Interactions of solved cores and smooth binding

python experiments/localized_core_pair_checks.py runs 122 conditions for the initial pair of localized cores. It retains the complete currents and both source variations, independently integrates the initial spatial energy, and verifies the allowed cancelling-current preparation and its fractional variation singularity.

python experiments/smooth_current_core_checks.py verifies smooth matrix and full field variations, refined depth-six cores, both spatial virials, unchanged frequencies and complete boosted equations and stress. It also checks the full ordinary/conjugate Hessian and bounded angular spectra, with an exact slow-block calculation for the muon. The same smooth coefficient choices apply across grades. These are inverse actions and finite response tests, without an observed vertex or full stability claim.

Dimensionless binding and spatial size

python experiments/scaled_gap_core_checks.py runs 89 conditions for the depth-dependent localized cores. It refines independent spatial profiles and boundary endpoints, verifies both virials with actual spatial derivatives, retains all five, six and ten ordinary Clifford directions, and checks canonical norm, frequency, size scaling, full boosted equations and every stress component. The stored profiles and derivatives make the size factors reproducible. The calculation supplies inverse fixed points, without deriving occupied mode selection, observed vertices or complete spatial stability.

Spatial coefficient frames from the field current

python experiments/rest_current_carrier_checks.py runs 60 conditions for the same-current spatial carrier. It verifies the complete covariant action and its field-dependent kinetic term, the unchanged frequency and linear response conditions, and a finite textured probe comparison. Direct time-form variations and an exact principal propagator expose a polarized high-wave-number limitation. The limitation is retained explicitly; the test is not a stability claim.

Localized frequency, inertia and response

python experiments/localized_current_inertia_checks.py runs 70 conditions for the localized oscillating field. It checks the complete current action, spatial fixed point, boosted field equation and stress, exact simplex contractions and canonical inertia in all six ordinary directions. A finite unit-norm probe comparison retains the full source and reciprocal target force.

python experiments/localized_current_response_checks.py runs 338 conditions for the spatial response. Independent Cartesian derivatives verify the angular reduction; direct radial matching confirms genuine growing controls. Finite electron and muon scans retain all tested Clifford partners, and an exact fast-block elimination resolves a misleading slow numerical mode. Full spatial stability and the master origin of the inverse action remain open.

Both reports preserve exact executed-source hashes and their numerical arrays. The response dataset includes complete finite spectra and projected generators. Neither passing count represents a proof of the unresolved physical premises.

Surface bending frequencies and response

python experiments/bending_surface_checks.py runs 151 conditions for the surface-bending spectrum and its nonlinear spatial response. The calculation retains both normal directions and verifies the actual curvature energy, exact sphere differential operator, fixed particle indices, moving-frame tension response and complete translation tensor. Independent third variations check canonical mode coupling, an exact resonance, reciprocal complex transfer and the scale-response identities. The surface and its time law are declared comparisons, with no derived master-field realization or completed particle inertia.

python experiments/surface_kinetic_projection_checks.py adds 25 conditions for the surface kinetic projection. Independent Cartesian field derivatives and boundary Fourier derivatives verify the complete normal current integral, profile independence at a fixed background, and cancellation for localized fields. Every complex spinor component and unitary basis covariance are retained. The test does not establish the prescribed core as a spatial master-field solution.

Physical premise (IDWT): Physical spacetime has infinitely many ordinary spatial dimensions plus time. Matter occupies up to ten spatial dimensions; all remaining spatial directions are unbound for every particle. Depth counts a pattern's bound spatial involvement within that space. “Observed” and “unobserved” describe an observer's access, not different kinds of dimension. Older projective and nested-geometry calculations below retain their additional hypotheses; they do not establish a separate physical manifold or compactified direction. See spatial meaning and mathematical scope.

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

The scalar Hartree, circulating-field, and fixed-oscillator projection checks verify auxiliary models. Their success does not establish the trajectories or stability of the actual electron orbits in the 6D demo.

Existing checks

spectral_count_checks.py and quasiperiodic_phase_checks.py verify spectral counts in a responsive cavity: protected ranks, changing spatial projectors, fixed benchmark frequency units, reciprocal phase variation and full nonlinear spatial trajectories. The harmonic confinement and occupied frame remain declared comparison inputs.

cavity_form_factor_checks.py checks the spatial and moving-cavity response using complete band transitions, signed energy-transfer moments, independent complex spatial quadrature, both polarized profiles and actual moving scalar and Dirac modes. The exact formulas are implemented in cavity_form_factors.py.

cavity_balance_checks.py checks the common cavity balance, including independent energy minimization, complete nonlinear breathing trajectories, reciprocal probe spectra and normalized spatial density marginals. These are declared inverse actions and spatial controls.

cavity_inertia_checks.py checks the moving-cavity inertia through complete spectral response, independent spatial Dirac residuals and analytic boosted spinors, and complete complex driven fields with time and spatial refinement. The quadratic control includes an input kinetic mass; the first-order control has a prescribed well and retains both Dirac signs. The equations are implemented in cavity_inertia.py.

coherent_normal_contact_checks.py verifies 203 conditions for the coherent normal-source contact limit: complete target spectra, exact operator errors and integer concentration thresholds, scalar self-energy bounds, full signed Dirac stationary gradients and fixed-population controls. Independent positive-density quadrature verifies the normalized source moments and concentration inequalities. The exact positive two-moment energy minimum is checked with independent quadrature orders and constrained positive variations. Both execution modes preserve the same mathematical results.

