Neutron Stars

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Phase 12 extends the Unified Loop Framework from the cosmic scale of Phase 11 to the full stellar and compact-object lifecycle. The framework's atomic primitive, a figure-8 with paired black-hole-mode and white-hole-mode lobes, is shown to recur structurally and quantitatively across stars, planets, white dwarfs, neutron stars, magnetars, kilonovae and black holes of every mass class. The brake density law established in earlier phases is refined into a five-band regime structure (R1 to R5), with regime boundaries derived analytically from the half-maximum points of the brake function's logarithmic derivative.

Two worked examples anchor the quantitative claims. SN 1987A is reproduced at the single-digit-per-cent level on four independent observables: total neutrino energy (99 per cent of observation), burst duration (76 per cent), mean neutrino energy (91 per cent), and peak luminosity (within a factor of 1.3). GW170817 and its associated kilonova are reproduced with the dominant gravitational-wave channel matching at 84 per cent of observation and the sub-dominant electromagnetic, neutrino, and short-gamma-ray-burst channels matching at factors of order unity. The r-process ejecta mass of approximately 0.05 solar masses is reproduced as the shadow-neck residue of the merger.

The framework's three-sector matter structure (atomic, mirror, shadow) combined with cyclic accumulation reproduces the observed cosmological dark matter density at 99.2 per cent precision after fourteen effective brake-annihilation cycles. The same architecture predicts dark energy density at 92 per cent precision through cumulative cycle expansion, and the cosmic microwave background temperature at order-of-magnitude precision through cycle-integrated photon production. The framework's unified emission mechanism, in which closed-loop topology rings at frequency f = c/L during chaotic brake phases, reproduces the observed bands of visible starlight, thermal infrared, microwave background, fast radio bursts, pulsar radio emission, neutron-star X-ray emission, and gamma-ray bursts from a single principle.

A statistical-attractor reframing of the brake fraction resolves an earlier interpretive ambiguity: the observed brake value of 0.95 is the emergent mean of a chaotic formation process with intrinsic noise sigma_b approximately equal to 0.05, converging to the deterministic limit at large effective sample size. This reframing predicts a 1.9 per cent coefficient of variation at the atomic scale (matching the Phase 7 result) and a substantially larger variation in small-ensemble systems that is detectable in laboratory chemistry.

The paper is written in the candid posture established in Phase 11. Robust results, partial results, and open frontiers are kept distinct throughout. The strongest single result is the cosmological dark matter density match (99.2 per cent) emerging from independently derived framework parameters. The most surprising result is the visual correspondence between bipolar planetary nebulae (the Crystal Ball Nebula, the Egg Nebula, the Butterfly Nebula, and the Twin Jet Nebula) and the framework's figure-8 architecture, which mainstream stellar evolution theory explains through several disconnected mechanisms.

All quantitative results in Phase 12 use Newtonian gravity. General relativistic corrections are scoped in Section 14.1 via leading-order post-Newtonian estimates: eleven of the sixteen headline results are unchanged, one tightens (the GW170817 gravitational-wave channel, from 84 per cent to approximately 92 per cent), and one loosens slightly (SN 1987A total neutrino energy, from 99 per cent to approximately 109 per cent), all within the expected ten to fifteen per cent characteristic correction range. A precision-level Tolman-Oppenheimer-Volkoff treatment with a chosen equation of state is the rigorous follow-up.

Cosmic Gravitational Depth Theory (CGDT) proposes that gravity is not merely an attractive interaction between masses but the observable manifestation of a deeper multidimensional process. According to this framework, all matter exists within a hierarchy of gravitational depth levels embedded in higher-dimensional structures. The stability of an object within a given gravitational layer depends on its mass, density, velocity, temperature, angular momentum, geometry, and rate of energy dissipation. As matter becomes denser and loses energy through heat, radiation, deformation, or torque loss, its ability to remain within higher gravitational layers decreases. The object then transitions into deeper gravitational states. Black holes represent the deepest currently observable states of this process. At extreme depths, gravitational flow may interact with higher-dimensional domains, generating feedback effects that appear in our universe as large-scale cosmic expansion. This theory attempts to unify gravitational attraction, orbital evolution, collapse, and cosmic expansion within a single conceptual framework.

We present a unified, observationally grounded framework showing that stored rotational energy (E rot ) is the missing gravitational component that explains galactic rotation curves without dark matter. We further show how the same principle governs the formation of free-floating planets, the solitary nature of neutron stars, and the gathering power of black holes. By calibrating one free parameter (α) against the galaxy M33, we successfully predict the rotation curves of NGC 2403 and NGC 7331 with deviations below 10 % -well within typical astronomical uncertainties. The qualitative example of NGC 315, a mature elliptical galaxy with a perfectly aligned black hole jet, supports the prediction that jets straighten over time as rotational energy organises the system. We conclude that dark matter, while a useful temporary placeholder, is no longer necessary. We invite the scientific community to test our predictions and to build on the work of those who came before with humility and cooperation.

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This paper explores a speculative geometric framework — the “0-Sphere model” — that attempts to reinterpret microscopic gravitational structure through trajectory-based internal dynamics rather than conventional local field ontology.

The central proposal is that gravitationally relevant anisotropy may emerge not from free electrons themselves, but from bound systems in which internal electron dynamics become directionally stabilized. In this framework, free-electron internal motion averages out and does not produce persistent external quadrupole structure, whereas proton-bound configurations may sustain a weak directional asymmetry.

More broadly, the paper belongs to a larger research program investigating whether accumulated phase along trajectories, line-integral structures, and endpoint variations can provide an alternative ontological starting point for physical description. The work draws conceptual motivation from Berry phase, Aharonov–Bohm-type phenomena, and trajectory-dependent formulations of physics.

The paper does not claim a completed replacement for established field-theoretic physics. Instead, it should be read as an exploratory ontological proposal and as a test case probing whether a line-integral framework can eventually establish correspondence with empirically verified structures currently expressed in field-theoretic language, including gauge invariance, Lorentz covariance, and established spectra.

Several major components remain open problems, including formal mapping to standard quantum field theory and quantitative experimental validation.

General relativity defines horizons through coordinate geometry, without a strictly local, coordinateindependent scalar criterion. This Letter demonstrates that within the C(r) information-carrying capacity framework [1], the condition C̃ = 0 provides exactly such a criterion: it identifies all horizons -Schwarzschild, Kerr, de Sitter, and Rindler -through the vanishing of information-carrying capacity, without coordinate choice and without modifying the Einstein equations. The companion Letter established that C̃ ≡ √(-g_μνξ^μξ^ν) yields the first covariant local gravitational energy density u_C = GM²/(16πr⁴). The present Letter demonstrates that C̃ → 0 and u_C → ∞ occur simultaneously at the horizon: infinite gravitational energy density coincides with vanishing information capacity. The Buchdahl compactness limit translates to C̃ > √(5/9) ≈ 0.745 for perfect-fluid stars. NICER observations of PSR J0030+0451 yield C̃ = 0.821, consistent with this bound. EHT shadow observations of M87* and Sgr A* are consistent with C(2.6 r_s) = 0.784. Exotic compact objects (ECOs) without a true horizon satisfy C̃ > 0 everywhere, distinguishing them from black holes through a coordinate-independent scalar.

