# n64 — the parameter card: bounds on the model, believing every experiment
# (2026-07-09; derivations below; honesty classes on every number)

Classes: [A] exact within the model's stated assumptions;
[B] order-of-magnitude from a measured shape; [C] conditional on
order-unity coupling in the units mapping (the toy's kappa = 1).

## The five parameters and their bounds

1. a — scaling dimension of the audit rate (fixes gamma_PPN)
   BOUND [A]: |a| < 5.8e-6.
   Source: Cassini |gamma_PPN - 1| < 2.3e-5 through gamma = (1-2a)/(1+2a).
   Consequence: the audit rate is state-independent to six digits;
   the knee is rigid across potentials to the same level.

2. l_s — the substrate length (sets where Newton starts alternating)
   BOUND [B]: l_s <~ 5 micrometers.
   Source: Eot-Wash-class short-range tests (no deviation at ~50 um at
   the percent level) against the measured n49 dressing profile
   (alternating, ~2-4% at r = 10-12 l_s, ~20% at r = 1-2 l_s).
   Note: no lower bound from data; Planckian l_s is fully allowed.

3. M_cap / rho_exhaust — the budget depth (the exhaustion scale)
   BOUND [B], two-sided IF the NS cliff is the cap (the model's
   registered reading, n63 blade 2):
     2.35 Msun <= M_cap <~ 2.5-3 Msun
   (floor: PSR J0952-0607 exists; ceiling: GW170817 remnant-collapse
   readings of the TOV maximum). Equivalently rho_exhaust ~ (5-10) x
   nuclear saturation density. Additional consistency [B]: the +19%
   bump must onset above the central density of ordinary 1.4 Msun
   stars (GW170817 tidal data GR-consistent at few percent), which the
   window above satisfies. If the cliff is NOT the cap, only the floor
   survives: M_cap > 2.35 Msun.

4. gamma_drain — the audit rate (the knee)
   FLOOR [C]: gamma >~ 1e12 s^-1.
   Source: J0737-3039 orbital decay (GR to 1.3e-4) through the measured
   drainage Q-factor Q = 0.02 gamma/Omega, at order-unity drag
   coupling. Same-direction floors (weaker or comparable): neutron
   interferometry through the measured contamination law dev = 2.81/R
   (n62); solar p-mode linewidths.
   CEILING [C]: gamma <= c/l_s ~ 6e13 s^-1 IF l_s sits at its
   short-range ceiling (the audit cannot outrun the substrate clock).
   THE WINDOW, stated with both class-C flags up: if couplings are
   order-unity, the knee lives in ~1-60 THz — the far-infrared. If the
   drag coupling carries gravitational suppression (likely), the floor
   collapses and only the n62 structural floor remains; if l_s is
   Planckian, the ceiling opens to ~1e43. The honest summary: the knee
   is bounded into a wedge on the (coupling, gamma) plane, pinned at
   one corner by pulsars and at the other by short-range gravity —
   the first quantitative habitat the knee has ever had.

5. c_drag (with kappa_read) — the friction coupling
   BOUND [C]: degenerate with gamma: pulsars bound the combination
   c_drag (Omega_orb/gamma)^2 < 1.3e-4 x (GR quadrupole power)/
   (binding x Omega); one constraint-curve on the (c_drag, gamma)
   plane. Toy value c_drag = 0.02 at kappa = 1 recorded for the
   mapping.

## Fixed, not free
- G_Newton = 1/S: matching observed G fixes the dressed stiffness in
  physical units once l_s is chosen — one relation between l_s and the
  substrate consumption unit, not a new freedom.
- gamma_PPN = 1 is then not a parameter at all: it is bound 1.

## What would move the card
- The units mapping (the standing theory debt) collapses every [C]
  into [B] or better.
- A measured knee anywhere turns the card into a one-parameter test:
  gamma read off, friction and PPN-rigidity predicted with no freedom.
- A compact object above ~3 Msun (non-BH, or any object the model must
  bookkeep) breaks row 3 and kills the model outright.

## The sentence the card earns
Believing every experiment we confronted, the model is ALIVE INSIDE A
WEDGE: audit state-independent to six digits, substrate finer than
five microns, budget exhausted near ten nuclear densities, knee
somewhere between the pulsar floor and the substrate ceiling — and
every side of the wedge is a named experiment that could still close it.