Lineum Experimental — Thermo Calibration (v1.1.0-exp)

Status: Draft (experimental track)
Scope: canonical core + explicit reservoir/noise; thermometer calibration; reporting of T and S.
Does not change core claims. Core stays zero-temperature deterministic; this doc defines an extra apparatus.

1. Goal (plain English)

Define a repeatable way to talk about “temperature” and “entropy” in Lineum by:

• adding a controlled reservoir (noise/dissipation),
• calibrating a thermometer (mapping noise → T) on a reference,
• choosing a clear entropy estimator,
• and publishing falsifiable checks + artifacts.

2. Apparatus

• Reservoir: complex zero-mean noise ξ with controlled amplitude σ_ξ; optional weak dissipation δ_T for stationarity.
• Reference thermometer: small harmonic patch (linearized ψ) with known response → use equipartition to fit T(σ_ξ).
• Production runs: canonical seeds (17/23/41/73) + calibrated T(σ_ξ); κ static (as in core).

3. Definitions

• Temperature (T): scalar defined by calibrated map (T = \mathcal{T}(\sigma_\xi)) from the reference experiment.
  Store (\mathcal{T}) and its fit params in *_thermo_fit.json.
• Entropy (S): choose one and stick to it (report both if needed):
  • Spectral entropy (S_{\mathrm{spec}}): Shannon entropy of normalized power spectrum of center trace.
  • Field entropy (S_{\mathrm{field}}): Shannon entropy of (|\psi|^2) histogram over the grid (fixed binning).
• Reporting: mean ±95% CI over sliding windows (same bootstrap as core).

4. Falsifiable checks

• (T1) Calibration sanity: on the reference patch, variance vs. σ_ξ follows the fitted (\mathcal{T}) within ±10%.
• (T2) Fluctuation–dissipation: with tiny δT, measured (S{\mathrm{spec}}) increases monotonically with T (no reversals).
• (T3) Reproducibility: at fixed T, (S) matches across seeds within ±10% band.
• (T4) Zero-T limit: as σ_ξ → 0, (S) approaches the deterministic baseline (core).

5. Outputs (per RUN_TAG_T)

• *_thermo_fit.json — parameters of ( \mathcal{T}(\sigma_\xi) ) (calibration run).
• *_thermo_summary.csv — T, S_spec, S_field (means + 95% CI).
• *_thermo_spectrum_plot.png — spectra across T.
• *_thermo_entropy_vs_T.png — (S) vs. (T) trend with CI.

6. Repro manifest (example)

• Base: canonical spec6_false_s41 (Δt=1.0e−21 s, grid 128×128, κ static, float64).
• Reservoir: ξ ~ 𝒞𝒩(0, σξ²), σξ ∈ {0, 1e−3, 2e−3, 5e−3, 1e−2}.
• Dissipation (optional): δ_T ≪ δ_core (e.g., δ_T = 1e−4).
• Windows/CI: as in core (W=256, hop=128, bootstrap 95%).

7. Notes & Risks

• “Temperature” here is operational (via calibration), ne „fundamentální T“.
• Entropy choice must be fixed before runs; měnit definici = nový experiment.
• All numbers live in output/ with the {RUN_TAG_T}_… prefix; HTML shows the calibrated T next to σ_ξ.

Track policy: This is experimental (v1.1.x-exp). Core v1.0.3-core zůstává beze změny a neobsahuje T ani S.