Three-Plane Scaffold: Numerical Field Data — Borromean Junction and Dirac Zero Modes
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This upload extends the zero-core exact-O Q=1 scaffold numerical evidence package with the N=144 reduced-operator Callias/JR diagnostics. The package contains the frozen N=144 bulk-certified zero-core state, co-registered labelled wall fields, Brunnian wall-sector audits, Callias mass-map degree audits, Callias known-control validation, doubled-operator finite-volume spectrum diagnostics, a physical-projection negative-control audit, and the reduced spin-isospin Callias operator audit with one-wall deletion controls. Main results included in this package: 1. The co-registered N=144 labelled wall fields preserve the scaffold Brunnian/Borromean wall-sector structure. The threshold sweep finds a stable pass band from p=1.5% to p=5.0%. 2. The labelled wall Callias mass map Phi=(W1,W2,W3) has stable signed shell degree +1 around the Brunnian triple core. 3. The doubled 8x8 finite-volume Callias spectrum contains a full-triple low sector and a one-wall deletion gap, but that doubled low sector is chirality-balanced. 4. A constant Clifford-monomial projection audit does not find a justified after-the-fact physical projection inside the doubled low sector. This negative control motivates using the reduced operator directly. 5. The reduced 4x4 spin-isospin Callias operator directly finds a full-triple low sector at N=144, crop halfwidth 10, and coupling g=2. The Hermitian reduced operator gives H_low = 3.543301899e-02 with four low modes. The Weyl/singular-value probe gives D_smin = 3.716889734e-02 with four low singular modes. 6. Deleting any one wall removes the reduced low sector and opens a large gap: delete_W1, delete_W2, and delete_W3 give H_low approximately 1.894 and D_smin approximately 2.000. This supports the chain: Brunnian labelled wall sector -> degree-one Callias mass map -> reduced finite-volume Callias/JR low sector -> disappearance of the low sector under deletion of any one wall. Important caveat: the reduced finite-volume spectrum is a low-sector diagnostic. The Callias mass-map degree supplies the topological index input; a full analytic Fredholm/index proof remains distinct from the finite-volume numerical evidence. Version note Adds the reduced-operator Callias evidence packet, including the physical-projection negative control and the reduced 4x4 spin-isospin operator audit with one-wall deletion gap controls.