The reciprocal normal stability calculation is checked by gapped_reciprocal_normal_checks.py. With the coarse and refined equal-norm trajectory reports supplied through --trajectories, it verifies 183 conditions: complete finite-gap density linearization, an independent angular block and quartic, canonical action variations, conserved moments and full nonlinear amplification. The trajectories retain both normal Dirac signs and the reciprocal target ray in their stated zero-spatial-kinetic mode control.

The complementary Dirac self-source and balanced normal geometric response have five complementary executable diagnostics. The canonical spectral reduction, complete scalar-square shell projection, full finite-gap Liouvillians and both reciprocal partners are checked independently. The normal and optimized executions each pass 925 conditions in total. All finite-mode conclusions retain their stated physical occupation and spatial assumptions.

The flat radial self-mass boundary and full-current localization condition have independent analytic and numerical controls. Both normal and optimized execution give the same 2,599 mathematical checks.

  • python experiments/local_self_mass_localization_checks.py checks smooth tail bounds, complete complex radial identities, root profiles and physical dilations.
  • python experiments/positive_current_localization_checks.py checks full matrix positivity, the scalar identity, signed controls and the spatial derivative of the actual mass-sign projector.

The nonexistence results use the hypotheses stated in their proofs. The textured six-dimensional field is a trial field that fails the stationary virial; it is not a computed bound particle.

  • python experiments/graded_current_tower_checks.py checks the full current contractions and coherent source sums.
  • python experiments/graded_current_actions_checks.py checks the root and smooth laws and their complete probe responses.
  • python experiments/smooth_current_projection_checks.py compares reduced currents with independent symmetric products.
  • python experiments/coherent_kernel_inverse_checks.py checks finite-band harmonic reconstruction and common positive-kernel constraints.
  • python experiments/saturated_projective_checks.py verifies spatial action derivatives and a direct first-order instability calculation.
  • python experiments/projective_jacobi_basis_checks.py checks the accelerated basis against independent special functions and differential equations.
  • python experiments/smooth_spatial_mass_selection_checks.py checks uniform spatial controls, complete probe occupations and the holomorphic shape force.
  • python experiments/smooth_spatial_response_comparison.py compares full probe operators on the recorded resolved spatial fields.

The last command reads the two saved spatial control reports named in its source. saturated_projective_continuation.py reproduces the fields; saturated_projective_response.py and saturated_projective_tracked_response.py refine their growing modes independently of the background cutoff. The tracked calculation requires --report, --case, --cutoffs and --target-oscillation; its scope is a specified frequency, not an exhaustive search for every instability.

graded_current_tower_flow.py and graded_current_root_flow.py retain all occupations in their stated invariant coefficient subspace. Their two tolerance refinements are compared using python experiments/graded_current_flow_comparison.py --coarse REPORT --fine REPORT. Each comparison adds ten checks of the complete complex trajectory and conserved quantities. These coefficient controls do not represent full spatial particle encounters, and the spatial examples do not establish the physical radius, selected norm or particle assignments.

  • mass_energy_response_checks.py verifies the energy constraints from scalar response with 812 checks. Exact ratio identities, free-limit bounds, signed-current sum rules, full complex source variations, canonical norm continuation and independent curved derivatives link energy to the same interaction response. Spatial Schur reduction, free spectral sums and actual changes of the common law check shape relaxation and inverse energy-frequency sensitivities.

  • excited_scalar_resonance_checks.py verifies the reciprocal response of excited spatial branches with 565 checks. Independent spatial current integrals derive the near-resonance matrix. Nonlinear continuation and increasing cutoffs retain full paired profiles, complex feedback, norm and phase identities, and independently differentiated stationary and response residuals.

  • inverse_scalar_law_checks.py verifies the inverse scalar-law reconstruction with 678 checks. Complete complex source residuals and action variations retain every scalar response component. Independent curved derivatives test pure-pair current zeros and reconstruct the same law and coupling derivative from two normalized nonlinear spatial branches.

  • inverse_simplex_causality_checks.py verifies the causal constraint on inverse dynamics with 702 checks. Exact curved differential commutators and independent Jacobi multiplication coefficients establish an unbounded norm for every inverse root allocation. Full paired quadrature and the original Dirac comparison retain both frequency branches and spatial derivatives.

  • inverse_simplex_response_checks.py with 911 checks. Complete complex frequency projectors retain both scalar channels. Exact beta integrals and independent curved quadrature check complete spatial self-sources; complex action variations and relative-phase reversal verify reciprocal mode response.

  • inverse_simplex_dynamics_checks.py verifies the inverse simplex dynamics. Independent complex root allocations and real polynomial recurrences classify the local candidates. Actual curved differential operators, complete spinor complements, noncommuting kinetic metrics and complex energy variations check their reconstructed action and exact frequencies.

  • projective_spectral_contact_checks.py with 4,079 checks. Independent Weyl dimensions, spatial kernel sums and mixed complex derivatives retain complete shell and point polarizations. Exact beta integrals and independent curved quadrature test the full smooth scalar source, its complementary residuals and complex reciprocal variations of the paired spatial action.

