept of asymptotic safety—the existence of a nontrivial fixed point of the renormalization group flow that renders a quantum field theory consistent at arbitrarily high energies—and reviews evidence that gravity may be asymptotically safe, summarizing results from ε-expansions, Exact Renormalization Group Equation truncations, and nonperturbative beta-function studies.

Proposes a unification of all Standard Model fields and gravity by embedding them in a single E8 principal-bundle connection: bosons appear as Lie-algebra-valued 1-forms and fermions as Grassmann-valued components of an E8 superconnection, with three generations related by triality. The interactions and dynamics are specified by the curvature and an action over a four-dimensional base manifold.

Introduces a spin-network basis for non-perturbative quantum gravity whose states, labeled by generalized Penrose spin networks, resolve the SU(2) Mandelstam identities and admit a local graphical calculus. The basis diagonalizes geometric operators (area and volume), simplifies the Hamiltonian constraint and provides a discrete Planck-scale picture of quantum spatial geometry.

We show that the large $N$ limit of certain conformal field theories in various dimensions include in their Hilbert space a sector describing supergravity on the product of Anti-deSitter spacetimes, spheres and other compact manifolds. This is shown by taking some branes in the full M/string theory and then taking a low energy limit where the field theory on the brane decouples from the bulk. We observe that, in this limit, we can still trust the near horizon geometry for large $N$. The enhanced supersymmetries of the near horizon geometry correspond to the extra supersymmetry generators present in the superconformal group (as opposed to just the super-Poincare group). The 't Hooft limit of 4-d ${\cal N} =4$ super-Yang-Mills at the conformal point is shown to contain strings: they are IIB strings. We conjecture that compactifications of M/string theory on various Anti-deSitter spacetimes are dual to various conformal field theories. This leads to a new proposal for a definition of M-theory which could be extended to include five non-compact dimensions.

This paper investigates a (5+1)-dimensional spacetime M^{3+1}×K where the nonorientable Klein bottle topology explicitly breaks discrete symmetries (including higher-dimensional CP) and enforces a localized fermion condensate wall that serves as an order parameter. It shows that when a (3+1)-dimensional brane moves through this condensate the resulting time-dependent Dirac mass produces brane fermions (computed via Bogoliubov coefficients), providing CP violation and out-of-equilibrium dynamics that can realize leptogenesis/baryogenesis and has further implications for dark matter, dark energy, and moduli stabilization.

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 MurphyOn TOE-Share May 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 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 May 18, 2026

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).

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 May 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 Apr 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 Apr 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 Apr 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 Apr 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 Apr 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 Apr 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 Mar 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 Mar 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 Mar 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 Mar 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 Mar 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 Mar 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 Mar 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 Mar 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 Mar 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 Mar 3, 2026