This twenty-volume sequence explains the current model, its important equations and representative results. Particle patterns have different dimensional involvement in one infinite-dimensional physical spacetime, with matter occupying up to ten spatial directions and time treated separately. The current portion model uses one fundamental per pattern kind and a count-multiplied average registration. The mass-count prescription, conditional action constructions and their unresolved physical bridges are kept distinct. Detailed derivations remain linked from each volume. For the connected mass, spin, color and charge argument with its glossary and reproduction guide, read the new particle-geometry case.

Reviewed Connections Added on 5 November 2026

The numbered volumes now connect the conditional binomial selector, corrected massive carriers, prepared spin/color/charge structures, compatible spatial planes and the orthogonal commuting tetrahedron. They also distinguish the centered-only moving law, the centered-window common-action construction and the separate fixed-exponent six-depth radial comparison. Each volume explains the results relevant to its subject, including supplied inputs and remaining physical identifications.

Reading Sequence

  1. Research map and current status — The infinite-dimensional physical picture with a ten-dimensional matter domain, common-frequency portions, mass and geometric property results, with reviewed constructions, new proposals and open selection problems distinguished.

  2. Physical premises and nested spatial sectors — One field in infinitely many ordinary spatial dimensions plus time, with matter occupying up to ten and every remaining direction unbound for every particle, literal deterministic electron trajectories, and distinct internal structure, free extension, phase descriptions and detector registration.

  3. Spatial operator and contact toolkit — Spatial count operators, Clifford and contact algebra, and a proposed connectivity Laplacian, with coefficient descriptions kept distinct from physical spatial fields.

  4. Same-field actions and canonical normalization — Explicit candidate actions and canonical charges, including the newer square-root cluster law and its supplied source leaf, alongside earlier constructions with their own domains.

  5. Simplex spectrum and sector assignments — The exact cumulative simplex count, maintained particle assignments, shared-scale constraints and common-frequency portion interpretation, with additive average registration and count selection distinguished.

  6. Spatial carriers and compatible geometry — Spatial carriers, compact ten-dimensional profiles and conditional geometric constructions, with center-arrangement rank, field support and particle depth kept separate.

  7. Localization and same-field support — An exact compact normalized profile and its supporting energy, a reviewed restricted finite shape basin, and earlier localization constructions with their separate dynamical assumptions.

  8. Current mass-operator candidates — Comparison of compact support, square-root cluster mechanics and earlier mass candidates, identifying supplied counts and source constraints, attainable references and missing full-field dynamics.

  9. Common scales across particle sectors — The electron-based numerical scale prescription and kind-specific fundamentals, including the common charged-lepton unit, with coefficient origin and neutrino calibration kept explicit.

  10. The competing outer depth-ten branch — The depth-ten charged-lepton target and earlier competing support branches, distinguishing the common-kind clock from action-specific frequency and radius comparisons.

  11. Spatial and dynamical stability — A reviewed nonlinear shape-energy bound on a fixed-ball relative-profile class, alongside linear and conditional persistence results, with domain invariance and physical lifetime still open.

  12. Complete energy, inertia and causal motion — The old complete boost coefficient and newer count-proportional square-root inertia, their source and charge constraints, exact clock-preservation condition and provisional covariant rigid embedding.

  13. Photon geometry and physical polarization — The extended-connection photon hypothesis, transverse polarization and free-direction completion premise, with observable timing, conservation and protected masslessness still to be derived.

  14. Same-field coupling across sectors — Reciprocal same-field amplitude, phase and shape response, including a reviewed one-component prescribed-probe susceptibility and its limits as a physical pair interaction.

  15. Pair geometry and reciprocal encounters — Two responding spatial patterns with their own fundamentals, orientations and internal phases, including cluster separation and joining terms required for complete reciprocal energy balance.

  16. Neutrino frequency and interaction controls — Depth-five simplex splitting tests with a common fundamental, separating absolute calibration, neutral handed geometry, weak response, flavor and spatial-support requirements.

  17. Composite and hadronic mass — Composite mass from complete same-field dynamics, distinguishing internal portions from observed quarks and retaining relative motion, joining energy and unresolved nucleon construction.

  18. Orbits, binding and observed spatial patterns — Literal external electron trajectories in four spatial directions, four-direction precession, nuclear orientation hypotheses and deterministic detector averages, with binding dynamics open.

  19. Flavor, charge and gauge geometry — Full spatial half-spin, minimal clock depth selection, independent color contact and relative charge geometry, including the conserved free angular charge and its interacting-law limitation.

  20. Observational comparisons and remaining proofs — A joint assessment of mass accuracy, geometric properties, compact support, inertia and response, with conditional evidence, independent-review status and remaining common-action and count-selection problems.