  • projective_jet_norm_checks.py with 469 checks. Complete interpolation matrices, independent tensor contractions, exact norm polynomials and spatial quadrature retain the full kinetic metric. Arbitrary complex scalar-source variations and isometric compression check the fixed-background response bound.

  • projective_derivative_simplex_checks.py with 2,577 checks. Independent full coordinate jets, physical tensor norms across projective charts, exact beta integrals and complete differential adjoints derive the simplex polynomial. Positive-weight quadrature retains cross terms and arbitrary complex spatial amplitudes.

  • projective_mass_inheritance_checks.py with 1,504 checks. All form and line-degree matches, an independent full Clifford algebra, normal rotations, complex normal derivatives, complete Schur variations and reconstructed canonical eigenvectors retain the normal components and their induced kinetic norm.

  • projective_spinor_simplex_checks.py with 2,399 checks. Two complete spectral descriptions and independent Weyl dimensions agree. Exact curved Jacobi differentiation, physical Gram quadrature, full complex variations and local Hodge channel identities check the simplex spectrum and Hermitian scalar action.

  • normal_dirac_extension_checks.py verifies the normal Dirac extension with 510 checks. Full parent Clifford matrices, spectral projectors, independent normal quadrature, complex action variations and actual curved Killing fields verify the induced norm and complementary source. Complete normal Fourier matrices check the positive kinetic square used in the analytic full-line binding argument.

  • round_local_scalar_gap_checks.py verifies the exact local scalar gap with 1,222 checks. Complete spatial variations, independent harmonic Gram integrals, exact secular determinants and canonical generators check the field, its full spectral-stability proof and the response to an added conformal current term. Physical energy and norm are retained.

  • conformal_current_response_checks.py verifies the conformal scalar-current response with 681 checks. Full spatial Clifford and Killing identities, complex current variations, exact canonical blocks and rational harmonic scans establish the stated response and instability of this candidate branch.

  • killing_spinor_simplex_checks.py verifies the Killing-spinor transfer with 1,213 checks. Independent spatial Dirac differentiation acts on arbitrary complex spinor jets. Exact polynomial and multiplicity checks retain both signs, while complete action variations test the mass insertion.

  • conformal_simplex_spectrum_checks.py verifies the conformal scalar simplex spectrum with 1,995 checks. Exact operator products, conformal commutators and independent spatial derivatives retain both zonal and complex angular fields.

  • constant_density_bundle_checks.py with 877 checks. An exact quartic polynomial identity, independent trace-copy normalizations, complete connection intertwining, and physical chart and Dolbeault checks retain the full spatial field. Norm, volume, energy and copy-charge checks keep the common scalar coefficient separate from a derived physical mass or stability claim.

  • local_current_jet_checks.py verifies local contact on physical derivatives with 423 checks. Independent symbolic polynomials, full complex variations through a 448-dimensional real Jacobian, both scalar polarizations, exact phase cancellations, and two covariant derivative constructions retain the written source coefficient. These are source identities, not full particle spectra.

  • tangent_band_contact_checks.py with 24,781 checks: complete occupation characters, all Dolbeault cohomologies and their independent Euler index, Serre duality, the full point spectrum and sharp bound, and independent spatial integration of all vector fields and the 120 quadratic generators with 84 independent sections. The result concerns a specified zero-form operator channel.

  • coherent_spatial_bundle_checks.py with 380 checks: chart transitions, the natural Chern connection, full coherent tensors, amplitude and ray derivatives, exact factorial norms, independent spatial cubature, local source leakage and complete complex variation of a reciprocal graph-pair action. No stability is asserted.

  • balanced_spatial_mass_checks.py with 434 checks: independent monomial integrals, nonconstant spatial density, balanced moments, source projections, physical-chart Dirac derivatives, full source Gram matrices and every nonzero linear frequency, including complex rotated fields and zero directions.

  • projective_linear_source_checks.py with 1,070 checks: independent complex angular averages, coherent density harmonics, full spatial source derivatives, two radial cutoffs, a separate screened differential solve, and exact nonlinear overlap conservation. These test specified kernels and their spatial limits.

  • scalar_gap_normalization_checks.py verifies the canonically normalized scalar gap with 543 checks: full complex derivatives, all degenerate polarizations, the collective pole and residue, nonlinear conservation, threshold and saturation limits, and exact cumulative shell moments. The specified instantaneous global kernel is a comparison, not a derived mass law.

  • nonlinear_mass_reduction_checks.py verifies the nonlinear spatial mass reduction with 500 checks: complex complementary solves, induced normalization, full real Schur Hessians, common-frame covariance, normalized energy and frequency, fifth-order remainders, independent six-dimensional spatial continuation and the fixed-action simplex-coefficient comparison. These are conditional operator tests, not a derived physical mass spectrum.

  • projective_source_projection_checks.py through independent normal-direction quadrature with all phases, exact normalized current blocks, weighted chain composition and both complete scalar-Dirac source variations under common physical rotations.

  • projective_normal_bundle_checks.py using ambient metric derivatives, normal curvature and loop transport, complete Clifford weights, physical line twists and invariant matrices.

  • coherent_kernel_consistency_checks.py tests cumulative kernel consistency and finite ray resolution, using full complex band matrices, direct and staged Schur elimination, independent beta/CP1 quadrature, exact spectra and controlled limits.

