4306 — Conditional mixer selection and the inner-face electron stopping boundary
Disposition
Pause this approach at the operator's request. We have conditional algebraic selection and exact finite obstruction results, not a derived electron, proton, physical gravitational frame or value of G. The next approach should retain these results without treating the trial adapters as source-selected physics.
This entry consolidates the subsequent investigations after entry 4305. Authorship: marici.Nima. Operator hypotheses and requested continuations supplied the search direction; they are not mathematical or physical evidence.
1. What the mixer investigation established
Given the declared port, counting metric, linear-isometry conditions and agreement policy, the conservative carrier/record exchange is selected conditionally. Within the common-frame-natural unital algebra-automorphism and one-factor policy, the hidden-port requirement selects the half-turn
R(X)=tr(X)I-X^T=Ad_J(X), L=R tensor I.
These assumptions do not select the entire physical model.
Independent endpoint frames expose a further requirement. The average of four exact middle-frame actions is the readable projector P=C^T C. Any invertible bank map commuting with those actions preserves its readable image and cannot satisfy C K C^T=0. The selected hidden sector instead transforms by a determinant character.
A relative endpoint orientation repairs covariance. Actual compatible marked Boolean states select counting-basis frames, but their relative sign is det(V). On orthogonal source edges,
det(V) Ad_J(V)=V.
Consequently the repaired hidden readout equals the ordinary readout on the tested factorizable source. The old ordinary/twisted sign difference is reference-dependent, not an established gauge-invariant gravitational signal.
Topological tetrahedral orientation alone does not repair the actual Boolean fiber-frame transformation: the latter can reverse the mixer's character while leaving diagram vertices and their oriented faces unchanged. Filled boundaries still retain orientation chains; vanishing H2 must not be mistaken for erasure of every retained witness.
For flat Boolean edge data, all relative sign-valued attachments are classified as plus or minus det(V). The negative convention changes all outputs by one sign, rather than selecting a new history-sensitive response.
2. The attached dynamics does extend beyond two edge factors
Retaining BOTH endpoint signs gives
U_o = E diag(o02 Ad_J, o12 L).
The carrier and bank signs have different endpoint characters. Repairing only the bank fails on 32 of the 64 tested frame assignments. Repairing both gives full-matrix covariance and norm conservation.
After the first empty-bank update, the bank's tensor flattening already has rank four. It cannot be reinterpreted as one pair of edge factors. Retained attachments nevertheless make the update well-defined and covariant through the permitted three advances. This closes a real implementation gap, but does not identify numerical feedback with the native tetrahedral constructor's evolution.
3. Recovered physical-frame work does not close gravitational normalization
The broader prior search recovered genuine conditional physical selectors and transport laws. In particular, the Einstein-sector two-polarization construction determines area and parallel-frame transport from supplied shape history, corner data and initial frame. It is incorrect to say that the programme has no physical realizations.
However, different admitted shape histories give different focusing and frame returns with the same determinant signs and intrinsic mixer. Proper orthogonal endpoint transport commutes with the attached update. Thus it transports that update rather than selecting its physical interpretation.
Raw Rosen-coordinate transport preserves an evolving metric, not the bank's fixed coordinate counting norm; identifying these matrices without an orthonormal-frame comparison would be invalid. No source identification between the Boolean fibers and physical transverse planes has been established.
The recovered construction is vacuum, Ric=0, and cannot determine G. Separately, the record model leaves physical clock/energy calibration and a dimensionless Planck-to-weak readout unbound. The older arithmetic identities and assigned formulas do not supply a matter/geometry coupling. No coefficient 1/90, -1/5280, exponent 15, prefactor 12 or particle mass has acquired a new physical derivation here.
4. Operator hypothesis: an electron appears at an innermost proton-like face
The proposed alternative was tested first geometrically, then as a localized mode. The existing viewer/source has a twelve-triangle tetrahedral boundary. Coning it to the symmetry-fixed center O gives a declared interior realization, not twelve established physical constituents.
It contains twelve equivalent cone cells, each of volume 2/9, and eighteen internal faces. There is no unmarked unique bottom cell. The retained seed arrow A->B permits the explicit incidence adapter selecting OAB, avoiding a camera-dependent choice; this is not a uniquely selected physical location rule.
Geometric birth tests
- Attaching another tetrahedron to an occupied internal face gives three cofaces: a branched complex, not an ordinary manifold-ball extension. Branching is not universally forbidden in WG, but needs its own interpretation.