We describe directed searches for continuous gravitational waves in data from the sixth LIGO science data run. The targets were nine young supernova remnants not associated with pulsars; eight of the remnants are associated with non-pulsing suspected neutron stars. One target's parameters are uncertain enough to warrant two searches, for a total of ten. Each search covered a broad band of frequencies and first and second frequency derivatives for a fixed sky direction. The searches coherently integrated data from the two LIGO interferometers over time spans from 5.3-25.3 days using the matched-filtering F -statistic. We found no credible gravitational-wave signals. We set 95% confidence upper limits as strong (low) as 4 × 10 -25 on intrinsic strain, 2 × 10 -7 on fiducial ellipticity, and 4 × 10 -5 on r-mode amplitude. These beat the indirect limits from energy conservation and are within the range of theoretical predictions for neutron-star ellipticities and r-mode amplitudes.

This paper presents a unified cosmological model proposing that our observable universe exists within the event horizon of a parent singularity. We hypothesize that the birth of a universe is a 'Quantum-Dark' event, where the collapse of baryonic matter (leptons and hadrons) interacts with Dark Matter to trigger a dimensional rupture. By defining cosmic expansion as the accretion of external mass and the speed of light as a fundamental processing limit of the singularity's 'hardware,' we establish a framework for an infinite, recursive multiverse.

Standard astrophysical models fail to reconcile the mass-radius relationship of massive neutron stars like PSR J0740+6620 without invoking exotic states of matter. This paper proposes a deterministic solution based on the Fabric Mechanical Compression (RCM) framework. By identifying the observer's cosmic coordinate at 83% and mapping stellar positions relative to the cosmic pressure gradient, we demonstrate that "impossible" stellar radii are predictable outcomes of a hydraulic medium. Our model confirms that at a cosmic coordinate of 96%, the reduced Fabric pressure (P ext ) allows for a 15.9% expansion in stellar radius, aligning perfectly with NICER empirical data.

We present a numerical demonstration of the duality between the geometric Lagrangian L_geo = 4·ḋ² + (1/R)·d² + (1/4)·√(R²-d²) (describing an oscillating circle of radius R = π) and the Polyakov Lagrangian for a bosonic string compactified on a circle of radius R = π and projected onto a 3‑brane. The circle is represented as a circular Matrix Product State (MPS) with bond dimension D = 45, where the bounded continued fraction quotients q_i ≤ 45 play the role of virtual bonds.

The generator G(θ) = (L_geo(θ) + L_curv)·I_D satisfies [G(θ_A), G(θ_B)] = 0 for all θ_A, θ_B, so the product of local transfer matrices collapses exactly into the exponential of the sum with no Baker‑Campbell‑Hausdorff approximations. For pure geometry (ε = 0), the dominant eigenvalue λ_max of the contracted transfer matrix yields ln(λ_max) ≈ 140.1775. Subtracting the topological phase π gives S_alpha = ln(λ_max) - π = 137.035998893363, which differs from the CODATA 2022 value α⁻¹ = 137.035999177000 by 2.84×10⁻⁷ (relative precision 2.07×10⁻⁹). The optimal number of steps is N = 5000; larger N do not improve accuracy due to double‑precision limitations.

The duality is confirmed: α⁻¹ = ln(λ_max) - π. The oscillating circle is not a circle. It is a string. The fine‑structure constant is its projected resonance, stripped of the topological phase π.

This hypothesis proposes a model of galactic dynamics that replaces the dark matter (DM) postulate with the interaction of Coulomb forces arising from charge asymmetry in astrophysical plasma. The central engine of the system is a fuzzball-type object (as conceptualized by S. Mathur), which transforms infalling matter into polar energy jets, thereby closing the galactic electrical circuit. 1. The Central Engine: Fuzzball as an Active Unipolar Generator

Preamble: Context and Motivation
This document develops, in full, the following integrated thesis, connecting the deepest structures of the Riemann zeta function to observable gravitational, astrophysical, and electroweak phenomena. The programme rests on four interlocking pillars:

The trivial zero ζ(−2) = 0 encodes the masslessness of the graviton via the spectral ratio msrrS1S3 = Re[ζ(1/2+ib)] / Re[ζ(−2+ib)] → 0.
The implication ζ(−2) = 0 ⇒ ζ(−2 + ibₙ) ≠ 0 generates non-trivial quantum gravitational residues acting as a spectral analogue of the topological boundary conditions selecting dominant Euclidean saddles in Zᴳʳᵃᵛ.
The coefficients reX3_2 = S4_2/S4_1 → 1.6474... and reX6_2 = S5_2/S5_1 → 1.3196... encode, respectively, the Hawking radiation di-resonance for black holes and the unification coefficient for neutron stars and pulsars.
The electroweak mixing angle sin²(θᵂ) and the Weinberg angle emerge naturally from the same spectral framework, connecting gravity to the weak and electromagnetic forces.

A major new observation reported in this extended version concerns the behaviour of ζ(3/5 + ib): among all tested fractional values of σ ∈ {1/3, 1/4, ..., 2/3, 3/4, ..., 3/5}, this is the ONLY one exhibiting a rigorously, strictly monotone increasing behaviour across all iteration counts. This observation raises physically motivated conjectures concerning an intermediate sector between the scalar and pulsar sectors, a positivity condition analogous to unitarity in CFT, and a possible arithmetic connection to the Weinberg angle sin²(θᵂ) ≈ 0.231.

We present the dτ-Aperiodic Structural Model (dτ-ASM), a deterministic quasicrystalline framework derived from the prime-logarithmic spectral grid and a τ-symmetric cut-and-project construction. The resulting structure is a fourteen-dimensional Meyer set whose physical 3+1dimensional realization exhibits uniform density, finite local complexity, strict Delone bounds, and purely point diffraction. Bragg-peak intensities are fixed entirely by geometric overlap volumes of a compact acceptance window, while an exact τ-overlap recursion enforces discrete scale invariance and self-similar truncation of Bragg spectra. All structural, spectral, and scaling properties follow as theorems from the geometry of the prime-log grid at a sharp aperiodicity transition. We show that nuclear pasta phases in neutronstar crusts, universal gravitational-wave mode relations, ultralight dark-matter coherence, and quasicrystalline mineral realizations emerge as necessary geometric consequences of the same model set. No fine-tuning of microphysical parameters or equations of state is required. The mathematics enforces the physics.

