2025/11/21 by Nala Trees
Mathematics · Physics and Astronomy · #Algebra #Algebraic Geometry #Algebraic and Geometric Analysis #Applied Mathematics #Artificial Intelligence and Robotics #Astrophysics and Astronomy #Black Holes and Theoretical Physics #Computer Sciences #Cosmology #Dynamic Systems #Dynamical Systems #Elementary Particles and Fields and String Theory #FOS: Mathematics #FOS: Physical sciences #Geometry and Topology #Harmonic Analysis and Representation #Mathematics #Non-linear Dynamics #Noncommutative and Quantum Gravity Theories #Number Theory #Other Applied Mathematics #Other Astrophysics and Astronomy #Other Physical Sciences and Mathematics #Other Physics #Partial Differential Equations #Physical Processes #Physical Sciences and Mathematics #Physics #Quantum Physics #Relativity #and Gravity
paper · doi:10.17605/osf.io/pm2cv
openalex publication_date 2025/11/21 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/11
The Spectral Geometry of Coherence is an 11 part series that rebuilds wave, gravity and prime number structure around a two channel ledger on declared windows. Parts 1 to 4 fix the analytic spine: a Gram matrix ledger for paired sectors, a unique way to read emergent time and speed from phase, a first order self adjoint Hamiltonian whose shear is locked to group delay, and a screen entropy that becomes a genuine geometric tension functional and entropy production density (REG). These ingredients yield near horizon timing bounds, capacity limits and relativistic compatibilities on the screen. Parts 5, 6 and 10 lift the same machinery into number theory, specifying a concrete Hilbert Pólya style operator pack for the Riemann zeta function, together with a Bost Connes based arithmetic thermostat and Dirac style coupling that feed into an Einstein form field equation set. Parts 7 to 9 and 11 develop corridor laws, microcurvature kernels, a gauge and gravity accommodating superalgebra, the associated “super” field equations, and a first order quantum gravity pack on a shared cone with BRST type differential, Ward identities and slow geometry maps that turn the ledger and capacity into testable curvature meters and lensing correctors. The series, framed as the HOLOGRAPH framework, makes clear which results are already analytically fixed and which are conjectural, and sets out explicit test pathways. The ledger, Hamiltonian, entropy and tension structures are intended as load bearing; the prime operator pack and first order quantum gravity constructions are presented as serious candidate routes for external expert review and empirical falsification.