- Stellar subdivision creates smaller cells while preserving the outer boundary and total volume. Further subdivision has no first positive minimum under that trial rule.
- Exhausting all 126 four-vertex subsets gives twelve existing cells, four larger unions of three cells, and four spatially degenerate candidates with at least three known faces.
- At OAB, the candidates are exactly its two existing neighbors and two coarse unions. No new smaller positive-volume tetrahedron is generated from the existing incidence data alone.
The native constructor completes a supplied path-coherence horn; it does not infer an apex, all incident edges and the remaining horn faces from a single face. Its completion/forget equivalence recovers an existing package when given its horn. Geometric incidence alone is not an admission into that typed constructor.
Localized mode tests
The actual geometric cycle is the rank-one projector
P_collective P_symmetry P_local = P_collective = u u^dagger/80.
An opposite-phase preparation on the two triangle blocks adjoining OAB passes local mode selection but has zero collective readout. An in-phase preparation becomes u/6, occupying all twelve blocks. Every nonzero-eigenvalue cycle mode lies in span(u), so none is confined to those two blocks.
Moreover P(u)=u, P(0)=0 and P(u+epsilon*d)=u for the interface contrast d. This cycle neither nucleates nor amplifies it. The full retained records can still contain d; zero active readout is not evidence that its history has been erased.
5. Why the nonlinear response lead does not yet supply an electron
The prior same-slot residual-composition algebra can detect the retained contrast: its zero first mean has a quadratic self-response 1/6 at the chosen unit amplitude. This is a valid conditional diagnostic, not an electron mass or a source-selected interaction. Doubling the input quadruples this response.
On the invariant local-mode coefficient space, the actual triangle stages are I,M,M with M_ij=1/12. Their generated linear operator algebra is span{I,M}. The proposed amplitude-dependent diagonal gate D(a) does not belong to it. Inserting that additional gate would distinguish
M D(a) D(a) M = M/6,
M D(a) M D(a) M = 0.
The existing circuit contains neither state-dependent gate. Native comparison composition receives and composes pointed equivalences; it does not select these numerical gates, same-slot incidence or averaging weights. The literal unit-amplitude I+D(a) trial is singular, so it also cannot silently be treated as an invertible represented comparison.
Stopping boundary: a detectable retained contrast exists, but the inspected construction supplies no birth, binding, lifetime or independent-particle observable for it. Continuing this branch requires a justified state-dependent local interaction or record-return law, explicitly connected to the actual ports. Adding such a law would be a new hypothesis, not completion of an already-derived electron mechanism.
This is a bounded failure of the inspected model, not a theorem excluding all inner-boundary excitations or all future approaches.
Durable evidence and verification scope
Packets:
research/nima/natural-mixer-selection.mdresearch/nima/local-frame-mixer-obstruction.mdresearch/nima/gravity-normalization-selection.mdresearch/nima/prior-search-after-normalization-stop.mdresearch/nima/retained-orientation-mixer-bridge.mdresearch/nima/pointed-boolean-frame-selection.mdresearch/nima/attached-record-dynamics.mdresearch/nima/physical-frame-mixer-comparison.mdresearch/nima/inner-face-electron-candidate.mdresearch/nima/inner-face-horn-candidate-audit.mdresearch/nima/inner-face-localized-mode.mdresearch/nima/inner-face-response-port-binding.md
Their checkers and result receipts are named in the packets. Exact tests were executed during the investigations: rational matrix covariance, attachment classification, finite incidence enumeration, complex local-mode projections, response ordering and invertibility controls. Historical Agda sources were inspected, not freshly reproved or extracted for these numerical adapters. Source-owner physical artifacts were not modified. No new physical observation or formal proof of particle identity is claimed.
Change-of-approach guard
Do not restart with another camera-selected face, smaller drawing, averaging schedule, or coefficient fit. Preserve the distinction between a retained witness, an observed mode and a physical particle. Any next proposal should state the actual source operation that creates/responds to a perturbation and the independent observable that could falsify its particle interpretation.
Sequence allocation: seqclaim-a0ed1257f61ebfd97b9537b4, value 4306.
Epistemic graph admission: proposal ep_c7ae8caf-57fd-4e79-85d0-c75546bc8227, event ev-000000015792-83915a3c-c686-4846-9098-8bd0f542d4cb, sequence 15792. Admission records source provenance, not scientific truth. Site validation: pnpm run build passed (VitePress and Pagefind). No Git commit or push is claimed.