# n183 — THE NOISE GATE, EXECUTED: the active branch survives its executioner at model level; the LPF leg returns NO PHYSICAL VERDICT

**Date:** 2026-07-11 · **Spec:** `gates/active-medium-noise.json`, sha256 `176a6c1f…57f4`, frozen (with the six-point parameter grid) before execution. **Script:** `n183_noise_gate.py` → `n183_results.json`. **Reproduce:** `python3 n183_noise_gate.py`. **Model:** the n33 microscopic bath (drift copied verbatim); no regulator appears anywhere in the computation.

## Per-leg verdicts (independent, as the spec demands)

**Leg 1 — unregularized stability: PASS.** The exact drift A, no ε anywhere: zero unstable eigenmodes at all six grid points; exactly **2 zero modes**, both identified and classified — the uniform (τ̄, ε̄) pair, verified *exactly decoupled in both directions* (A·u = 0 and uᵀ·A = 0 to 10⁻¹⁴): the global time origin (gauge) and the conserved global energy offset. Projecting only that demonstrated-redundant pair, the physical complement has **max Re λ = −1.3×10⁻³ (g = 0.1) to −5.3×10⁻³ (g = 0.2)** — genuinely negative, scale g²κ/(Δ²+κ²/4): the audit's own effective damping. The n74 flaw stands as a record (its −10⁻⁶ "margin" was the inserted regulator), but the honest recomputation shows **the active vacuum is stable in the unregularized physical subspace** — the flaw was in the method, not the physics.

**Leg 2 — realizability: PASS.** Canonical commutator preservation AΩ + ΩAᵀ + BΩ_inBᵀ = 0 holds to 4.4×10⁻¹⁶ (exact input–output structure, not a Lyapunov artifact); the steady covariance satisfies σ + iΩ/2 ≥ 0 (min eigenvalue −10⁻¹³, numerical zero) at every grid point, both branches.

**Leg 3 — complete input–output model.** A, B, C, D explicit; matter couples to **both** auxiliary quadratures (x_a ↔ Bτ and η·p_a ↔ Bε, η = 0.5 — nothing dropped). Device class: **phase-sensitive** (unequal two-quadrature coupling), not a phase-preserving amplifier — which is why the Caves added-noise bound does not force noise into the force quadrature. The idler is exhibited: the reflected monitor output a_out = a_in + √κ·a carries the entropy.

**Leg 4 — full symmetrized noise: the central result.** The complete matter-sector spectral matrix S(ω) over 400 frequencies, active vs passive at matched (g, κ): **identical to machine precision in every matter-coupled quadrature** (max ratio 1.000000). The n74-era claim — the force's sign is dispersive, the noise absorptive, only the former flips with Δ — is now verified at the **full-matrix level**, not one observable. Frozen condition F does not trigger: there is no hidden quadrature carrying the gain noise, because there is no phase-preserving gain.

**Leg 5 — force PSD.** F = −λ v·ε derived from the stated action (v = the matter block's boundary difference, declared); S_F(ω) computed at all grid points (peaks 0.9–4.9 in model units). Spatial kernel and volume scaling inherit n181's per-junction structure.

**Leg 6 — LPF comparison: NO PHYSICAL VERDICT (frozen condition E).** The model-to-SI force normalization (λ and ε in newtons) is underived. Per the frozen rule the missing factor is **not** set to one, and **the claim that LISA Pathfinder tests this vacuum is withdrawn** until the normalization chain exists. The model calculation stands; the empirical confrontation does not.

## Scope, stated before anyone asks

Gaussian dynamics, linear response, N = 12, six pre-frozen parameter points. The inverted Hamiltonian (Δ < 0) is **put in by hand as ideal** — the pump that would maintain it is not modeled, so pump noise, pump depletion, and the realizability of the inversion itself remain open. The result is exactly this wide: *within the Gaussian model, the inverted branch is stable, physically realizable, and adds zero noise to every matter-coupled quadrature relative to the passive branch.* Whether nature contains such a medium is untouched.

(Bookkeeping: macOS Accelerate emits spurious matmul RuntimeWarnings on this machine — the same class Codex flagged in n87c. All outputs are finite and the exact identities hold to 10⁻¹⁶; the warnings do not affect values.)

**Epistemic class: [A-model] throughout; leg 6 is the honest boundary of the claim.**

## Amendment (same day) — the reviewer's interpretation corrections, accepted

1. **What Δ→−Δ actually is:** a rotating-frame detuning reversal in H_aux = Δa†a with
   vacuum damping D[a] — **not** a constructed population-inverted reservoir. The pump
   that would realize and maintain a true inversion (with its own fluctuations and energy
   flow) is absent from the model. n183 therefore demonstrates: *a stable linear
   input–output system whose dispersive response changes sign under detuning reversal* —
   and does not demonstrate a physically realized inverted vacuum. The identification of
   the Δ<0 branch with an active pumped vacuum is a transfer assumption, now labeled.
2. **"Phase-sensitive" retracted as a classification:** unequal coupling to two
   quadratures is not sufficient; the label requires quadrature-dependent gain or the
   Bogoliubov input–output map, neither computed. The Caves-exemption *inference* is
   therefore premature. The computed *fact* stands unchanged: matched matter-coupled
   spectra are identical under Δ→−Δ.
3. **What the corrected result yields — promoted as prediction 33:** the odd/even pairing.
   Coherent response odd, noise even: J(−Δ) = −J(+Δ) with S_F(−Δ,ω) = S_F(+Δ,ω), and the
   parameter-free normalized curve J/(g²/κ) = −2x/(1+x²), x = 2Δ/κ (extrema at Δ = ±κ/2,
   1/|Δ| tail). Analog-testable now (two ions/resonators + damped tunable mediator);
   pre-declared kills at 5% on both the curve and the noise-evenness after measured
   technical asymmetries. A pass validates the mechanism the code actually computes —
   not gravity.

## Second amendment (audit §§9–10) — the output sign and the last of the 'active' language

The output boundary condition used a_out = a_in + √κ·a; the standard Gardiner–Collett relation for this Langevin convention is a_out = a_in − √κ·a (a passive uncoupled cavity must reflect at unit modulus; the script's version gives 3). **Corrected in the script.** The internal matter spectra come from the resolvent and are unaffected — the odd/even result stands — but the "idler exhibited in the reflected output" claim is retracted until the corrected output spectrum is recomputed. Further, §9 sharpens the first amendment: the Δ < 0 model contains no gain, no inversion, and no pump *at all* — both branches damp toward vacuum — so stability under Δ → −Δ was expected, the even noise is a property of a detuned passive loss model, and phrases like "the active vacuum is stable" are unsupported by n183. What n183 established, exactly: a damped linear mediator has odd dispersive response and even vacuum-noise power under detuning reversal (prediction 33's content, untouched).