Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== Converting the geometric story into physics-grade results will require a few well-posed mathematical steps: ===
# Boundary field and antiperiodic condition → spinor: produce a boundary Lagrangian on S² that supports a fermionic spinor section (antiperiodic boundary condition). Show explicit construction (spin bundle on S², Dirac operator on shell) and verify angular momentum eigenvalues are half-integer. (This is standard mathematics/topology — Hopf fibration/S³→S² language helps). PhilArchive<ref>{{cite web|title=PhilArchive|url=https://philarchive.org/archive/NIETTUv146|publisher=philarchive.org|access-date=2025-12-16}}</ref>Rochester School of Arts & Sciences<ref>{{cite web|title=Rochester School of Arts & Sciences|url=https://www.sas.rochester.edu/pas/assets/pdf/undergraduate/su-2s_double_covering_of_so-3.pdf|publisher=Rochester School of Arts & Sciences|access-date=2025-12-16}}</ref>
# Composite tensor field from EM boundary stress: compute the averaged, symmetric bilinear of tangential EM fields across an interacting shell and show it transforms like a rank-2 field. Then compute its effective coupling to matter (does it reproduce the linearized Einstein coupling T_{μν}?). Use double-copy results as a guide for the amplitude-level mapping. Physical Review Links<ref>{{cite web|title=Physical Review Links|url=https://link.aps.org/doi/10.1103/PhysRevLett.105.061602|publisher=Physical Review Links|access-date=2025-12-16}}</ref>arXiv<ref>{{cite web|title=arXiv|url=https://arxiv.org/html/2403.08637v1|publisher=arxiv.org|access-date=2025-12-16}}</ref>
# Energy bookkeeping: show explicitly that local absorption+emission conserves energy and that the emergent long-range attractive effect does not require net loss of energy (resolve classic Le Sage/Maxwell objections). This will likely require thermodynamic/statistical averaging over many events and explicit entropy accounting.
# Empirical handles: look for small QAT corrections to known phenomena (e.g., small modifications of gravitational redshift that depend on local EM activity, or signatures in plasma environments where coherent EM structure is strong). Those would be the way to falsify or support the hypothesis.