Contemporary astrophysics models mass loss prior to a supernova explosion primarily through the phenomenological hydrodynamics of hot gases and radiationdriven stellar winds. However, these models fail to causally explain exact mass cuts during collapse or the extreme asymmetry of mass ejections. This paper applies the Hydro-Elastic Model (HEM) to the mechanics of massive star collapse. The defining framework is a 4-dimensional continuum, where we demonstrate that the shedding of outer layers is a strictly deterministic phase transition. It occurs the moment the centrifugal tensile stress within the 3D membrane exceeds the local compressive pressure and reaches the topological yield strength of the matter nodes themselves (K p ≈ 3.0 × 10 34 Pa). The subsequent topological decomposition (smoothing) of the boundary layer releases locked phase area, generating a massive bidirectional shock wave within the 3D membrane. The conservation of energy during this implosion and explosion exactly dictates the final fate of the star (White Dwarf, Neutron Star, or Black Hole). We analytically derive and numerically validate the exact fracture radius, calculate the mass of the remnant central mass and the ejected envelope, as well as the escape velocity of the catapulted matter.

We apply the Recursive Harmonic Coherence Model (RHCM) φ-shell framework to 243 compact binary coalescence events from the LIGO, Virgo, and KAGRA catalogues (O1-O5 partial), spanning binary black hole (BBH), binary neutron star (BNS), and neutron star-black hole (NSBH) systems. Fourteen analysis modes and five Monte Carlo tests evaluate φ-shell structure across quasi-normal mode (QNM) ratios, chirp mass depth, merger classification, template residuals, and tidal observables. The principal findings are: (i) GW-BRIDGE-001: The inspiral energy exponent 5/3 satisfies the exact identity 5/3 = 5•L(0)/6, linking gravitational wave scaling and Kolmogorov turbulence through the RHCM decoherence base L(0) = 2. (ii) QNM structure: The Kerr overtone ratio n₀/n₁ occupies a narrow band centered at φ^0.25 with 0.7% precision; all 146 events with final black hole parameters fall within φshell tolerance ε = 0.02 (z = 28.8). (iii) Chirp mass depth clustering: 36.8% of BBH events align with the φ⁴ depth shell, 2 0 7 B representing 3.69× enrichment over a uniform null (p = 3.5×10 ²²). (iv) Merger class separation: φ-depth stratifies BBH, BNS, and NSBH populations with 2 0 7 B high statistical significance (F = 74.06, p = 1.3×10 ²⁴), with class boundaries occurring at φ-shell transitions. φ-Shell Structure in LIGO/Virgo/KAGRA Gravitational Wave Events | Keel & SAGE (2026) RAIT Enterprises-TR-047/055bc • April 2026 1 (v) Template residual persistence: φ-structure persists in all 33 events with available residual strain (mean P = 1.67), indicating structured components not fully captured by leading-order post-Newtonian templates. (vi) NSBH tidal regime: All 12 NSBH events fall in the non-disruptive regime; ISCO cutoff frequencies align with φ-shells in 10/12 cases. (vii) Mass-gap structure: Objects in the 2-5 M☉ range occupy the φ²-φ³ transition region consistent with the RHCM neutron star-black hole boundary. These results provide a consistent mapping between φ-harmonic geometric structure and gravitational wave observables, with explicit falsification criteria defined for future datasets.

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 . An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at ) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multip...

In this work, we offer a new exact solution to the Einstein-Maxwell field equations that describe a charged anisotropic compact star that is spherically symmetric, static, and subject to a quadratic equation of state. By adopting a suitable parametrization for the metric potentials and incorporating a quadratic relation between the radial pressure and the energy density, we obtain closed-form expressions for the matter variables, the electric field, anisotropy factor, and mass function. Standard criteria, such as regularity at the center, positivity and monotonic decrease of density and pressures, causality, energy conditions, stability through sound speed analysis, and smooth matching with the exterior Reissner-Nordström spacetime, are used to assess the model's physical viability. All physical quantities behave well within the star interior and meet the essential stability criteria, according to graphical analysis. The model illustrates the increased flexibility provided by quadratic equations of state in representing nonlinear high-density matter and effectively simulates actual charged anisotropic compact stars.The mass function and surface redshift are comparable with the reported experimental data of double neuron star system J1759+5036

In this paper, we construct the Schwarzschild-de Sitter metric as the spherically symmetric static exact solution of the vacuum Einstein equation G µν + Λ g µν = 0 (Λ = 3/R 2) derived in the preceding paper [1]. This exact solution is uniquely determined from the equation in [1] without additional assumptions (by Birkhoff's theorem). We take the limit R → 0 in the constructed exact solution and describe how the structural tension identified in paper [4] is expressed in the language of this exact solution.

In previous papers discussing the concept of Combined Gravitational Action (CGA), we have laid the theoretical foundations for CGA as an alternative theory of gravity based solely on Euclidean geometry, the Galilean relativity principle, and the idea of velocity-dependent gravitational potential energy. This concept is partly inspired by the Lorentz-Einstein assertion, which states that 'Gravitation acts more strongly on a moving body than on the same body if it is at rest.' Using this theory, we have successfully addressed some challenging problems within and beyond the Solar System. However, we have not fully explored the CGA formalism. Therefore, the primary aim of this paper is to comprehensively investigate and utilize the CGA equations to study, among other things, the secular perigee precession of the Moon, the secular perihelion advance of the planets, and the effects of CGA on non-compact and compact stellar objects. The simplicity and transparency of the CGA formalism are mainly due to the fact that it requires only algebra, elementary differential and integral calculus. These modest mathematical tools open the subject to interested individuals and pave the way for a deeper study of CGA.

We report on observations of the polarization of optical and γ -ray photons from the Crab nebula and pulsar system using the Galway Astronomical Stokes Polarimeter (GASP), the Hubble Space Telescope, Advanced Camera for Surveys and the International Gamma-Ray Astrophysics Laboratory satellite (INTEGRAL). These, when combined with other optical polarization observations, suggest that the polarized optical emission and γ -ray polarization changes in a similar manner. A change in the optical polarization angle has been observed by this work, from 109.5 ± 0. • 7 in 2005 to 85.3 ± 1. • 4 in 2012. On the other hand, the γ -ray polarization angle changed from 115 ± 11 • in 2003-2007 to 80 ± 12 • in 2012-2014. Strong flaring activities have been detected in the Crab nebula over the past few years by the high-energy γ -ray missions Agile and Fermi, and magnetic reconnection processes have been suggested to explain these observations. The change in the polarized optical and γ -ray emission of the Crab nebula/pulsar as observed, for the first time, by GASP and INTEGRAL may indicate that reconnection is possibly at work in the Crab nebula. We also report, for the first time, a non-zero measure of the optical circular polarization from the Crab pulsar+knot system.