  • spatial_oscillator_projection_checks.py checks weighted source marginals and spatial point contact. Exact occupation sums, independent spatial/Fourier quadrature, full mode matrices, rotated inclusions and bilinear partial traces verify the distinction between a linear source count and a physical current.

  • local_scalar_profile_checks.py verifies spatial contact normalization and the identities used in the massless radial theorem. Checks include an exact massive profile, independent Cartesian derivatives with complex spinors, spatial quadrature, Bessel fundamental matrices and illustrative radial tails.

  • coherent_pair_variation_checks.py verifies complete pair deformation and the aligned ambient Hessian, with independent FS quadrature, full complex frame covariance, exact conservation balances and reversed nonlinear trajectories. coherent_pair_algebra.py supplies the cross-degree products and both reciprocal derivatives.

  • graph_contact_variation_checks.py verifies the defined graph action, its cancelling projector-curvature terms, complete coefficient Hessian and reciprocal ray trajectories with common mode-frame covariance.

  • coherent_contact_variation_checks.py checks the complete smooth quartic action by independent FS quadrature, variational derivatives, coherent extrema, all mode Hessian sectors and full nonlinear coefficient evolution. coherent_mode_algebra.py supplies normalized symmetric products and exact large-band coefficients.

  • polarized_pulse_collision_checks.py checks exact collision geometry, independent nonlinear Hamiltonian evolution, reciprocal pulse delays, complex-polarization source cancellation and full spatial spectral radiation with direct forced-mode normalization.

  • retarded_displacement_checks.py checks the full spatial Hessian reduction, positive spectral moments, variational response bounds, soft logarithm and outgoing spatial modes.

  • null_spatial_wave_checks.py checks exact finite null pulses, canonical spatial norms, complete moving planes and the independent complementary source and quartic action.

  • spatial_charge_generator_checks.py checks local charge continuity, complete spatial kinetic commutants, neutral-kernel evolution and orbital-plus-spin conservation.

  • soft_photon_response_checks.py checks full spatial symplectic/current integrals, complete reciprocal source feedback, photon phase and polarization response, the magnetic-moment benchmark, and the moving-frame normalization in canonical spin response.

  • collective_translation_wave_checks.py checks full-source translation waves, exact kinetic coefficients, normal and conjugate partners, physical-space identities and Cartesian refinement.

  • spatial_polarization_structure_checks.py checks complete spatial Clifford descriptors, equal-current radial fields, reciprocal six-inside-ten rotation dynamics and omitted texture response through independent full spatial equations and nonlinear evolution.

  • periodic_polarization_checks.py checks full occupied-polarization sideband tensors, input-conditioned kernels, complete spectral residues and normal-momentum opening with spatial covariance.

  • antilinear_dirac_checks.py checks complete spatial antilinear intertwiners, arbitrary-field scalar interference, nonlinear source transformations and nested projection compatibility.

  • paired_periodic_response_checks.py checks both nonlinear nested Cartesian sources, scalar centers, deformation sidebands and independent full-field versus two-clock moment response.

  • slow_shape_pole_checks.py checks full ordinary/conjugate shape resolvents, slow poles, signed canonical residues, radial refinement and the distinction between a small pole and total response.

  • nested_bifrequency_checks.py checks complete anisotropic two-frequency fields with both profiles readjusted, independent spatial equations and the finite containing-source frequency limit.

  • periodic_current_checks.py checks the full spatial number-current sidebands, occupied-polarization selection, exact normal continuity and current reconstruction after feedback.

  • radial_bifrequency_checks.py checks arbitrary complex radial profiles in the full spatial field, separate number and symplectic weights, nonlinear radial reconstruction, inherited oscillating growth and stationary current-clock derivatives.

  • periodic_dirac_response_checks.py checks complete periodic spatial source variations, exact finite spectral sideband criteria, independent time-dependent forcing and matched full-field and moment Floquet equations, including scalar-center response.

  • source_frequency_checks.py checks spatial bilinear and cubic source frequencies, normal transition clocks, exact normalized two-frequency solutions of the full field equation, current continuity, source curvature and normalized response scaling.

  • incoming_shape_mode_checks.py checks exact spatial helicity restriction bounds, complete ordinary/conjugate Dirac shape modes, reciprocal incoming and forced responses, and cancellation between spatial components at low forcing frequency.

  • dirac_reflection_symmetry_checks.py checks full differential reflection symmetries, independent Cartesian spectral multiplicities, physical rotation commutators and scalar moment compression within one polarization multiplet.

  • dirac_polarization_wave_checks.py checks the complete spatial polarization frame, gapless normal modes, exact nonlinear polarized waves, scalar source preservation and changing bound spatial currents.

  • nested_shape_visibility_checks.py checks persistent spatial kernels, independent exact rational ranks, common-coefficient Dirac feedback, complete lower breathing response and quadratic frequency barriers across nested depths.

  • coupled_scalar_envelope_checks.py checks reciprocal scalar envelope couplings from full nested spatial profile response, energy derivatives, common and relative amplitude modes, and the complete ordinary/conjugate stability matrix pencil.

  • normal_dirac_transport_checks.py checks exact normal boosts of full spatial Dirac modes, scalar source invariance, density and current normalization, polarization-dependent centroid shifts, and the specified scalar envelope action and spectrum.

  • spatial_shape_transfer_checks.py checks complete polarized shape response, nested tensor restrictions, dynamical opening of static zeros, reciprocal weak-contact response, both spatial preparations and low/high-frequency completeness identities.

