One Transported Marked Lattice Resolves All Four Finite Conductor--Energy Tangencies
Question
Entry 382 found a one-step marked coefficient lattice at [ (r,s)=left(1,\frac12 ight). ] Freeze that lattice before visiting the remaining finite tangencies: [ (w_{111},w_{101},w_{110};w_6,w_7,w_8,w_9) =(1,0,0;0,0,0,0). ] Does this same lattice make the canonical seven-coordinate marked-to-algebraic projection logarithmic at all four centers without adding support or carrier data?
Frozen centers and test
In the generic (x=1) chart, [ (u,v)=(E_T,ell_3)=(r^{-1},s^{-1}). ] The four source centers become [ (1,2),quad(2,1),quadleft(\frac23,-1 ight),quad left(-1,\frac23 ight). ] At each center use both point-blowup charts [ u=u_0+t,quad v=v_0+t ho, \qquad v=v_0+t,quad u=u_0+t ho. ] The frame, Kummer shear, seven projected columns, finite field, 20 exceptional directions per chart, 55 normal samples per direction, and the weight vector are unchanged from Entry 382. No per-center weight or denominator is fitted.
The implementation was repaired during this test so the transformed Laurent bounds are computed from the normalized jets rather than emitted as constants. Its certificate output was also changed to valid JSON.
Exact finite-field result
| source center | ((u,v)) | raw ((minord A_t,minord A_ ho)) | weighted | bad masks | nonzero coordinates | |---|---:|---:|---:|---:|---:| | ((1,\frac12)) | ((1,2)) | ((-2,-1)) | ((-1,0)) | ((120,120)) | 54 | | ((\frac12,1)) | ((2,1)) | ((-1,0)) | ((-1,0)) | ((0,0)) | 27 | | ((\frac32,-1)) | ((\frac23,-1)) | ((-1,0)) | ((0,1)) | ((0,0)) | 0 | | ((-1,\frac32)) | ((-1,\frac23)) | ((-1,0)) | ((0,1)) | ((0,0)) | 0 |
Thus only the first center actually requires the positive marked weight. The transported lattice remains admissible at the other three. At the last two centers the tested projection vanishes to positive normal order; this is a statement about the frozen seven-coordinate projection, not vanishing of the full Gauss--Manin connection.
Every reconstructed denominator is generated by the predeclared tangent direction. The first two centers have root set ({0}); the last two have no denominator root. No residual irreducible support occurs.
Verdict
The hostile claim [ \boxed{ ext{one fixed marked coefficient lattice cannot resolve all four finite conductor--energy tangencies}} ] is falsified for the canonical seven-coordinate projection.
The narrow surviving statement is [ \boxed{ ext{the weight }w_{111}=1 ext{ extends across all four centers, and no new support or carrier stratum is required.}} ]
Classification
| Datum | Classification |
|---|---|
| four point-blowup centers | existing conductor--energy carrier |
| (w_{111}=1) | sector-specific conductor/Rees coefficient lattice |
| roots ( | |
| ho=0) | frozen tangent directions |
| vanishing at the last two centers | projection behavior in the coefficient system |
| residual support | none |
| new carrier datum | none found |
Epistemic boundary
This is an exact generic-fiber de Rham computation for the canonical seven-coordinate projection. It does not test the five exact-lift-gauge coordinates, the four elliptic base points, extension through the complete discriminant, integral normalization, or compatibility with the physical relative chain.
The next finite falsifier is the same predeclared lattice at the four elliptic base points. A required new weight is a coefficient-architecture failure; an irreducible denominator outside the frozen base-point directions is the carrier-level falsifier.
Evidence
research/benincasa/marici-gm/src/bin/marked_tangency_support.rs;research/benincasa/all-marked-tangencies-certificate.json;research/benincasa/triple-soft-exceptional-resolution-certificate.json;- Entries 370, 380, and 382.