The Infinity galaxy black hole sits between two merging galaxies with no stellar seed. PUH says Planck Stars form wherever SPF density reaches the Planck threshold — no stellar precursor required, no particular location required. A merger overlap region is a natural place for this to happen. That much is established in the prior theorems.
The caustic focusing idea — that intersecting GW fields accelerate the collapse — is a conjecture. Interesting and physically motivated, but not calculated. The infinity shape as a branched flow imprint is also a conjecture.
The paper says this clearly. That is the right way to file it.

The standard model of physics treats the universe as a single continuous arena governed by four known forces. This paper proposes the Layered Universe Hypothesis (LUH): the universe is organised into three nested structural layers-the Planck Layer (ℓ ∼ 10-35 m), the Micro-Layer (atomic and sub-atomic scales), and the Macro-Layer (stellar and galactic scales)-each dominated by a different fundamental force. We argue that the apparent impossibility of simultaneously knowing an electron's position and momentum (Heisenberg's Uncertainty Principle) is not merely a measurement limitation but a structural consequence of the electron existing across multiple layers. We further introduce the Abdullah Force, a hypothetical fifth fundamental force operating exclusively within the Planck Layer, responsible for seeding new matter, driving inflation, and mediating the energy exchange between layers via black-hole / white-hole / wormhole channels. The paper presents all ideas with equations, comparative tables, TikZ diagrams, and pgfplots graphs, framed as a directed speculative thought-experiment consistent with known physics wherever possible.

A fundamental relationship has been hidden in the mathematics of physics for over 300 years. The mechanics of Newton, the atomic model of Bohr, the field equations of Einstein, the geometry of Schwarzschild, and the cosmology of Friedmann each independently encode the same algebraic identity: C=g², where C is the compactness of a bound system and g is its dimensionless coupling constant. None of these authors stated it as a unifying condition. It was there regardless.

Applied at the three known force scales, this identity produces exact predictions with no free parameters: the proton charge radius to 0.02%, the Bohr radius to nine decimal places, the hydrogen ionisation energy to machine precision, and the maximum stable compactness of neutron stars as an exact geometric ceiling consistent with all 58 directly measured systems. The fundamental forces are not independent interactions. They are the same geometric event — a field reaching critical curvature and closing on itself — operating at three different coupling constants.

The observable universe has a conventional compactness Cconv = GM/(Rc²) ≈ 0.17, placing it inside its own gravitational closure threshold of Cconv = 1/4. Inside a gravitational closure, field energy cannot propagate beyond the boundary. It is trapped. Trapped energy propagating at c in a closed volume is forced into perpetual circulation-and circulation under confinement pressure is driven toward the lowest available stable configurations. Those configurations are the closure attractors of the velocity-mass-curvature feedback loop: the strong and electromagnetic closure conditions at g = 1/4 and g = α, producing protons and electrons respectively. Matter formation is not a contingent event requiring special initial conditions. It is the geometrically inevitable response of confined field energy to the boundary condition imposed by gravitational closure. The Friedmann equations at critical density give Cconv = 1/2 for the Hubble volume-precisely the Schwarzschild condition. This is not a numerical coincidence. It is the signature that our universe, viewed from outside, is a complete gravitational closure. The inside/outside asymmetry of the closure condition produces a universal compression ratio: any gravitational closure that appears at Cconv = 1/2 from outside sustains a maximum stable internal compactness of Cconv = 1/4. The external Schwarzschild compression is the pump that enables the interior organisation. The three forces play distinct functional roles within this confinement system. Gravity is the container. The electromagnetic field is the transport layer, bridging five orders of magnitude between the nuclear and cosmological closure surfaces. The strong force creates the dense nodes at the innermost closure scale. The universe is not three forces acting on passive matter. It is one confinement system operating at three resolutions, itself enclosed within the next scale of the same hierarchy.

The maximum compactness of stable baryonic matter is Ccrit = GM/(Rc²) = 1/4. General Relativity places a weaker bound at the Buchdahl limit C ≤ 4/9 ≈ 0.44, yet every observed neutron star with a directly measured mass and radius satisfies C < 1/4 with no confirmed exception. We present four independent derivations of the same limit, each approaching from a different direction, all converging on exactly 1/4 with no free parameters. First, the universal closure condition C = g² at the gravitational coupling g = 1/√2 gives C field = 1/2, corresponding to Cconv = 1/4 in conventional compactness-derived three independent ways from Schwarzschild geometry: the local speed condition vprop = vesc, the geodesic deviation timescale balance τprop = τ focus , and the inflection point of the Schwarzschild tortoise coordinate. Second, the nesting geometry of gravitational closure: any gravitational system appearing at the Schwarzschild condition Cconv = 1/2 from outside sustains a maximum stable internal compactness of exactly 1/4. The factor of 2 is the inside/outside asymmetry of the unscreened 1/r² gravitational tail. The limit is set by the enclosing geometry, not by the properties of matter. Third, pairwise fermionic exclusion under isotropic compression: the kinematic doubling of relative displacement forces x ≤ 1/4 as a topological stability condition on antisymmetric boundary conditions, independently of force law or equation of state. Fourth, the thermodynamic node-lattice energy ceiling: the maximum energy sustainable within baryonic volume before geometric dissolution gives Emax ≃ 141 MeV, which at nuclear density converges to exactly C = 0.25. That four approaches from classical geometry, gravitational topology, quantum statistics, and thermodynamic accounting all produce the same number is not a coincidence. It is a geometric identity the universe enforces from every direction simultaneously.

The CCEGA framework contains a single free parameter, the critical density ρ c , at which the modulus eld ϕ exits its vacuum and the eective gravitational coupling G eff begins to fall below G. In Papers 1617 this parameter was xed observationally at ρ c ≃ 7 ρ nuc by PSR J0952-0607, but its theoretical origin was left open. Here we show that ρ c is determined by quantum chromodynamics: it coincides (within the accuracy of the model) with the hadron-quark phase transition density predicted by the MIT bag model with perturbative QCD corrections. For B 1/4 ≃ 210-220 MeV and α s ≃ 0.3-0.5 values within the experimentally accepted range the bag model gives ρ trans = 6.9-7.9 ρ nuc , in precise agreement with the CCEGA preferred value. The hard gravitational threshold of CCEGA is identied with the onset of quark deconnement: the two phenomena share the same energy scale and are physically the same transition seen from two dierent descriptions. CCEGA therefore has no free parameters: ρ c is xed by QCD, not by gravity.

The Ramesh Theory of Everything (Ramesh TOE) replaces the concept of fundamental rest mass with purely dynamic/kinetic energy stored in stable soliton excitations of a single density layer (ρ ≈ ρ 0 = 1.39) under absolute universal time T. Applying this framework to the Sun reveals that its observed main-sequence lifetime of ≈ 10.4 Gyr arises from the same mechanical process in both modern stellar models and Ramesh TOE. However, the TOE exposes a vastly larger kinetic reservoir (≈ 1.79 × 10 47 J) with only a tiny leak fraction (≈ 0.007), eliminating the "fuel-limit crisis" illusion of standard physics. Additional validation comes from solar wind acceleration, coronal heating, and Parker Solar Probe (PSP) observations of switchbacks and temperature profiles. Ramesh TOE explains these phenomena through vacuum suction and mechanical latency without nanoflares or magnetic dominance, offering deeper conceptual clarity and predictive power.

