Calculation record

Finite checks of spatial polarization and descending one-field coupling.

All models are conditional. No particle coupling constants are fitted.
Explicit runtime checks remain active under Python optimization.

Research context

  • Bilateral polarization coupling

    Keeping both objects polarized gives covariant tensor pairings, distinct source and response zeros, and a reciprocal orientation model with exactly conserved relative overlap.

  • Coherent spatial overlap

    Exact complex Gaussian overlaps retain both objects' shapes, polarizations, and spatial phases, while normalized opposing lobes give a concrete low-momentum source cancellation.

  • Descending photon source

    A higher-sector field sources a photon mode by projection over its bound coordinates while retaining normal propagation, with reciprocal feedback fixed by the same action.

  • Dirac source linearization

    The written scalar Dirac self-interaction gives an explicit real-linear response with ordinary and conjugate mode couplings determined by the higher spatial field.

  • Generalized sector coupling

    A common interaction on arbitrary nested sectors yields reciprocal responses, normalized vertices, and testable coupling relations, with neutrinos as a channel-specific control.

  • Isotropic polarization comparison

    Uniform five-dimensional null-axis and six-dimensional complex-structure tensors have identical photon-plane overlap distributions under an explicitly isotropic preparation.

  • Photon plane coupling

    Restricting a magnetic two-form overlap to the photon's actual two-plane gives a rank-two projector and an explicit polarization-dependent coupling diagnostic.

  • Polarized response spectrum

    A normalized two-sided mode coupling gives an exact finite-time polarization response matrix whose dark inputs depend on both spatial overlap and the target spectrum.

  • Spatial source complementarity

    Projecting a normalized odd-dimensional rotation tensor and its null-axis vector onto a lower spatial subspace gives an exact complementarity identity and conditional source-strength bound.

  • Diagnostic catalog

    Reproduction commands and scope descriptions for every local finite diagnostic and helper.

Interpret numerical checks within the assumptions and limitations documented in these notes.