OpenCretin — the mode-occupancy waterfall

gibbs speciation → cascade + CR (no temperature) → the 3p elevation, resolved level by level. Drag the trapping and watch T_exc float.

Knobs (inputs, all flagged)

Funnel knobs — 589→819 harvest

Readouts

T_exc (3p)
excitation temp, a READOUT
× Boltzmann
n3p elevation
photon occ. n̄
trapped-field strength
free Na
radiating fraction (gibbs)
funnel η — 819 harvest
P₈₁₉ escaped / 3d de-excitation · ceiling shown

The four-level waterfall: 3s → 3p → 3d → 4p. Bar height = population (log). The dashed mark on 3p is its Boltzmann value; the gap above it is the elevation the trapped field drives.

T_exc(3p) vs trapping escape factor g₀ at the current T/seed. The elevation is a SURFACE in the trapped field, resolved by the cascade — not a pressure gate (W3, corrected).

The 589→819 funnel efficiency η = P₈₁₉(escaped) / (total 3d de-excitation), swept over the 819 escape fraction g₈₁₉ at the current density/superradiance regime. The dot is the current operating point; the dashed line is the hard ceiling g₈₁₉/(1+g₈₁₉) set by 819 self-trapping. The device thesis, told straight: the 589 trap builds the 3p reservoir fine (elevation shown), but at full flame density 3d is quenched back to 3p ~40× faster than it radiates 819, so η sits at ~1e-3 — quench-limited and flat. η climbs only when 819 outruns kQ: thin the sideband (g₈₁₉↑), drop density (kQ↓), drive it superradiant. All three together reach η≈0.95.

The ionization boundary (W4): P_Dline/P_total vs temperature. As Saha ionizes the sodium, free-free + free-bound continuum switches on and overtakes the line near ~16,000 K. The device is a D-line emitter at flame T (≤4000 K); only the extreme-pulse core becomes a continuum-with-a-dip. P_Dline/P_total is a FUNCTION over OOMs, not a number.

Assumptions tail — what this cell rests on

Load-bearing

  • BEAR The trapped field enters as the dimensionless photon occupation $\bar n$ (stim/spont $=\bar n$). RUN $\bar n{=}0\to$ chemistry, $\bar n{=}\bar n_\text{LTE}\to$ Boltzmann, $\bar n{\uparrow}\to$ elevation toward $g_1/g_0{=}3$.
  • BEAR $\bar n \approx \bar n_\text{LTE}(1 + g_0 f_\text{trap})$ — trapping piles photons in the mode. ASSUME the real g₀·f_trap at device geometry is stage-3 (2-D Λ-iteration), not yet solved.
  • BEAR Speciation from gibbs (free Na, n_e) is the radiating inventory. RUN validated to JANAF; caught the doc's NaOH-30× error.

Shortcuts (owed)

  • ASSUME 4-level CR (3s/3p/3d/4p); no ionization stage in the levels (Na⁺ via gibbs only). Saha ionization boundary + core/sheath zones: next.
  • ASSUME radical pool [H],[OH] crude-T-scaled; single cell (0-D), not yet the core/sheath gradient.
  • ASSUME gibbs table is equilibrium speciation; finite vaporization kinetics not checked (Damköhler).

Weird (the device's signature)

  • Temperature is nowhere defined — populations are the state, T is a readout. The three temperatures {kinetic, excitation, brightness} do not coincide.
  • The 3p elevation is a surface in n̄, resolved by the waterfall — NOT a 1/P pressure gate.
  • NaCl is a closed mass loop (rewicks, latent heat recovers); the speciation partition sets seed inventory, not an energy loss.