The Multi-Cell Matter-Carrier Interface in the Axis Model: Signed Occupancy Geometry and a Conditional Postparent Hamiltonian
Andrew Morton · Public preprint · Geometry and conditional composition
Identifies the geometry of a three-cell internal carrier and constructs the additional conditional dynamics needed to select its frame incidence.
Abstract
The Axis parent supplies a localized U(1)_G-charged line–plane cell with projector-resolved longitudinal and transverse structure. The certified F15 localization sector contains one complex charged mode with charge-conjugate sectors; the carrier projector P_i is a local-frame geometric readout, not a charged one-particle multiplicity or a dynamical coordinate of the certified charged-cell phase space. For three same-polarity cells, the signed occupancy tensor has a nonnegative anisotropy invariant that vanishes uniquely when the occupied frame lines form an orthogonal triad, and its weighted extension further requires equal occupation of those three lines.
We sharpen the provenance boundary at action level. In the literal frozen F15 theory the relative projectors occur only in the line–plane readout: the action, sources, constraints, and functional measure contain no corresponding relative-incidence variable. The frozen theory therefore supports genuine common-mode multi-charge dynamics but induces no potential that distinguishes coincident from orthogonal frame incidence. In particular, no orthogonal-triad selector is generated by the existing scalar, charged-field, screened-vector, or declared heavy-response interactions.
We then construct the canonical conditional postparent completion used by the matter chain. A neutral count-matched collective incidence register and a positive repeated-incidence penalty isolate an exact square-free ordinary sector with degree dimensions (1, 3, 3, 1) and a bare H_slot repeated-incidence gap U_slot The original quadratic attachment parameters admit the provenance-diagonal form
H_att = U_inc R_rep + g_pair binom(N, 2), U_inc = U_slot + κ_x, g_pair = −κ_x/3,
so only one quadratic direction is frame-incidence sensitive; the remaining term is a central pair interaction and remains relevant when cell number can change. For U_slot > κ_x/3 > 0, the fixed-polarity degree-three ordinary state is unique within the declared local attachment tower and projects to the rank-one internal carrier
B_σ^int ∼ (3z^σ, 6x).
The collective register, its population map, and its composition coefficients are explicit inputs beyond frozen F15. The result closes the conditional internal composition interface and supplies the canonical F17 frame-incidence fiber used by the downstream classical common-envelope construction. A controlled signed many-body quantization, ordinary/complement mixing bound, physical three-cell mass shell or pole, spin and exchange statistics, Standard Model representation and electromagnetic-charge provenance, generation selection, and flavor normalization remain separate certificates.
Scope
The occupancy geometry is exact, but the frame-incidence dynamics and their coefficients are added inputs beyond the frozen charged-cell action. The internal carrier is not yet a physical quantum particle, and the (1, 3, 3, 1) counting does not establish spin or exchange statistics.
Paper and supporting files
The deposit includes a minimal reproducibility archive with a deterministic verifier and reference JSON and CSV outputs for the finite algebraic and attachment-energy checks.
Read the current paper and supporting files on Zenodo
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Stable classical common-envelope body
Abstract checked 28 August 2026 · v2 · public release 17 August 2026.