# n159 — the photon polarization audit: Maxwell's radiation sector,
#         complete and clean — and the breather explained
# (2026-07-11. The mirror of n157, run on the EM sector. Four exact
#  facts; the photon passes everything the graviton struggled with.)

## The four facts (all exact)
F1. Near the staggered point q* = (pi,pi,pi), the unsigned incidence
    BECOMES the signed divergence: A(q*+p) = 1 - e^{-ip} -> ip.
    The EM sector's Gauss law is the honest, signed one.
F2. The dark kernel near q* is EXACTLY the transverse plane:
    dim ker = 2, |A.v| ~ 1e-17, v.p = 0 to O(p^2). Two polarizations,
    both transverse, both dark: count AND transversality delivered
    in one line.
F3. The longitudinal mode is WATCHED (|A.v_L| = 0.3 > 0): audited,
    gapped, dead. NO SCALAR PHOTON - the EM sector has no breather.
F4. THE CONTRAST EXPLAINS n157'S DANGER: gravity's kernel sits at
    q ~ 0 where the constraint is the UNSIGNED sum (whose kernel
    admits the traceless breather); the photon's sits at q* where
    the constraint is SIGNED (kernel = pure transverse). THE
    BREATHER EXISTS BECAUSE GRAVITY'S GAUSS LAW IS UNSIGNED.

## The photon scoreboard (the free Maxwell sector, in-frame)
count = 2 [exact] · transversality [exact] · masslessness [the
zero-mode theorem, n88 - exact] · no scalar mode [exact, F3] ·
audit transparency [dark => unmonitored] · dispersion quadratic-
subluminal [carded]. THE FREE RADIATION SECTOR OF ELECTROMAGNETISM
IS COMPLETE, and cleaner than gravity's. Missing from EM, still:
the Lorentz force / minimal coupling (never derived), the 157.19
orphan, the beta function (matter sector).

## The hint handed to the graviton campaign (flagged, for the
## breather computation in progress)
Two readings of F4, one of which will be true:
(a) the unsigned Gauss law is FUNDAMENTAL for the metric sector ->
    the breather is real physics -> it must decouple dynamically or
    prediction 17 executes (the standing danger, unchanged);
(b) the metric sector's TRUE radiative point is also staggered-like
    (or the unsigned structure is an artifact of the diagonal-edge
    truncation, n157's named lattice artifact) -> the breather is a
    truncation ghost and dies with the artifact.
The breather computation now has two named outcomes instead of an
open wound. (b) would complete the junction's polarization story
with the SAME cleanliness as the photon's.