Boris Batenin

HOLOMORPHIC HOPF–BELTRAMI MAXWELL MODES ON THE ROUND THREE-SPHERE: Exact Construction, Conformal Transport, and Penrose Representation

This work develops an explicit global construction of a distinguished family of null electromagnetic modes on the Einstein cylinder ℝ × S³. The starting point is the Hopf geometry of the round three-sphere and a global orthonormal frame X₁, X₂, X₃. For every homogeneous holomorph...

S³ LIGHT-TRISPHERE ATLAS: A Technical Atlas of an Interactive First-Principles Scientific Universe

S³ LIGHT-TRISPHERE ATLAS is an interactive scientific atlas that brings astronomical data, geometric constructions and computational models into a shared environment for exploration. This technical preprint by Boris Batenin and Andrei Preece documents seven worlds, 133 laboratori...

Quantum Support and Classical Actuality: A Translation-Map Audit and Coupled Causal Test

This work examines a foundational question that precedes many debates about quantum superposition: what mathematical map is required to translate quantum support into definite classical actuality? Quantum states, Born probabilities for a fixed measurement, and Boolean truth valua...

Killing–Beltrami Algebra and exact Reductions of Navier–Stokes Flow on the Three-Sphere

This paper develops an exact, SO(4)-equivariant interaction algebra for incompressible Navier–Stokes flow with Ebin–Marsden viscosity on the round three-sphere S³. Its central result is a chirality-dependent Killing–Beltrami intertwining law: for a Killing field Kτ and a signed c...

Killing–Beltrami Algebra and exact Reductions of Navier–Stokes Flow on the Three-Sphere

This paper develops an exact, SO(4)-equivariant interaction algebra for incompressible Navier–Stokes flow with Ebin–Marsden viscosity on the round three-sphere S³. Its central result is a chirality-dependent Killing–Beltrami intertwining law: for a Killing field Kτ and a signed c...

Finite-Dimensional Spectral Closure and a Relative Forced Singular Branch for Navier–Stokes on the Round Three-Sphere

This study develops a unified mathematical framework connecting finite-time singular dynamics, exact spectral closure, and geometric structure in the forced incompressible Navier–Stokes equations on the round three-sphere S³_R. Building on five explicitly stated assumptions about...

Finite-Dimensional Spectral Closure and a Relative Forced Singular Branch for Navier–Stokes on the Round Three-Sphere

This study develops a unified mathematical framework connecting finite-time singular dynamics, exact spectral closure, and geometric structure in the forced incompressible Navier–Stokes equations on the round three-sphere S³_R. Building on five explicitly stated assumptions about...

Pregeometric Relational Dynamics and Universal Causal Structure: Spectral Constraints, Response Limits, Universal Null Calibration and Functional Consistency of Light

This work develops a unified framework for pregeometric relational dynamics, asking how locality, geometry and a universal causal structure can arise as effective properties of an underlying system that is not assumed to possess a manifold, metric or causal order from the outset....

Pregeometric Relational Dynamics and Universal Causal Structure. Spectral Constraints and Conditions for a Common Low-Energy Cone

This work develops a concrete spectral framework for pregeometric relational dynamics, asking whether quasilocality, spatial geometry, and a universal causal structure can arise as effective properties of a closed system whose fundamental description contains relations rather tha...

Acyclic CIVP–Index Locking, Molecular Corner Statistics, Entropy–Flux Structure, and Capacity Selection in Trace-Free de Sitter Gravity

This work develops a type-safe statistical and operator-algebraic framework for sector selection in trace-free de Sitter gravity, built around intersecting null boundaries and the quantum characteristic initial-value problem (CIVP). The construction begins with a positive atomic...

The Fermi Non-paradox: Statistical Experiments, Observational Indistinguishability, and SETI Null Results

Statistical Experiments, Observational Indistinguishability, and SETI Null Results reframes the Fermi question not as a cosmic verdict, but as a problem of statistical inference under limited observational power. The central claim is simple but decisive: a SETI null result constr...

Capacity-Fixed Trace-Free Gravity and Non-Perturbative Edge-Partition Boundary Selection

This work reframes the cosmological-constant problem by separating what gravity determines locally from what must be selected globally. The exact trace-free field equation Rμν − ¼Rgμν = 8πG(Tμν − ¼Tgμν) places every constant vacuum-stress shift in the kernel of the source project...

Finite Dilation Algebra of Round Euclidean B⁴/S³. Valuation Profiles: Exact Invariants, Homogeneous Gravity Closure, and Executed Null Tests

What if the homogeneous dark-sector problem could be reduced from an arbitrary function of cosmic scale to a finite algebra of geometrically admissible profiles, with exact invariants that can be tested directly against numerical cosmology? This work develops such a construction...

Homothetic Valuation Spectrum of a Quasilocal B⁴ Filling and an Effective Residual Sector on Compact S³

This work develops a geometric-variational framework for classifying homogeneous residual sectors in a closed FLRW cosmology with spatial carrier Σ ≃ S³. The four-dimensional ball B⁴_A is used exclusively as an auxiliary quasilocal filling and valuation structure, not as a physic...

Finite Dilation Operator Algebra of Homothetic B⁴/S³ Valuations and Homogeneous Closure Tests for Valuation Dark Energy

What happens when a geometric reconstruction is forced to become a finite, testable algebra rather than an arbitrary background fit? This work develops a finite dilation-operator framework for homothetic B⁴/S³ valuations in closed FLRW cosmology. The physical carrier remains the...

Homothetic Valuation Spectrum of a Quasilocal B⁴ Filling and an Effective Residual Sector on Compact S³

This work develops a geometric-variational framework for classifying homogeneous residual sectors in a closed FLRW cosmology with spatial carrier Σ ≃ S³. The four-dimensional ball B⁴_A is used exclusively as an auxiliary quasilocal filling and valuation structure, not as a physic...

Homothetic Valuation Spectrum of a Quasilocal B⁴ Filling and an Effective Residual Sector on Compact S³

This work develops a geometric-variational framework for describing an effective residual sector in a compact cosmology while keeping the physical arena strictly four-dimensional: M = I × S³_A. The four-ball B⁴. A is introduced only as a quasilocal filling, geometric measure, and...