  • nested_dirac_pair_checks.py checks complete anisotropic spatial Dirac fields, independent radial representations, coupled nested profiles under one scalar coefficient, their scaling, and reciprocal derivatives of both partner sources.

  • angular_dirac_response_checks.py checks full spatial dipole and quadrupole Dirac sources, their polarization Gram matrices, radial operators, reciprocal conjugate response, and the translation zero mode of the centered interaction. Independent full-field finite differences verify the source and its energy Hessian.

  • spatial_dirac_mode_checks.py checks complete spatial rotation modes and currents, self-consistent scalar Dirac radial profiles, basis convergence, virial identities, and nonlinear evolution of an unstable radial perturbation.

  • dressed_coupling_checks.py verifies reconstructed spatial source vertices, their physical norm, full-operator energy shifts, and finite-frequency continuity identities. These three diagnostics write timestamped reports and retain their checks under Python optimization; physical particle and current identification remains subject to the assumptions of each model.

  • spatial_coupling_mechanism_checks.py checks full photon transition matrices, balanced spatial rotation modes, nested embeddings, nonlocal source variations, quadrupole shape vertices, reciprocal scattering, direct wavepacket propagation, and neutral-doublet transport. Run python experiments/spatial_coupling_mechanism_checks.py; its timestamped report preserves previous evidence, and checks remain active under python -O. These are conditional mathematical mechanisms, not fitted particle couplings. Derivations are linked from Generalized sector coupling.

  • polarization_coupling_checks.py checks two-sided polarization, photon-mode projection, nonlinear Dirac source derivatives, spatial source complementarity, finite-time response, and coherent spatial overlaps. See the spatial-polarization section of Generalized sector coupling.

  • generalized_coupling_checks.py checks weighted spatial reciprocity, coupled energy conservation, canonical vertex normalization, same-field response rank, Gaussian coupling profiles, and neutral versus weak channel selection. See Generalized sector coupling.

  • resonance_profile_checks.py checks Coulomb integrals, zonal overlaps, cyclic spectra, dispersion response, radial form bounds, chiral mass curvature, quartic conservation, and rotation multiplicities. See Resonance and profile tools.

  • spectral_analysis_checks.py checks recurrence, continuum memory, bounded perturbations, Gaussian profile geometry, simplex zeta continuation, spatial projections, and null calibration. See Spectral analysis tools for the full derivations and hypotheses.

  • spatial_profile_checks.py checks spatial Gaussian contacts, harmonic confinement examples, and stress conservation under fibre integration. See the Interaction operator tools for the derivations and their domain assumptions.

  • interaction_operator_checks.py checks normalized Green marginals, projected variations, colour singlets, angular parity, Dirac heat curvature, and anomaly identities. See the Interaction operator tools for the additions, their assumptions, and their application to V2.

  • mass_transfer_checks.py checks exact band moments, oscillator convolutions and overlaps, weighted evaluation bounds, heat sums, and sphere counts. See the Counting mode tools for their assumptions and the open resonance question.

  • foundation_transfer_checks.py verifies centred scalar variations and covariance, separated barrier and lift identities, and reciprocal simplex sums. See the Nested spatial tools for the assumptions of these conditional results.

  • localized_polarization_stationarity_checks.py compares spatial first variations in five and six dimensions under a separately fingerprinted protocol, retaining the same kernel and omitting compensating channels.

  • frozen_magnetic_texture_checks.py verifies a fingerprinted protocol for spatial polarization textures, independently compares analytic curvature with nonlinear Fourier energies, and reports rejected preparations without treating a scientifically negative outcome as a broken test runner.

  • accurate_cylindrical_continuation.py is an optional-argument shooting tool requiring a fresh --output path; it is not automatically run by the suite.

  • cylindrical_orbit_stability.py takes a corrected candidate and fresh --output path, computing full-coordinate Floquet matrices and optional fixed-Casimir nonlinear growth probes. It is not an automatic suite entry.

  • cylindrical_refinement_checks.py recomputes ten candidate closures with boundary-segmented DOP853 and Radau, plus the exact linear block splitting.

  • dimensional_necessity_checks.py checks response-rank identities, averaging counterexamples, and the same-equation five-dimensional inclusion. Its optional --integrate mode also reproduces three five-dimensional orbits; --output accepts a fresh evidence path. Optional --output writes a fresh evidence report.

  • spinor_response_poles_checks.py derives and verifies the coupled source/spinor frequencies in five and six dimensions, checks the nonlinear variational derivative, and reproduces small-perturbation evolution.

  • dimensional_magnetic_kernel_checks.py compares the existing constrained magnetic kernel in five and six dimensions, checks envelope-anisotropy selection, and verifies the vector channel in five-dimensional scalar exchange.

  • moment_kernel_checks.py checks the scalar coupled moment model's stationary covariance, full Hessian, and mixed-source response. It requires NumPy and does not derive an embedding, spinor lock, or physical frequency.

  • ckm_count_audit_checks_2026_09_05.py checks ranks, degree-loss support, kinetic-metric normalization, unitary completions, and rephasing-invariant CP examples. It does not fit or derive the physical CKM matrix.

  • progress_checks_2026_09_05.py checks static versus frequency-dependent reductions, colour-pair coefficients, projectors, contact spectra, and conditional common-anchor ratios.