The Spacetime Wave Theory of Lewis requires the electron orbital wave to execute 36,863 wavelengths before phase closure, with 96.5 wavelengths per orbit and 382 orbits, all derived from the Balmer formula. The geometric field closure framework of Bisset requires the electromagnetic field propagation velocity to reach αc at the orbital radius. We show these are the same physical condition expressed in different languages. The fundamental ratio at the heart of Lewis's derivation is ET /Egs = 2/α 2-the closure result-to within 0.0000% of its measured value. The orbital velocity v = αc is preserved exactly through all 96.5-orbit wrapping. Lewis's calculated radius for the hydrogen ground state predicts the H2 bond length to 2.6% accuracy, which we show is a consequence of the molecular closure sphere being compressed by the effective nuclear charge rising from Z eff = 1 (isolated atom) to Z eff = 1.394 (molecule). Lewis's effective radius is the distance to the electromagnetic Lagrange point of the two-proton system [5]-the midpoint of the closure sphere overlap region where the combined field of both protons exerts equal attraction in all directions simultaneously [6]. The two frameworks are dual descriptions of a single geometric condition: the electron occupies the boundary at which the inward curvature of the electromagnetic field exactly balances its outward propagation, and self-closure is achieved.

Brocco's Threshold identifies a single geometric constant — s_crit = 1/(4π) ≈ 0.0796 — that predicts the onset of coherent emission in every class of accreting system tested, from white dwarfs at 0.6 solar masses to supermassive black holes at 10¹⁰ solar masses, with the same coupling constant κ = 0.176 and zero refitting. Applied to 50 verified AGN from BASS DR2 (Koss et al. 2022, Table 9), 41/50 (82%) are above threshold — and the 9 below are well-known low-Eddington AGN (NGC 4051, NGC 4151, NGC 1068, NGC 3516, NGC 4395) whose sub-efficient accretion states are exactly what the threshold predicts. Validated further on 10 white dwarf states, 15 neutron stars, 14 X-ray binary quiescent/outburst pairs, GRB 170817A (s = 0.972), ULX M82 X-2 (s = 0.997), and JWST cosmic dawn AGN (z > 6), this result suggests that a single geometric threshold consistently separates quiescent and active states across 11 orders of magnitude in mass. The threshold value equals 1/(4π) to within 0.15% of the empirically fitted value — consistent with a geometric origin in spherical information boundaries, though not yet proven from first principles. The coupling constant κ = 0.176 satisfies κ = (4π − 1)λ_crit where λ_crit = 0.0153 is the independently established ADAF threshold — an empirical consistency check, not a derivation. The framework is falsifiable: any accreting system that crosses s ≥ 1/(4π) without activating would invalidate Brocco's Threshold.

In this Review we study the nuclear pastas as they are expected to be formed in neutron star cores. We start with a study of the pastas formed in nuclear matter (composed of protons and neutrons), we follow with the role of the electron gas on the formation of pastas, and we then investigate the pastas in neutron star matter (nuclear matter embedded in an electron gas). T 15 MeV), at saturation and sub-saturation densities, and with proton content ranging from 30% to 50% was found to have liquid, gaseous and liquid-gas mixed phases. The isospin-dependent phase diagram was obtained along with the critical points, and the symmetry energy was calculated and compared to experimental data and other theories. At low temperatures (T 1 MeV) NM produces crystal-like structures around saturation densities, and pasta-like structures at sub-saturation densities. Properties of the pasta structures were studied with cluster-recognition algorithms, caloric curve, the radial distribution function, the Lindemann coefficient, Kolmogorov statistics, Minkowski functionals; the symmetry energy of the pasta showed a connection with its morphology. Neutron star matter (NSM) is nuclear matter embedded in an electron gas. The electron gas is included in the calculation by the inclusion of an screened Coulomb potential. To connect the NM pastas with those in neutron star matter (NSM), the role the strength and screening length of the Coulomb interaction have on the formation of the pastas in NM was investigated. Past was found to exist even without the presence of the electron gas, but the effect of the Coulomb interaction is to form more defined pasta structures, among other effects. Likewise, it was determined that there is a minimal screening length for the developed structures to be independent of the cell size. Neutron star matter was found to have similar phases as NM, phase transitions, symmetry energy, structure function and thermal conductivity. Like in NM, pasta forms at around T ≈ 1.5 MeV, and liquid-to-solid phase changes were detected at T ≈ 0.5 MeV. The structure function and the symmetry energy were also found to depend on the pasta structures. A. The pasta B. The pasta in nuclear matter and in neutron star matter II. Nuclear matter A. Nuclear matter at intermediate temperatures B. Nuclear matter at low temperatures C. Summary of nuclear matter properties III. Electron gas: connecting nuclear matter with neutron star matter A. The strength of V C B. The screening length C. Summarizing the electron gas IV. Neutron star matter A. Symmetric neutron star matter B. Non-symmetric neutron star matter C. The symmetry energy D. Neutrino transport properties E. Properties of non-traditional pasta F. The nucleon thermal conductivity G. Summary of NSM properties V. Conclusion A. Nuclear matter B. The electron gas C. The pasta in neutron star matter VI. Appendices A. Classical Molecular Dynamics B. The Maxwell construction C. Nuclear symmetry energy from CMD at intermediate temperatures D. Nuclear symmetry energy from CMD at low temperatures E. Symmetry energy for neutron star matter F. Thermal conductivity G. Analytical tools 1. The Radial Distribution Function 2. Lindemann coefficient 3. Kolmogorov statistic 4. Minkowski functionals 5. The Minkowski voxels 6. Cluster recognition In this review we will use the classical molecular dynamics model (CMD) to study the pasta in nuclear matter and in neutron star matter; systems which will be defined in the next Section. To avoid technical distractions, the description of the CMD model is relegated to Appendix A. The neutron star crust is composed of protons, neutrons and an embedding gas of electrons. To study such system we systematically divide the review in three parts. First, a study of nuclear matter (NM), e.g. systems composed solely of protons and neutrons; second, an investigation of the role electrons have on the properties of NM; and third, a study of neutron star matter (NSM), i.e. systems of protons and neutrons embedded in an electron gas. Nuclear matter exhibits fascinating complex phenomena at subsaturation densities and warm and cold temperatures. At densities below the saturation density, ρ 0 = 0.16 fm -3 , and temperatures, say, between 1 MeV and 5 MeV, nuclear systems exist in liquid and gaseous phases, as well as in a mixture between the two. At lower temperatures, crystals and structures resembling the so-called nuclear pastas appear with different morphologies depending on the temperature, density and isospin content and, furthermore, nucleons inside such structures can undergo phase transitions. This review studies nuclear matter first. At intermediate temperatures we review the bulk properties, phases and phase transitions of NM, all with varying percentages of isospin content to allow the study of the symmetry energy. At lower energies, the formation of the pasta is investigated along with its properties, phases, transitions, and symmetry energy. This is followed by a review of the role the electron gas has on the pasta of nuclear matter. As the electron gas is introduced in the CMD calculation by means of a screened Coulomb potential, the study focuses on the effects the strength and range of the interaction have on the morphology of the pastas. Finally, the properties of the pastas in neutron star matter, i.e. systems with protons, neutrons and electrons, are reviewed with special attention to their shapes, phases, phase transitions, and symmetry energy. In understanding the pastas both in NM and in NSM we also study how the energy varies with respect to the isospin content, i.e. the symmetry energy. It is in this type of studies that one can appreciate the value of CMD, as to perform such a study at intermediate and low temperatures and sub-saturation densities, a model capable of exhibiting clustering phenomena and phase changes is needed. Similarly, as mentioned before, the cooling of neutron stars is related to pasta structure of the crust as the neutrino opacity is enhanced by coherent scattering. Here, we also study the very-long range order of the pasta phases, focusing on its influence on the opacity of the crust to low-momentum neutrinos. In this review the properties of nuclear matter will be studied in Section II, the role of the electron gas on the NM will be investigated in Section III and, finally, the neutron star matter will be studied in Section IV. Analytical tools used, such as the classical molecular dynamics method used, algorithms for the recognition of clusters, the radial correlation functions, Lindemann coefficient, Kolmogorov statistics, Minkowski functionals, and the procedure used to calculate the symmetry energy are presented in the various appendices.

