Kernels
Kernel files are the domain-level working documents for the framework. They are more detailed than the compendium and less speculative than research-track notes.
Files
| File | Role |
|---|---|
| statics.md | Representation structure, static inputs, octonionic internal structure |
| dynamics.md | Reduced dynamics, two-branch transport, scaling laws |
| epistemics.md | Observability, projection, hidden-sector access |
| consistency.md | Algebraic, dynamical, gauge, and selection consistency |
| interpretation.md | Safe and stronger interpretive readings |
| phenomenology.md | Candidate observables and prediction-readiness |
| topological.md | Tenfold/DIII/topological transition track |
| diii-anomaly-bridge.md | Focused comparison of the DIII boundary anomaly with the matter-content anomaly constraints |
| w3-kappa-sign-correlation.md | Fixes the relative sign tracking between the DIII winding number W3 and the transport coupling kappa_u |
| g2-spin23-intersection.md | Fixes the literal compact overlap G2 cap Spin(2,3) and records its U(2)-level irrep content |
| t1-3plus1-branching.md | Branches the static T1 tensor (3 + 1) matter seed under SU(3) x K and under the literal U(2) overlap, and sharpens what the hypercharge ansatz can fix on the bare left-handed seed |
| right-handed-completion-screening.md | Shows that the first obvious enlargement (T1 + T2) tensor (3 + 1) still cannot realize the right-handed singlet completion or make J^{01} nontrivial in hypercharge |
| minimal-right-handed-singlet-candidate.md | Identifies the smallest algebraic repair that creates weak singlets, shows J^{01} becomes useful there, and isolates the remaining left/right unification tension |
| unified-carrier-hypercharge-test.md | Tests the smallest unified carrier containing both doublets and singlets and proves a neutral-S_aux no-go for one global Y = a J^{01} + b Q7 |
| unified-carrier-projector-fix.md | Gives the minimal three-term projector enlargement that resolves the unified-carrier conflict algebraically and localizes the remaining burden to justifying the projector term |
| even-line-exotic-branch-obstruction.md | Shows that the projector/vacuum repair is only a selected-slot fit: the complementary T2 even-line sector survives with exotic weak-doublet charges |
| minimal-physical-subcarrier-candidate.md | Defines the first explicit operator-level candidate for the physical static subspace by projecting onto the T1 even line and the odd weak-singlet channel |
| branch-casimir-superselection-candidate.md | Rewrites the explicit physical-subcarrier projector as observable-branch selection on the even line plus minimal total weak-spin selection on the odd line |
| odd-sector-epsilon-channel.md | Sharpens the odd half of the superselection rule by showing that the weak-singlet selector is exactly the antisymmetric SU(2)-invariant epsilon channel |
| even-sector-observable-projector-descent.md | Sharpens the even half of the superselection rule by identifying it with the reduced observable/readout-sector projector already built into the ambient scaffold |
| conditional-static-spectrum-closure.md | Packages the current static line into an explicit conditional proposition: under the current observable-branch and auxiliary-sector rules, the reduced one-generation spectrum is exactly reproduced |
| auxiliary-projector-casimir-rewrite.md | Rewrites the projector term as the Casimir-zero projector on the reducible auxiliary SU(2) block 1 + 2, making the fix basis-independent |
| quaternionic-auxiliary-block-screening.md | Screens the existing quaternionic slice as a source of the auxiliary 1 + 2 block and shows that its natural visible SU(2) action gives only the irreducible complex doublet |
| auxiliary-vacuum-doublet-candidate.md | Records the best current positive candidate for the auxiliary 1 + 2 block: the vacuum-plus-single-occupancy sector of a standard fermionic completion of the existing quaternionic doublet |
| full-fock-auxiliary-obstruction.md | Shows that the full fermionic completion 1 + 2 + 1 is not usable by itself in the current hypercharge fit because the top wedge creates extra weak doublets with right-handed-style hypercharge values on the wrong SU(2) type |
| open-problems.md | Proof debts, blockers, and priority order |
| u-selector-bracketing.md | Brackets the status of the octonionic selector u (kinematic vs dynamical) and lists where each reading is required |
| kappa_u-moment-map-lemma.md | Formalizes the uniqueness of the exchange-odd cross-coupling slot -\kappa_u Im_u(AB) on branch space |
| discrete-symmetries.md | Ledger of the distinct Z2 flips (u reversal, reduced orientation, exchange, branch sign) to prevent concept mixing |
| orientation-rule-upgrades.md | Clean upgrade routes for deriving the operational orientation rule \kappa_u > 0 (bulk stability vs ambient selector vs readout coupling) |
| orientation-d1-bulk-stability.md | Focused D1 attempt: why reduced linear stability cannot fix the sign and what a bulk stability principle would have to add |
| upstream-selector-program.md | Packages the current pivot: the static branch is paused at conditional closure, and the live burden is now to derive the observable projector and auxiliary rule from an upstream selector |
Claim Level
Kernel files may identify Level 5 conjectural directions, but strong claims should be mirrored in ../CLAIM_LEDGER.md before they become paper-facing.