  • common_anchor_action_checks_2026_09_05.py verifies the exact Case-A/Case-B count mismatch for the current common-anchor action audit.

  • two_electron_depth6_checks_2026_09_05.py checks the dimensional counts, Gaussian unobserved-impact coefficient, and a conditional lock metric example. Its base-kernel exponent N=12N=12 is a trial input, not a derived transfer of the electron mass-band degree to the base-coordinate interaction.

  • two_electron_pair_invariant_check_2026_09_05.py verifies the exact collapse of the complex-structure alignment invariant to the Fubini--Study pair overlap, C_J=(4 nu-1)/3.

  • two_electron_scalar_quartic_check_2026_09_05.py verifies the exact two-packet expansion of the current depth-six scalar quartic and its incoherent two-electron cross term.

  • dimensional_em_green_function_check_2026_09_05.py verifies the three- versus six-spatial-dimensional electrostatic Green-function coefficients used to test full-dimensional electromagnetic propagation.

  • operator_lift_kernel_check_2026_09_05.py verifies the block-operator distinction between direct projection and effective reduced dynamics used in the electromagnetic inverse-lifting audit.

  • hidden_visible_lock_schur_check_2026_09_05.py verifies the exact self-adjoint 3+3 lock block, its three zero/three restoring modes, and its vanishing relaxed Schur complement.

  • free_electron_pair_rotation_check_2026_09_05.py computes R=-J1 J2, its characteristic polynomial and overlap trace from Clifford bilinears. The canonical real split is 2+4; a 2+2 subdivision of that active space is not canonical.

  • free_electron_pair_quaternionic_check_2026_09_05.py computes the symbolic generic quaternionic identities and solves the active commutant at an exact nondegenerate representative.

  • free_pair_equivariant_operator_check_2026_09_05.py solves the simultaneous commutant equations: symmetric span {P0,P4}, four skew generators, and no commuting mixed maps. This is not a classification of all covariant operators.

  • free_pair_scattering_mixed_rank_check_2026_09_05.py checks minors and exact saturating examples for the specified one- and two-outer-product ansatzes.

  • beam_adapted_frame_link_check_2026_09_05.py verifies the exact relation between Fubini--Study pair separation and relative SO(3) frame-link mismatch in a common beam-selected 3+3 split.

  • two_electron_relative_lock_check_2026_09_05.py verifies the conditional relative unobserved/visible separation theorem for two individually locked electrons in a common beam-adapted 3+3 frame.

  • two_electron_com_relative_energy_check_2026_09_05.py verifies the exact center-of-mass reduction of two individual beam locks to one relative restoring energy.

  • electromagnetic_mixed_block_rank_check_2026_09_05.py verifies that a simple 6D bivector has mixed 3x3 block rank at most two, while the direct depth-two electromagnetic lift has zero mixed block in a beam-adapted observed plane.

Reproduce the finite checks

From the repository root, run the registered diagnostic scripts:

python3 -B experiments/run_checks.py

For the independent audit suite without the two long continuation searches:

OPENBLAS_NUM_THREADS=1 OMP_NUM_THREADS=1 python3 -B experiments/run_checks.py --skip-continuation --jobs 3 --report experiments/results/audit-2026-09-07/reproduction-suite.json

Exclusions are named in the output and report. The archived-state refinement test still runs; its diagnostic success does not imply candidate acceptance.

The runner uses the current Python interpreter, reports failures with nonzero exit status, and disables bytecode writes. The checks require SciPy, SymPy, mpmath, and NumPy; they do not install dependencies. electron_pair_algebra.py supplies the shared explicit Clifford construction. correction_checks_2026_09_06.py covers the normalization, topology prerequisites, action/frequency, rank-two Hessian, Clifford-commutator domain, and numerical corrections.

The original two larger audits can also be run individually from the repository root:

python3 experiments/progress_checks_2026_09_05.py
python3 experiments/ckm_count_audit_checks_2026_09_05.py

The check script uses SymPy. It checks finite algebra and comparison operators. It does not install dependencies, modify the modules, fit an amplitude, solve the V2 master equation, or predict a baryon mass.

Status vocabulary: checked algebra denotes a verified identity or spectrum for the specified operator; conditional mechanism denotes a sufficient construction whose physical premises remain unproved; source audit records what particular inspected passages say; withdrawn inference identifies an earlier conclusion that exceeded its calculation; open denotes a remaining proof obligation.

Complete complex projective spatial pair

Local scalar response and spatial kernel limits

Local autonomous polarized Dirac collisions

python experiments/local_polarized_collision_checks.py runs 153 checks of local polarized pulse coupling and changing nonlinear compatibility. Full Clifford reconstruction and physical rotation tests retain all traveling polarizations. Exact source-zero crossings, independent spacetime integration, complex action derivatives and weak-scattering convergence test both responses. Complete nonlinear evolution is compared with an independent Fourier/DOP853 solver and three spatial refinements. Matrix norm, momentum, support and energy checks constrain the evolution; normalization does not remove either sign of the observed compatibility change. Continuous positive-frequency integrals separately test the vanishing conjugate channel. These flat, transversely homogeneous controls do not identify particles or depth selection.

