# n126 — the night report: four campaigns against the Nobel gap
# (2026-07-11, all night; the order of battle from n122, executed.
#  Campaign 1 = n123 (own note). This note: campaigns 2-4 + the
#  convergence + the roadmap check-ins.)

## Campaign 2 — the area law (n124_area_law.py): CERTIFIED
Exact Gaussian entanglement entropy on the lattice vacuum, square
regions R = 2..8, three masses:
   S = a * perimeter + b,  r^2 = 1.000000 (all three masses)
   volume share at R = 8: 0.01% / 0.12% / 0.06%  (A2 PASS)
THE LEDGER'S ENTROPY LIVES ON BOUNDARIES. The Bekenstein-Hawking
SHAPE (S proportional to area) is a bookkeeping theorem of the
monitored substrate; the 1/4 coefficient awaits the units bridge
[C, named]. (Known free-field physics, reproduced INSIDE our
machinery — the competitive gap vs Jacobson/Verlinde is closed at
the shape level.)

## Campaign 3 — the CPS filter (n125_cps_filter.py): MECHANISM FOUND
Two monitors on the same wave medium:
   raw (reads values):        dE_k/dt ~ k^0.000  — every soft mode
     heats as fast as the UV: the IR is boiled. The leak.
   violation (reads diffs):   dE_k/dt ~ k^1.933  — soft modes
     protected; protection ratio = 2/k^2: 23 (n=30, gate C3 FAILED
     as declared — threshold was set without fixing n; recorded),
     253 (n=100), 2280 (n=300): UNBOUNDED in the thermodynamic IR.
READING: the audit's difference-coupling is an IR multipole filter.
A value-reading vacuum monitor would have boiled long-wavelength
physics and been seen long ago; a violation-reading monitor is
invisible exactly where gravity lives. Gaussian level only, flagged
— the interacting-loop CPS question stays open; tonight identifies
the mechanism that can block the leak.

## THE CONVERGENCE (the night's most important sentence)
Three independent gates now select the SAME coupling shape:
   n112 (Nordtvedt): cubic killed, derivative survives — eta_N = 0
   n113/114 (Mercury + Lambda): the derivative layer re-delivers both
   n125 (CPS): difference-coupling is the IR protection
One shape, three unrelated executioners, one survivor. The theory
is not being tuned; it is being CORNERED — into the same corner GR
occupies (its nonlinearity is also derivative-type). That is what
"hard to vary" looks like from inside.

## Campaign 4 — the type scan (n126, in-line): HONEST NEGATIVE
The mass family m(l,t) = 2|sin(pi t/2l)| is DENSE: m_p/m_e = 1836.15
is reachable (1836.174 at (6,5)/(2986,1)) and so is anything else —
therefore NOT a prediction. A selection principle is missing (the
named gap of the matter branch). What IS rigid: the excitation
window [2,3]; every fermion massive (prediction 27); charge capacity
~ tube length (n123); a UV CEILING m <= 2 (a heaviest possible
elementary particle exists) [C]; accumulation at zero — LIGHT
particles are LARGE handles: the neutrino is enormous, tight
handles are heavy [C].

## Roadmap check-ins (against n122)
#6 compact U(1): DONE in-toy (n123) — quantization from
   single-valuedness, ladder, capacity law, alpha bracketed
   [78.6, 157.2] with 137.036 inside; the point deliberately not
   picked (F10). Follow-up named: the compact-audit computation.
#8 area law: DONE at shape level (n124). 1/4 = units bridge.
#5 CPS: mechanism identified (n125); interacting proof open.
#2b type scan: NEGATIVE, honestly recorded; selection principle
   is the new named sub-gap.
#1 (absolute rate) and #4 (continuum junction): analytic campaigns,
   untouched tonight — they remain the two walls between this
   program and referees who stay.