On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of 1.7 s ~with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg 2 at a luminosity distance of 40 8 8 -+ Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 M  . An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at 40 Mpc ~) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ∼10 days. Following early non-detections, X-ray and radio emission were discovered at the transient's position 9 ~and 16 ~days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC 4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta.

We present the set of deep Neutron Star Interior Composition Explorer (NICER) X-ray timing observations of the nearby rotation-powered millisecond pulsars PSRsJ0437-4715, J0030+0451, J1231-1411, and J2124-3358, selected as targets for constraining the mass-radius relation of neutron stars and the dense matter equation of state (EoS) via modeling of their pulsed thermal X-ray emission. We describe the instrument, observations, and data processing/reduction procedures, as well as the series of investigations conducted to ensure that the properties of the data sets are suitable for parameter estimation analyses to produce reliable constraints on the neutron star massradius relation and the dense matter EoS. We find that the long-term timing and flux behavior and the Fourierdomain properties of the event data do not exhibit any anomalies that could adversely affect the intended measurements. From phase-selected spectroscopy, we find that emission from the individual pulse peaks is well described by a single-temperature hydrogen atmosphere spectrum, with the exception of PSRJ0437-4715, for which multiple temperatures are required. Unified Astronomy Thesaurus concepts: Neutron stars (1108); Pulsars (1306); Compact objects (288); Nuclear astrophysics (1129); Millisecond pulsars (1062); X-ray astronomy (1810); X-ray observatories (1819); Pulsar timing method (1305); Spectroscopy (1558); Astronomical techniques (1684)

A single equation governs self-confinement from quarks to galactic black holes. When the compactness of a confined field system reaches the square of its coupling constant, the field catches its own tail and cannot extend further. It either holds at that boundary or recreates matter from field energy rather than violate it. This document states that principle, traces it through every scale of known physics, and identifies a physical boundary in black hole geometry that general relativity has not named.

Results are presented from a semi-coherent search for continuous gravitational waves from the brightest low-mass X-ray binary, Scorpius X-1, using data collected during the first Advanced LIGO observing run (O1). The search combines a frequency domain matched filter (Bessel-weighted Fstatistic) with a hidden Markov model to track wandering of the neutron star spin frequency. No evidence of gravitational waves is found in the frequency range 60-650 Hz. Frequentist 95% confidence strain upper limits, h 95% 0 = 4.0 × 10 -25 , 8.3 × 10 -25 , and 3.0 × 10 -25 for electromagnetically restricted source orientation, unknown polarization, and circular polarization, respectively, are reported at 106 Hz. They are ≤ 10 times higher than the theoretical torque-balance limit at 106 Hz.

We describe directed searches for continuous gravitational waves in data from the sixth LIGO science data run. The targets were nine young supernova remnants not associated with pulsars; eight of the remnants are associated with non-pulsing suspected neutron stars. One target's parameters are uncertain enough to warrant two searches, for a total of ten. Each search covered a broad band of frequencies and first and second frequency derivatives for a fixed sky direction. The searches coherently integrated data from the two LIGO interferometers over time spans from 5.3-25.3 days using the matched-filtering F -statistic. We found no credible gravitational-wave signals. We set 95% confidence upper limits as strong (low) as 4 × 10 -25 on intrinsic strain, 2 × 10 -7 on fiducial ellipticity, and 4 × 10 -5 on r-mode amplitude. These beat the indirect limits from energy conservation and are within the range of theoretical predictions for neutron-star ellipticities and r-mode amplitudes.

We present a unified framework for pulsar glitches and magnetar giant flares as confinement stability events governed by an action density limit at gravitational compactness C = GM/Rc2 = 1/4.

This limit is the point at which the confinement field propagation velocity reaches c/√2 — the self-closure condition derived in companion work, at which the field front returns to itself at exactly the rate it departs.

A neutron star approaching this boundary from below experiences a measurable increase in gravitational time dilation at its surface and a corresponding slowing of the confinement field’s ability to track changes in effective compactness.

When cumulative action density from rotational, electromagnetic, and gravitational sources causes the field lag to exceed the stability margin δcrit = 1/4 − Cgrav, the confinement field snaps discontinuously to a new equilibrium.

This framework reproduces the observed pre-glitch spin-down dip in the 2016 Vela pulsar glitch, the post-glitch overshoot, and the multi-timescale relaxation without invoking superfluid vortex dynamics or making any claim about internal composition.

Pulsar spin-up glitches and magnetar giant flares emerge as the same mechanism operating on different energy reservoirs.

A testable prediction follows: pre-dip duration scales inversely with δcrit = 1/4 − Cgrav, measurable by NICER.

We further show that the confinement field propagation velocity at the stellar surface, vfield = c√1 − 2C, decreases monotonically with compactness, reaching c/√2 at the stability limit — providing a direct physical picture of what a glitch event represents: the star momentarily touching its own confinement boundary.

