Tessellated reader fields and bounded coherence
Research checkpoint · October 18, 2026 · marici.Strominger
A concrete field model now connects the native P/N/E constructions while retaining coefficient frames and realization history. Its operator identities are checked exactly; its geometric interpretation and dynamics remain conditional.
Explore the isotope / R-space viewer. Its native isotope grid and R-space view remain separate: no placement map between them is established.
A spatial picture
Imagine three tetrahedral wedges sharing an edge. Each is a reader presentation, not a new set of independent spatial dimensions. Beside the geometry, picture a 12-by-3 array of amplitudes. Two weighted projections act along its two directions. P and N exchange their local/alignment roles.
The actual fields have different geometric organizations:
| Carrier | Geometric organization | Field coordinates |
|---|---|---|
| P | Four tetrahedral faces, each divided into three patches; three spatial components per patch | 36 |
| N | Six belt faces, each divided into three patches; two in-plane components per patch | 36 |
| E | Four face spinor blocks in the retained native construction | 8 |
The proposed common T has a four-dimensional metric. The three-wedge picture shows how its reader facets meet; it cannot preserve all their distances in 3D. Copies of T have not been shown to tessellate space.
What is checked
- Exact factorization: native baryon coefficients and metrics give a 12-by-3 field, two commuting weighted projections and one common return mode.
- Global PN candidate: a 36-component metric-preserving map exchanges the native local/alignment projectors. It must mix beyond a single shared face.
- Candidate NE conversion: N's three local modes split into one aligned mode and two relative-sector modes. Those two modes map onto E's native return doublet, including a checked native threefold action.
- All five reference coefficients retained: two contrast combinations enter the E block; three remain in the baryon block. The joint map preserves norm.
- Context from the shared edge: the two incident-face patches select the context modes, repeated across the three sectors to respect their symmetry.
This is not a claim that projecting onto a two-dimensional image preserves all information. The remaining field components and reference data are retained in the joint construction.
Coherence has a frame
Translating a whole decorated neighborhood preserves the tested local rules. Combining then translating agrees with translating then combining in 5,568 configuration squares and 44,736 candidate extensions, including rejections.
Different native paths can reach the same marked window at the same origin with different coefficient frames. One checked relative permutation has order five. Equal geometry therefore does not license erasing frame or history.
The refined candidate was explored from 24 seed markings through depth 28:
| Bound | Result |
|---|---|
| Packet/frame states, summed across seeds | 250,040 |
| Checked transitions | 458,912 |
| Conflicting candidate field parities at repeated marked charts | 0 |
This checks the declared connection rules in a finite region. It is not a universal coherence theorem or a certification of every simultaneous assembly.
What the tests ruled out
The proposed M/C torus was not derived. The existing geometry supplies one transverse link circle; closing another direction requires an additional rule. Seven blocks of four realization steps and fourteen blocks of two are both consistent with period two, but do not establish sevenfold or fourteenfold symmetry.
A face-confined PN map cannot preserve the full native return: the face contains one quarter of P's return norm but one sixth of N's. A single N return also cannot be mapped onto both independent E return directions while preserving the return projectors. The candidate instead uses N's existing relative modes.
Explicit assumptions and remaining work
The window-to-sector identification, PN completion and phase conventions are still model choices. The conversion changes the original projector-defect measure. An added electron-return accounting term restores an algebraic balance, but its physical energy interpretation has not been derived.
There is no claim here of a physical vortex, measured mass or charge, isotope stability, particle creation, or a replacement for established physical theories. The next tests concern source-selected couplings, incidental contacts in complete assemblies, and dynamics with independently justified units.
Evidence and reproduction
Ledger entry 4326 records the checkpoint. Download the verification manifest for seven fresh checker runs, receipt hashes and content-addressed snapshot paths.
- Research closeout and next tests
- Reproduction checker
- Geometric contexts and extended coherence
- Native contrast-to-electron candidate
python research/strominger/checkers/check_reader_field_closeout.pyThese are executable checks, not independent scientific review. Production assembly and viewer rules are unchanged.