4326 — Tessellated Reader Fields and Bounded Framed Coherence
The checkpoint
This investigation asked whether the native P/N/E readers could carry one organized field structure across the tetrahedron–octahedron tessellation. The result is a reproducible conditional field architecture, with exact operator reconstructions and bounded coherence tests. It is not a physical identification of particles or a completed theory of their interactions.
The public explainer gives the spatial picture. The research closeout records the constructions, failed branches and next discriminating tests.
Native field structure
Both native baryon fields have 36 coordinates. Their actual support blocks, complex coefficients and metrics reconstruct a 12-by-3 tensor organization. After explicit coordinate changes, the two directions carry commuting weighted projections; P and N exchange their local/alignment roles. Their common return has rank one.
This organization has concrete geometric realizations. P uses twelve centroid-edge patches on a tetrahedron, with three spatial components per patch. N uses eighteen patches on a six-face belt, with two intrinsic plane components per patch. The source weights, rather than just the dimensions, are reconstructed exactly.
The proposed T organizes three reader facets sharing an edge. Its metric is four-dimensional. No tessellation by copies of T, independent M/C torus, or physical vortex follows from that incidence picture.
Conditional PN and NE connections
A full metric-unitary PN candidate satisfies
It mixes beyond a single shared face. A face-supported extension is obstructed: the chosen face carries one quarter of P's normalized return norm, but one sixth of N's. The complement action of the global map is explicitly chosen, not uniquely forced by geometry.
N already contains a two-dimensional relative-sector subspace,
An exact partial isometry maps it onto E's native return doublet and intertwines a retained native order-three electron action. This converts modes rejected by N's alignment; it does not intertwine N's rank-one return with E's rank-two return. A direct-sum exchange retains the remaining field information without cloning it.
The full-five candidate sends two contrast combinations to E and leaves three combinations in the baryon block. Shared-edge patches select the context modes; coherent repetition across sectors gives C3 equivariance and a reducing five-dimensional N subspace. The window-to-sector identification, inherited phases and PN completion remain model inputs.
Coherence with retained frames
Rigid translation and combination commute in the bounded tests: 5,568 configuration squares and 44,736 candidate extension squares agree, including rejected combinations. Different native paths may nevertheless reach the same marked window and origin with different coefficient frames. One relative comparison has order five; equal endpoints do not erase history.
The refined connection was tested on 24 seed markings through depth 28:
| Recorded quantity | Count |
|---|---|
| Packet/frame states, summed across seeds | 250,040 |
| Checked transitions | 458,912 |
| Conflicting candidate field parities at repeated marked charts | 0 |
This result concerns the declared field-transport rules in the explored graph. It is not a universal-depth theorem or a certificate for every simultaneous assembly and incidental field contact.
Retained exclusions and accounting
The two-step geometric recurrence does not make seven blocks of four or fourteen blocks of two into new symmetries. Two frame-related histories also do not automatically supply two independent physical modes.
The candidate contrast-to-E exchange does not conserve the original defect operator. The augmented quantity
is conserved by the constructed exchange, but the added electron-return term is explicit dimensionless bookkeeping. Its physical energy interpretation, normalization and dynamics are not derived.
Scope. These are exact algebraic constructions and bounded executable checks. No independent scientific review, universal coherence theorem, mass, charge, isotope stability, physical time or particle-creation law is claimed. The experimental terminal P-to-E support permission is separate and unchanged. Production generation and viewer rules are unchanged.
Durable verification
python research/strominger/checkers/check_reader_field_closeout.py
Seven central checkers were freshly rerun. The closeout manifest verifies ten selected receipt hashes and retains content-addressed copies of the receipts.
- Fresh verification manifest
- Closeout runner
- Global PN construction
- Native contrast-to-E construction
- Full-five candidate
- Extended frame test
Number allocation: seqclaim-a12bf5f15281f9a09483fc83 on
marici-ledger-entry. Research report admission:
ev-000000016183-00d9231f-dce3-4554-b610-d1d70bea1f1f.
Graph admission records policy-valid provenance, not truth certification.
The next tests are source selection of the coupling conventions, field sewing at incidental contacts of complete assemblies, and dynamics with independently justified units. The bounded checkpoint is closed; those obligations remain open.