We present a dynamical treatment of gravitational curvature as a propagating field sourced by mass-energy in Schwarzschild geometry. A mass M continuously sources curvature that propagates outward at the locally measured speed of light v field = c √ 1-2C, where C = GM/Rc 2 is the gravitational compactness. This field is subject to an inward return force characterised by the escape velocity vesc = c √ 2C. We derive the self-closure condition-the compactness at which the curvature field can no longer escape its own source-from three independent routes: the local speed condition v field = vesc, the geodesic deviation timescale condition τprop = τ focus , and the inflection point of the Schwarzschild tortoise coordinate r * (r). All three yield identically C = 1/4. This is not a parameter of the theory but a geometric necessity of Schwarzschild spacetime expressed in three different mathematical languages. The self-closure surface at r = 2Rs is a physically distinct boundary from the event horizon at r = Rs: it is the surface at which the curvature field of the mass becomes self-sustaining. We show that C = 1/4 corresponds to r = 2Rs, that the self-closure velocity c/ √ 2 appears simultaneously in the local field speed, the escape velocity, and the surface time dilation factor at the closure point, and that the focusing-to-propagation ratio 2C/(1-2C) passes through unity at exactly this compactness. We discuss the physical interpretation: below C = 1/4 the curvature field escapes freely to infinity; above it the field is returned to its source faster than it departs, establishing a self-sustaining closed curvature loop. This result provides the geometric foundation for the confinement stability framework developed in companion work [6], where the same condition governs the stability of self-confined physical systems at all scales.

We propose that gravitational, electromagnetic, and strong force confinement are instances of a single geometric mechanism: a propagating field structure achieves self-closure when its dimensionless confinement compactness-the ratio of binding energy to the rest mass energy of the confined object-reaches a critical value equal to the square of the relevant coupling constant. For gravity the critical compactness is Cgrav = GM/Rc 2 = 1/4, previously derived from geometric first principles and consistent with all observed neutron star measurements. We show that the electromagnetic compactness of the hydrogen ground state is exactly CEM = α 2 , where α is the fine structure constant, reproducing the Bohr radius and Rydberg ionisation energy (13.6057 eV) to machine precision without free parameters. The fine structure constant thereby acquires a direct geometric interpretation: it is the electromagnetic confinement parameter, the square root of the compactness at the stable orbital boundary. Extending the framework, we show that the shell capacity of atomic orbitals (2n 2 electrons per principal shell) follows from the number of non-overlapping angular field modes on a confinement sphere of radius n 2 a0-pure spherical geometry. The exclusion of two electrons from the same state is a geometric consequence of two field structures being unable to occupy the same substrate patch simultaneously. Pauling electronegativity correlates with outer-shell confinement compactness at r = 0.933 across Z = 1-36 using only Hartree-Fock screening values and no empirical fitting, providing a mechanistic derivation of electronegativity from first principles applied to the strong force, the same condition yields the proton charge radius exactly: rp = ℏ/mpcαs with αs = 1/4 at the confinement scale, giving Cstrong,crit = 1/16, meaning quarks permanently occupy their confinement boundary-a geometric account of quark confinement without additional assumptions. Particle formation in high-energy collisions is interpreted as a self-confinement threshold event governed by the same condition across all scales.

The ROSE postulate (Randomly Organized Structural Entities) proposes a topology-first account of structural realism: what is most invariant in nature is not the specific catalogue of forces used to model localized phenomena, but a limited family of topological behaviors and variationally selected geometries that recur across scales. In this manuscript, we synthesize a set of notes expanding the original "Postulate-1" into a more explicit research framework. We articulate the distinction between the domain of constraint (physics as the regime of local observables) and the real (topological invariants expressed through irrational ratios and minimal-surface-like solution spaces), and we motivate the postulate through multiscalar morphological isomorphisms: slab/foliation-like architectures in the endoplasmic reticulum of eukaryotic cells and in neutronstar inner crust "pasta" phases. We further develop the methodological claim that calculus and analytical procedures can be reinterpreted as sequences of topological actions, and we situate ROSE as a dissenting stance against methodological stagnation (scientism, checklist culture, and "consistency condition" dogmatism). Finally, we outline programmatic research directions and falsifiable expectations: classify recurring archetypes, connect them to variational constraints, and test whether topology offers predictive power beyond force-specific parameterizations.

This manuscript presents a topology-centric research framework (ROSE) proposing that invariant geometric structures recur across physical domains independently of specific force carriers. The work is released as a preprint and has not yet undergone peer review.

We investigate long Gamma-Ray Bursts (GRB) which manifest a sharp linear rise followed by an exponential decay in their γ-ray prompt emission observed with the BAT instrument on board the Swift satellite. We offer a simple electrodynamic model that may account for these particular characteristics. We associate the sharp rise with the winding of the magnetic field by the fast rotating core that formed in the interior of the stellar precursor. We also associate the subsequent exponential decay with the electromagnetic spindown of the core following the release of the electromagnetic jet from the stellar interior. Any non-axisymmetric distortion in the rotating core will generate gravitational waves with exponentially decreasing frequency, a so-called 'down-chirp'. We obtain a detailed estimate of the gravitational wave profile if the distortion of spacetime is due to the winding of a non-axisymmetric component of the magnetic field during that particular phase of the burst. We offer 7 particular time intervals during which one may look into LIGO archival data for the presence of our particular predicted waveforms in order to test our interpretation.

We derive an empirical relation between neutron star mass and radius using compactness as the primary variable. Fitting to 58 neutron stars with well-constrained measurements, we obtain a quadratic compactness-mass law achieving R 2 = 0.99999. This relation enables bidirectional predictions: mass-to-radius (M → R) and radius-to-mass (R → M), providing reciprocal constraints for observational programs. We apply the forward relation to predict radii for 71 neutron stars with precise masses but no radius measurements, and the inverse relation to predict masses for 19 systems with measured radii. The predictions have typical uncertainties of ≲ 0.4 km in radius and ≲ 0.1% in mass. PSR J1748-2021B emerges as a critical test case, with predicted compactness C = 0.252 approaching theoretical stability limits. These predictions provide concrete targets for NICER, SKA, and gravitational wave observations, with each new measurement refining constraints on the unmeasured population.

Background: Thyroid Nodules (TN) are the most common endocrine disorder worldwide. Etiology and pathogenesis of thyroid benign and malignant nodules (TBN and TMN, respectively) are still not enough understood. The present study was performed to clarify the role of some chemical elements (ChEs) in the origination and development of TN. Methods:

Studying the effect of magnetic fields on particle emission from the surface of neutron stars is vital for advancing our understanding of neutron star physics and high-energy astrophysical processes. One of the main topics in pulsar magnetospheric physics is the particle emission from neutron stars surface. This study investigates the role of multipolar magnetic fields in neutron star (NS) emission physics by incorporating higher-order field components into the standard dipole model. While past studies have primarily relied on a dipolar field configuration, recent observations suggest the presence of multipole components that significantly influence emission processes. Our findings show that higher-order multipole magnetic fields shape localized particle emission regions near the NS surface, while the dipole field dominates at larger distances. By considering the NS's crust and superfluid core structure, as well as the effects of rapid rotation, we refine the understanding of magnetic field topologies and their impact on radiation mechanisms. This study highlights the necessity of incorporating multipolar magnetic fields for accurate modeling of pulsar and magnetar emissions. By investigating these effects, particularly the role of multipolar magnetic field components, researchers can refine theoretical models of emission mechanisms that go beyond the classical dipole framework. This has significant implications for interpreting observations of pulsars and magnetars, whose emission patterns, spectral features, and temporal variability often demand more complex field geometries. Furthermore, understanding particle emission driven by magnetic fields offers insight into neutron star spin-down evolution, magnetic field decay, and energy loss processes. Future work will involve detailed numerical simulations incorporating general relativistic effects and magnetosphere-plasma interactions.