Complete scalar source response and null directions

python experiments/local_scalar_response_rank_checks.py runs 2,116 checks of complete scalar response. Independent nonlinear source differences verify the real-linear derivative; full spectra, multiplicities, determinants, exact inverse maps and singular values test both nonzero and null scalar backgrounds. Selected channel zeros and occupied-ray projection are distinguished from the full source rank. Full complex Clifford evolution in three, six and ten spatial dimensions checks transverse scalar activation against an independent nonlinear scalar oscillator, including positive density, total energy and its first integral. The activation control is an unbound plane with both signs of free kinetic energy; it is not identified with an incoming physical particle.

Full spatial plane response and kinetic null classes

python experiments/scalar_plane_response_checks.py runs 2,594 checks of kinetic scalar nullity, the complete null-plane response, and moving nonlinear scalar planes. It verifies every depth from one through ten for the kinetic class classification. Full spatial Clifford symbols, conjugate Fourier variations, exact spectra, positive evolution metrics and Jordan vectors test the plane equations. Independent nonlinear time evolution checks the stable, critical and unstable null backgrounds; independently solved forced stationary branches check the nonnull static response at fixed positive density. Common physical rotations, currents, spin boosts and full resolvent determinant ratios check the covariant response. These unbound controls establish neither physical particles nor gauge assignments.

Projective spatial nesting constraints

Positive-frequency scalar vertices and spatial packets

python experiments/positive_scalar_vertex_checks.py runs 1,798 checks of positive-frequency scalar vertices. It tests full positive bands at spatial dimensions two through ten, canonical singular strengths, chirality blocks, physical rotation covariance, complex spatial interference and containing-direction kinetic leakage.

python experiments/scalar_packet_collision_checks.py runs 101 fast checks of the complete three-dimensional local scalar solver, including comparison with an independent four-component adaptive integrator and second-order convergence. --packet-size N instead runs a larger localized collision; its recorded numerical observations require spatial, time-step and box refinement before interpretation. These are scalar-field controls, not measured particle coupling rates.

Axial full spatial Dirac family

python experiments/axial_scalar_checks.py runs 192 checks of axial spatial Dirac packets. Independent Cartesian differentiation at dimensions three, five, seven and nine verifies the full angular field equation and common physical rotation covariance. Independent spatial radial integration, complete matrix exponentials, quartic variations and nonlinear evolution check kinetic normalization, all complex source components, conserved momentum and reciprocal polarization response. The five-dimensional localized controls include both an exact polarization mismatch and nonzero coupling. These checks establish the specified angular family and finite regulator; individual packet results still require convergence checks.

Full-polarization scalar wave quartets

python experiments/scalar_quartet_checks.py runs 2,158 checks of resonant scalar wave quartets. It constructs complete Clifford waves at spatial dimensions three, five, seven and nine, builds every spatial Fourier coefficient of the local current and source, and checks both reciprocal gradients and the sharp normalized transfer bounds. Independent energy variations, positive free frequencies, generated-mode detuning, conserved momentum and polarization matrices, and full vector amplitude evolution are included. The four-mode equation is a first-order resonant reduction, not an exact invariant subspace or a physical scattering-rate prediction.

Localized spatial compatibility functional

python experiments/packet_compatibility_checks.py runs 26 checks of localized spatial compatibility. An independently integrated free kinetic equation accumulates the complete local scalar square. Complex directional variations verify its gradient; full nonlinear evolution approaches the first-order scattering map and checks the vanishing first-order change of the contact functional. Canonical norms and positive-frequency preparation are verified for both complete textured incoming patterns.

Localized scalar encounter refinements

Localized scalar wave encounters record full Cartesian spatial, time-step and box refinements, with an independent axial control. The 101 fast checks in scalar_packet_collision_checks.py include the complete continuum reflection, all four incoming frames, positive-band covariance and local nonlinear source covariance. Optional --packet-size runs retain every complex spatial component and report both chiral norms and conserved-quantity errors. The transfer is a classical canonical-norm quantity, not an observed particle rate.

Time-ordered spatial contact

python experiments/packet_time_order_checks.py runs 50 checks of time ordering of spatial compatibility. Independent complex differentiation verifies the source Hessian and the second generator. Time-quadrature refinement, source-order reversal, full nonlinear field errors and symmetrized coupling refinement check the quadratic contact law. A frozen-transport control keeps its full spatial contact exactly conserved within numerical tolerance.

Scalar Born frequency accounting

python experiments/scalar_born_checks.py runs 1,205 checks of scalar Born frequency accounting. Every full Clifford module from spatial dimension two through ten checks the complete positive and negative scalar vertices, massive detuning gap and massless angular denominator bound. Independent local spatial Fourier extraction retains both coherent permutations; full forced-mode evolution verifies finite-time frequency response and common physical rotation covariance. These are mathematical and conditional field checks, not a particle-antiparticle assignment.

Direct spatial coupling variations

python experiments/spatial_packet_variation_checks.py runs 28 checks of the direct first and second coupling variations used for localized spatial compatibility. Independent local scalar differentiation, canonical norm variations, time-ordered generators and complete nonlinear evolution verify the contact coefficient. Positive renormalization of both outgoing patterns separates their shape-dependent contact from norm redistribution.

Oscillator response tails

python experiments/oscillator_response_tail_checks.py runs 105 checks of spectral weights in oscillator response through independent exact normal occupations, beta integration, growing and decaying tail blocks, shared-degree differences at one total cutoff, and full complex reciprocal Schur elimination.

