# n88 — the EM-sector confrontation: unexpected results, parameters refined
# (2026-07-10; includes the death of our own F9 — the first settled forecast)

## 1. HEADSTONE 28 — the screening claim, killed by its own gate (F9 run)
The bet (F9/P-III): the measured S(q) growth toward the infrared is
vacuum screening, QED's direction. RUN TODAY: the log-running test
fails decisively — equal ln(2) steps give dS = 1.815 then 0.467
(ratio 0.26; running demands 1.00), and in 3D the steps collapse
26.4 -> 7.0 -> 1.8. Meanwhile S(L) = S_inf - c/L^2 fits to THREE
DIGITS (residuals ~0.005 on ~200). Verdict: NOT running — finite-size
convergence to a constant continuum coupling. The "QED-direction"
prediction was a misreading, and it is retired at full prominence
(forecast ledger annotated; theory page, predictions page, and the
v2 paper corrected the same day; the v3 paper never carried it).
REFINED PARAMETERS the death leaves behind:
   S_inf(2D) = 202.588 +- 0.01 (fit residuals), c = 1400
   S_inf(3D) = 493.83  +- 0.3,  c = 5138
The continuum couplings are now pinned to 4-5 digits — sharper than
the screening story ever was. First forecast settled: against us,
by us, eleven days after signing.

## 2. The photon-mass test — passed BY THEOREM, and it sharpens A4
Bound: m_gamma < 1e-18 eV (PDG). Naive worry: the substrate regulator
mu gives every phonon a mass ~ mu*(hbar c/l_s) — at l_s ~ fm that is
~keV, violated by 21 orders. THE FRAMEWORK'S ESCAPE IS STRUCTURAL and
was measured long ago: the audited (Gauss) sector's zero mode is EXACT
at every mu (|W(q*)|/max ~ 1e-32, n46b) — protected by the
conservation law itself, not by tuning. CONSEQUENCE, sharpening
assumption A4: light cannot be a generic substrate phonon (those are
mu-gapped); LIGHT MUST BE THE GAUSS-SECTOR COLLECTIVE MODE, whose
masslessness is gauge invariance. The photon-mass bound converts A4
from a choice into a requirement — the framework's photon is massless
by theorem or the framework is dead by 21 orders. No middle.

## 3. Coulomb-law precision — l_s refined by NINE ORDERS
Laboratory inverse-square tests (Williams-Faller-Hill class) bound
fractional deviations at |q| < ~1e-15 at r ~ 0.1-1 m. The substrate
dressing (measured, n49) has envelope ~0.2*(l_s/r), alternating.
Conservative (alternation averaging ignored): 0.2*l_s/r < 1e-15 at
r = 0.5 m gives
   l_s < 2.5e-15 m  — sub-femtometer, below the proton radius.
The old Eot-Wash bound (5 um, from gravity) is superseded by nine
orders because the SAME substrate now carries electromagnetism, and
Coulomb is tested a billion times better than Newton. Consistency:
the Lorentz-invariance push (n80) already wanted the substrate deep-UV;
Coulomb makes it quantitative. Corollary for the n64/n86 cards: the
gamma ceiling c/l_s rises to >~ 1e23 s^-1 — the knee's allowed band
widens upward; the pulsar floor (5e14, class C) remains the sharp edge.

## 4. The fine-structure-constant discrepancy — the framework takes a side
The two most precise alpha measurements disagree at 5.4 sigma
(Cs recoil, Berkeley 2018 vs Rb recoil, LKB 2020). In this framework
alpha = 1/S_inf is a substrate constant, and the audit-invariance
chain (a = 0) makes it environment-independent. THE FRAMEWORK BETS:
the alpha discrepancy is experimental systematics, not physics —
the same falsifiable posture it took on the CODATA G spread. Symmetric
stance, now on both fundamental-constant controversies: any confirmed
environmental or method dependence of alpha kills the audit-invariance
chain at its EM end.

## 5. Electron g-2 (13 digits) — the boundary it draws
The most precise agreement in physics constrains any substrate
modification of QED loop structure. In the framework, loops live in
the matter sector (unbuilt); g-2's message is a standing wall in the
same class as the tensor junction: the matter sector, when built,
must reproduce QED perturbation theory to 13 digits at accessible
scales — i.e. the substrate corrections must enter only at (q*l_s)^2
~ (m_e * l_s / hbar c)^2 < 1e-17 with l_s < 2.5 fm. Consistent, and
named as the matter sector's precision target.

## The refined card (EM entries, post-n88)
- S_inf = 202.588 (2D) / 493.83 (3D): continuum couplings, 4-5 digits.
- l_s < 2.5e-15 m [Coulomb tests; supersedes Eot-Wash by 9 orders].
- Photon mass: 0 by theorem (Gauss-mode masslessness) — A4 sharpened
  to a requirement.
- alpha: environment-independent (the bet on the 5.4-sigma
  discrepancy: systematics).
- gamma ceiling: raised to ~1e23 s^-1; the knee's band is now
  [5e14 (pulsar floor, class C), 1e23] — wide but two-sided.
One forecast settled against us, four parameters sharpened, one
assumption converted to a requirement, one new falsifiable stance.
The EM sector ends the day more constrained than the gravity sector
ever was — as befits the force that metrology loves best.