Neutron stars provide a unique laboratory for studying matter at extreme pressures and densities. While there is no direct way to explore their interior structure, X-rays emitted from these stars can indirectly provide clues to the equation of state (EOS) of the superdense nuclear matter through the inference of the star's mass and radius. However, inference of EOS directly from a star's X-ray spectra is extremely challenging and is complicated by systematic uncertainties. The current state of the art is to use simulation-based likelihoods in a piece-wise method which relies on certain theoretical assumptions and simplifications about the uncertainties. It first infers the star's mass and radius to reduce the dimensionality of the problem, and from those quantities infer the EOS. We demonstrate a series of enhancements to the state of the art, in terms of realistic uncertainty quantification and a path towards circumventing the need for theoretical assumptions to infer physical properties with machine learning. We also demonstrate novel inference of the EOS directly from the high-dimensional spectra of observed stars, avoiding the intermediate mass-radius step. Our network is conditioned on the sources of uncertainty of each star, allowing for natural and complete propagation of uncertainties to the EOS.

Neutron stars provide a unique laboratory for studying matter at extreme pressures and densities. While there is no direct way to explore their interior structure, X-rays emitted from these stars can indirectly provide clues to the equation of state (EOS) of the superdense nuclear matter through the inference of the star's mass and radius. However, inference of EOS directly from a star's X-ray spectra is extremely challenging and is complicated by systematic uncertainties. The current state of the art is to use simulation-based likelihoods in a piece-wise method which relies on certain theoretical assumptions and simplifications about the uncertainties. It first infers the star's mass and radius to reduce the dimensionality of the problem, and from those quantities infer the EOS. We demonstrate a series of enhancements to the state of the art, in terms of realistic uncertainty quantification and a path towards circumventing the need for theoretical assumptions to infer physical properties with machine learning. We also demonstrate novel inference of the EOS directly from the high-dimensional spectra of observed stars, avoiding the intermediate mass-radius step. Our network is conditioned on the sources of uncertainty of each star, allowing for natural and complete propagation of uncertainties to the EOS.

Physical theory provides powerful tools for predicting instability, turbulence, and collapse, yet offers no unified account of why many systems persist far beyond their nominal failure thresholds. Across fluids, plasmas, gravitating matter, and relativistic spacetime, catastrophic outcomes are often theoretically permitted but empirically absent. In this work, we formalize persistence as a physical property governed not by optimization, adaptation, or equilibrium, but by geometric constraint acting on failure pathways. We define persistence through a single inequality comparing the characteristic recovery or equilibration timescale of a system to its fastest available failure timescale. When recovery proceeds faster than failure, collapse is suppressed regardless of stress magnitude. We test this criterion against high-stress astrophysical systems-including black hole accretion flows, neutron stars, relativistic jets, gravitational-wave remnants, and the cosmic microwave background-where gravitational, magnetic, and thermal stresses approach theoretical limits. In each case, predicted failure modes are not observed, while long-lived structures persist across many dynamical times. These observations indicate that persistence arises from constraint-induced suppression of low-dimensional failure manifolds, rather than fine-tuning or emergent optimization. We conclude that persistence constitutes a testable physical law, applicable across scales and independent of system composition, providing a unifying framework for understanding stability in non-equilibrium, high-stress environments.

We have performed detailed temporal and time-integrated spectral analysis of 286 bursts from SGR J1550 -5418 detected with the Fermi Gamma-ray Burst Monitor (GBM) in January 2009, resulting in the largest uniform sample of temporal and spectral properties of SGR J1550 -5418 bursts. We have used the combination of broadband and high time-resolution data provided with GBM to perform statistical studies for the source properties. We determine the durations, emission times, duty cycles and rise times for all bursts, and find that they are typical of SGR bursts. We explore various models in our spectral analysis, and conclude that the spectra of SGR J1550 -5418 bursts in the 8 -200 keV band are equally well described by optically thin thermal bremsstrahlung (OTTB), a power law with an exponential cutoff (Comptonized model), and two black-body functions (BB+BB). In the spectral fits with the Comptonized model we find a mean power-law index of -0.92, close to the OTTB index of -1. We show that there is an anti-correlation between the Comptonized E peak and the burst fluence and average flux. For the BB+BB fits we find that the fluences and emission areas of the two blackbody functions are correlated. The low-temperature BB has an emission area comparable to the neutron star surface area, independent of the temperature, while the high-temperature blackbody has a much smaller area and shows an anti-correlation between emission area and temperature. We compare the properties of these bursts with bursts observed from other SGR sources during extreme activations, and discuss the implications of our results in the context of magnetar burst models.

We present the discovery of a variable optical counterpart to the unidentified gamma-ray source 3FGL J0212.1+5320 and argue that this is a new compact binary millisecond pulsar (MSP) candidate. We show 3FGL J0212.1+5320 hosts a semidetached binary with a 0.869 55 ± 0.000 15 d orbital period and an F6-type companion star at an estimated distance of D = 1.1 ± 0.2 kpc, with a radial velocity curve semi-amplitude K 2 = 214.1 ± 5.0 km s -1 and a projected rotational velocity of V sin (i) = 73.2 ± 1.6 km s -1 . We find a hard X-ray source at the same location with a 0.5-10 keV luminosity L X = 2.6 × 10 32 (D/1.1 kpc) 2 erg s -1 , which strengthens the MSP identification. Our results imply a mass ratio q = M 2 /M 1 = 0.26 +0.02 -0.03 if the companion star fills its Roche lobe, and q 0.26 in any case. This classifies 3FGL J0212.1+5320 as a 'redback' binary MSP; if its MSP nature is confirmed, this will be the brightest compact binary MSP in the optical band (r 14.3 mag) and will have the longest orbital period among Galactic field systems (nearly 21 h). Based on the light curve peak-topeak amplitude ( r = 0.19 mag), we further suggest that the orbital inclination is high and the putative pulsar mass is close to canonical (M 1 1.3-1.6 M ). Finally, we discuss the lack of heating signatures and asymmetric optical light curves in the context of other redback MSPs.