# n57 — pre-registration: budget exhaustion (written before any code)

**New prediction from the model's own structure.** The monogamy budget
is FINITE: couplings cannot be drained below zero (k = 1 + dk > 0). The
quadratic theory ignores this bound; physical drainage cannot. At
extreme consumption the bound activates, and three consequences follow,
registered here before computing:

- P1 (SATURATION OF GRAVITY): the pair interaction's effective coupling
  G_eff(F) = V_int(F)/F^2 is constant in the linear regime and
  DECREASES once the bound activates — gravity weakens per unit mass^2
  at extreme compactness. Kill: G_eff constant or increasing past
  activation.
- P2 (THE DRY CORE): around a super-critical consumer, a contiguous
  region of maximally-drained links appears (dk at the bound) — an
  exhausted-vacuum core where no further drainage is possible: the
  model's analog of a horizon, produced by bookkeeping exhaustion, not
  by geometry. Kill: no contiguous saturated region forms.
- P3 (THE CORE GROWS WITH MASS): the core radius r_core(F) increases
  with consumption — the analog of the Schwarzschild radius growing
  with mass. Report the measured law r_core(F); no functional form is
  registered (the toy decides).
- Physical reading, if P1-P3 pass: this class of theories predicts NO
  singularities — potentials bounded by budget depth — and modified
  strong-field behavior (weakened attraction near exhausted cores),
  the natural habitat of horizonless-object / echo phenomenology.
  Registered as a structural prediction of the CLASS; strong-field
  numbers in physical units are out of the toy's reach and not claimed.

## Method
Ring N=200, info-metric cost G (n46), sum rule A dk = -c, plus the
physical bound dk_e >= -0.95 (margin from k=0 declared). Solver:
active-set iteration — solve the equality-constrained minimum, clamp
violated edges to the bound, re-solve on the free set, iterate to a
fixed point (report convergence). Consumers: opposite-parity pair at
d = 51, F swept 0.5 -> 6.0. V_int(F) from the cost functional as in
n46; core = maximal contiguous run of edges at the bound around a
consumer.

## Gates
- S0 (solver): at F small (no clamping), the active-set solution
  matches the unconstrained one to 1e-10.
- P1 gate: G_eff(F)/G_eff(0.5) < 0.9 at the largest F with a
  converged solution AND monotone decreasing past activation.
- P2 gate: contiguous saturated run >= 3 edges at some F <= 6.
- P3: r_core(F) reported with its fitted growth law (exploratory).

## Companion predictions registered by name (deferred, own gates later)
- n58 MACHIAN INERTIA: the gap-weighted inertia depends on the vacuum's
  spectrum; at finite temperature m_inertial shifts while consumption
  (m_grav) does not — a computable EP-violation channel delta(m_i/m_g)
  vs T. Requires the thermal Gaussian fidelity machinery
  (Banchi-Braunstein-Pirandola); deferred, not guessed.
- n59 LAMBDA-KNEE LINK: the idle cost of self-monitoring is a vacuum
  energy: Lambda ~ hbar * gamma_drain * (idle information density). If
  Lambda_observed sets gamma_drain, the decoherence knee is pinned near
  cosmological rates and NO knee exists in any laboratory band — which
  is itself a discriminating prediction (drainage-with-cosmological-
  knee vs DP floor vs GR nothing). The toy computation: idle density
  from the vacuum's own metric.
- n60 SHORT-RANGE SHAPE: if sub-substrate deviations from Newton are
  ever observed, this class REQUIRES them to alternate in sign with a
  ~1/r envelope (measured, n49) — unlike any Yukawa modification.
  Standing falsifier against future short-range gravity data.

## RESULTS (same day; n57_exhaustion.py)
- S0 PASS (6.6e-14). Solver caveat declared: monotone active set (no
  release) after the releasing variant cycled; the clamp set may be
  conservatively overestimated.
- P1 as registered: FAIL — but by richness, not absence. G_eff first
  RISES at activation (1.07, 1.19 at F = 1.5, 2.0 — a near-critical
  STRENGTHENING bump, unregistered, flagged exploratory) and then
  saturates hard: 0.76, 0.53, 0.30, 0.19, 0.13 by F = 6 — gravity
  weakens 7.6x per unit mass^2 at extreme consumption. The registered
  monotonicity clause was wrong; the saturation is real.
- P2 as registered: FAIL in 1D, for a dimensional reason visible in
  hindsight: the 1D staggered flux is CONSTANT along the ring (1D
  Gauss), so when it saturates it saturates EVERYWHERE — 101 of 200
  edges clamp at once (one full sublattice). No LOCALIZED core can
  exist in 1D. Two consequences recorded: (i) in 1D the model has a
  MAXIMUM TOTAL MASS on a compact universe (beyond global saturation
  the sum rule is infeasible); (ii) the dry-core prediction lives in
  d >= 2, where flux dilutes with distance and saturation localizes —
  n57b (2D) owed, with the core-radius law as its registered target.
- P3 void in 1D (no localized core to measure).
Standing prediction set after n57: saturation of G_eff at extreme
consumption (measured, 1D), a near-critical strengthening bump
(exploratory), a maximum mass on compact 1D (structural), localized
exhausted-vacuum cores in d >= 2 (registered, to run), plus n58-n60 as
named. The class predicts NO singularities: the budget bounds the well.