Complete radial polarization fields

python experiments/radial_polarization_checks.py runs 234 checks of complete radial polarization fields, including independent Cartesian derivatives in dimensions two through ten, full angular current, common physical rotations, the complete real scalar Hessian and the integrated polarization matrix.

Nonzero same-field support background

python experiments/nonzero_support_background_checks.py runs 4,140 exact rational checks of the nonzero support background and joint Schur bound. It verifies force cancellation, completing-square elimination, both sides of the full three-block stability threshold, and the lowest-harmonic bottleneck at every maintained index and depth.

Finite biased support compatibility

python experiments/biased_source_compatibility_checks.py runs 40 exact checks of the finite biased support and mode-selection boundary. It solves one exact finite-harmonic Gram system per maintained depth, verifies the selected orthogonality equations, and checks that the next unselected mode fails. python experiments/biased_source_infinite_checks.py separately sums the complete even-harmonic space at 50 and 80 decimal digits. Its 48 checks confirm convergence, the selected cancellations and a nonzero next-mode residual at every maintained depth. It also verifies that the transparent point has response-sector real-amplitude curvature −4∥ui∥2-4\|u_i\|^2, so separate positive curvature is required for stability.

Fixed-norm response spectrum

python experiments/constrained_response_spectrum_checks.py runs 69 checks of the fixed-norm response eigenvalue. It evaluates the infinite even-harmonic response norm at 50 and 80 decimal digits, verifies its contribution to the constrained standing frequency and tests whether one response coefficient preserves the simplex frequency rule under equal canonical normalization and frozen source profiles. The response-to-simplex ratios are nonconstant at every maintained depth with more than one mode; dynamically selected amplitudes and profiles are outside this diagnostic.

Localized-action assumptions and independent algebra

python experiments/localized_action_audit_checks.py checks the complete potential by mixed second differences in arbitrary complex field directions, and verifies the exact slow Schur complement and characteristic determinant without assuming that the two binding Hessians commute. Full coefficient calculations at depth six confirm that arbitrary positive shell weights retain the coherent frequency rule as their partial sum. These checks therefore do not select the binomial weights physically.

The same diagnostic verifies an explicit unit-norm family whose mass current is positive and whose field current is strictly timelike, but whose classical energy tends to negative infinity with spatial wave number. This rules out a global fixed-norm minimum; it is not a spectral instability claim. All 75 conditions pass in the preserved report.

Trace and exchange current contraction

python experiments/partner_current_metric_checks.py verifies arbitrary current variations, the exact symbolic conserved-form polynomial, full potential Hessians, retained oscillator source variations, and the initial interaction of solved cores. It independently reduces the complete frozen spinor and partner operator and checks its high-momentum amplification and positive conserved norm. The selected report passes 169 conditions. Its helper is partner_current_metric.py; the inverse contraction choice does not derive the shell weights or full spatial nonlinear stability.

Higher angular current response

python experiments/localized_harmonic_response_checks.py checks complete angular multiplicities, direct Cartesian derivatives and arbitrary complex Hessian closure in six and ten ordinary dimensions. It then computes 200 finite spectra of the same smooth core at the assigned electron and muon frequencies, retaining every interior form degree at five higher angular labels, two radial discretizations and both current metrics. All 1439 conditions pass. The helper localized_harmonic_response.py supplies the angular matrices. Finite scans do not settle the infinite spatial problem.

Combined positive-response route comparison

route-decision-checks.py computes the shared infinite-harmonic Gram matrix and uses it for fixed-norm frequency shifts, finite-bias compatibility, the scale-covariant size test and a normalized background Schur lower bound at depths two, three, four, five, six and ten. The selected report passes 108 cross-precision and algebraic checks. The source vectors are algebraic controls; the background stiffness bound is conditional on the stated unit normalization, not a solved full same-field Hessian.

Common-background radius action

The maintained route-decision-checks.py now evaluates the finite carrier with one explicit radius-background action, using archived spatial hopping integrals and both common gap controls 1000 and 10000. Its 356-check report verifies the pressure independently from the full smallest singular vector, the common-radius force cancellation, zero field-radius mixed block and the radial Schur curvature. The action is an inverse construction; its reference radius, background stiffness and angular second variation are not selected by the master field.

Whole-depth conformal-current Hessian

The same route-decision-checks.py also evaluates a separate whole-depth current candidate. Its 988-check report records the joint bare Hessian on nine common zonal metric directions and the common background threshold for all maintained modes at two common strengths. A pointwise quadratic criterion proves positive fixed-profile conformal curvature for every smooth direction on the tested spinor branches; the depth-two form has the finite zonal result. Independent quadrature of the unexpanded transported energy checks qq and q2q^2 derivatives for depth-two form and depth-six spinor controls. The full positive-wave action yields the reported threshold at unit phase charge. The inverse background's physical origin, traceless tensor geometry and complete field stability remain open.

Joint candidate equation sheet

joint-candidate-equations.py recomputes the current response, linked radial and whole-depth current equations from shared maintained assignments in one run. Its 32-row report includes the two common strength controls, response bias and size diagnostics, finite-strength frequency spreads, separate support thresholds, the depth-two nine-direction form control and higher-depth pointwise spinor margins. Its key frequencies, forces, Hessians and thresholds agree with the larger independent route-decision report to the displayed precision. This compact script is for rapid comparison; the candidate actions are not merged.