# n65 — pre-registration: the Mercury gate (PPN beta) + the frame-dragging
# blade (before any code)

## Blade A — Mercury: the model's beta, measured
Perihelion precession measures beta_PPN (the Phi^2 nonlinearity of
g_00) at the 1e-3 level or better; GR has beta = 1 and the precession
formula (2 + 2 gamma - beta)/3 leaves NO room: beta = 0 would put
Mercury off by a third. A quadratic drainage theory has EXACT
superposition — no field nonlinearity — so its only Phi^2 channel is
the STATE-DEPENDENCE of the information metric (the n50 second-order
channel, already measured to exist with ratio-4.1 scaling). The gate:
does that channel produce beta = 1, some other number, or a
position-dependent non-number?

Registered construction (Dicke weak-field dictionary, declared):
- E1(s) = linear-in-F_M part of a test dipole's maintenance energy at
  cell s in the field of source pair M (the cross term; defines the
  potential Phi(s) = E1(s)/F_t).
- E2(s) = F_M^2 part of the same maintenance energy (via G' = G[K(dk_M)],
  the n50 machinery), cell-averaged.
- From E_static(m) = m(1 + Phi + (beta - 1/2) Phi^2 + ...) (expansion of
  m sqrt(g00) with g00 = 1 + 2 Phi + 2 beta Phi^2):
    beta_toy(s) = 1/2 + E2(s) * F_t / E1(s)^2 * V_t0-normalization,
  with the exact normalization fixed in the script header before
  running and the F_M-scan (0.15, 0.3) verifying orders.
- GATE M-A1 (constancy): beta_toy(s) constant across s = 6..20 cells
  within 20% — if beta is not a constant, the PPN mapping itself fails
  and the model has no beta to compare (recorded as such).
- GATE M-A2 (the number): report beta_toy. Mercury tolerates only
  beta = 1 (to ~1e-3-1e-4 with modern data). |beta_toy - 1| of order
  unity = the model is DEAD against 43 arcseconds per century unless
  its unmeasured dynamical completion changes the static answer —
  which would then be the LAST wall, carrying three experiments.

## Blade B — frame dragging: no computation needed, verdict from data
GP-B (19%) and LARES/LAGEOS (~2%) measure the gravitomagnetic sector
= GR. The static drainage model has NO g_0i sector: the constraint is
instantaneous-plus-relaxation; the only motion effect is the audit lag
(measured, n61), which the fast audit suppresses as Omega/gamma — NOT
a v/c gravitomagnetic channel. VERDICT REGISTERED BEFORE ARGUMENT: the
model as it stands predicts zero frame dragging and is KILLED by
LARES at 2% — survivable only by the same relativistic dynamical
completion that the radiation sector (spin-2, binary pulsars' quadrupole
FORM) already demanded. The wall now carries three experiments: GW
polarizations, pulsar quadrupole form, and measured frame dragging.
This is recorded as the model's second-sharpest standing kill after
any beta failure, and the honest statement is: THE STATIC MODEL IS NOT
A COMPLETE THEORY OF GRAVITY AND THESE DATA PROVE IT; the open
question is only whether its static sector is the correct limit of a
completion that has the missing sectors.

## Honesty clauses
- The Dicke mapping for beta shares the semantic minefield that killed
  three clock readings; M-A1 (constancy) is the internal check that
  the mapping is meaningful before the number is read.
- One background geometry (source pair), one F_t; robustness scans
  deferred if the gate outcome is marginal.

## RESULTS (same day; n65_mercury_gate.py) — HEADSTONE 23
- M-A1 PASS, emphatically: beta_toy is position-independent to 0.00%
  across cells 6-20. The model HAS a definite beta.
- M-A2: beta_toy = 0.512. Structurally exact reading: beta = 1/2 is
  g_00 = (1 + Phi)^2 — the square of the linear potential, no genuine
  gravitational nonlinearity; the state-dependent channel (n50)
  contributes only +0.012 where GR needs +0.5. Mercury's precession
  under this beta: (2 + 2 gamma - beta)/3 = 1.163 x GR — a 16% excess,
  ~7 arcsec/century, against a measurement good to 1e-3. THE STATIC
  MODEL'S SECOND-ORDER SECTOR IS DEAD AGAINST MERCURY.
- Flags: linearity ratio 2.126 vs 2 (6% cubic contamination in E1 at
  F_M = 0.3, unexplored); the normalization ambiguity is recorded (an
  alternative charge-based dictionary gives an absurd beta = 92,
  discarded; the PRE-REGISTERED rest-cost dictionary fired the gate).
- Blade B stands as registered: LARES (2%) kills the absent
  gravitomagnetic sector outright.
VERDICT — HEADSTONE 23: the static drainage model is dead as a
complete theory of the solar system, three times over and pointing at
ONE missing organ: the relativistic dynamical completion (g_0i, the
Phi^2 self-sourcing, the quadrupole form — frame dragging, Mercury,
and binary-pulsar waveforms are the same wall seen from three sides).
What survives, stated precisely: the FIRST-ORDER sector (gamma = 1 in
the strong-monitoring regime, the linear redshift, Newton's force with
owned sign) and the QUANTUM sector (the decoherence knee, untouched by
any of this). The model is no longer a candidate theory of gravity; it
is a candidate LIMIT of one, and the completion — if it exists — must
generate beta = 1/2 -> 1 and g_0i from the retarded sector the static
constraint never had. That construction, or the final funeral, is the
program's remaining question.

## VERIFICATION PASS (same day, on demand: "verifie que tu as raison")
Three suspicions tested against the verdict:
1. STRONG-FIELD ARTIFACT? Phi = 30 at F_M = 0.3 put the extraction
   outside the weak-field regime. Scan: beta at F_M = 0.3, 0.15,
   0.075, 0.0375 (Phi = 30 -> 3.5): 0.5115, 0.5126, 0.5128, 0.5129 —
   F-INDEPENDENT to 0.3% and converging to 0.513 in the weak-field
   direction. The dimensionless ratio is clean; the kill is not an
   amplitude artifact. beta_toy = 0.513 (weak-field extrapolated).
2. CHANNEL ATTRIBUTION CORRECTED: the F^2 term is NOT dominated by the
   n50 self-energy channel (2.0e-8, 0.65% of it) but by the CROSS
   channel — the test-source interaction through the linearly-deformed
   metric (3.11e-6): a genuine second-order gravitational nonlinearity
   of the model, parity-charged, bigger than we knew. The record's
   attribution is corrected; the number is unchanged.
3. CONSTANCY GATE DOWNGRADED, honestly: the 1D potential is nearly
   flat over cells 6-20 (E1 varies by 4e-4), so position-constancy was
   weak evidence for the mapping. The F-scan above is the strong
   evidence and it replaced it.
The dictionary caveat that remains (shared with every PPN extraction,
including our gamma): the first-order normalization E = E_t0(1 + Phi)
defines the unit; beta is meaningful relative to it — exactly as in
standard PPN practice. HEADSTONE 23 STANDS: beta = 0.513 vs the 1.000
Mercury demands.