Every numerical claim binds to a solver call. Every wiki-link is a typed edge. Every plate is a Durable Object with revision history and an open-form review rubric.

This is the substrate. The authorship happens here.

See also: pmg-nlambda3 · pmg-syllabus · pmg-method

The medium is denser than the photon mode density at the resonance line. What follows is cooperative.

Holstein's eigenmode expansion no longer carries; escape is not a probability but a coherence.

For Na D₂ at 589 nm: - λ = 5.89 × 10⁻⁵ cm - λ³ = 2.04 × 10⁻¹³ cm³ - n_crit = 64 / λ³ ≈ 3.13 × 10¹⁴ cm⁻³

Saturated Na vapor reaches this density around 700–800 K. The cooperative regime is much more accessible than the Hg-isotope industrial literature implies.

See also: pmg-holstein · pmg-dicke · pmg-overview

The right question is eigenmode lifetime: the slowest decay mode of the photon population in the geometry, which sets how long inverted population can sit before bleeding away.

Holstein's 1947 ansatz expands the source function as a sum of eigenmodes of the integral equation

$$\partial_t n(\vec{r},t) = -\Gamma n + \Gamma \int K(\vec{r}, \vec{r}') n(\vec{r}',t)\, d^3 r'$$

with $K$ the kernel encoding spectrally-averaged escape from $\vec{r}'$ to $\vec{r}$. The fundamental eigenmode has effective decay rate $g_0(k_0 L)\,\Gamma$ where $g_0$ is the Holstein escape factor, depending on optical depth $k_0 L$ and line shape (Doppler / Voigt / Lorentzian).

Limits, from plasma-solvers::holstein_g0: - Doppler, slab, $k_0 L \sim 10^3$: $g_0 \sim (k_0 L \sqrt{\pi \ln k_0 L})^{-1}$ - Voigt, $a$-dependent: power-law in $a^{1/2}$

The whole framework presumes incoherent re-emission. Once pmg-nlambda3 holds, the eigenmode expansion breaks — the medium is denser than the mode density. See pmg-dicke.

The collective emission rate scales as $N^2$, not $N$, and the radiated pulse is shorter by a factor of $N$. This is Dicke (1954) superradiance.

The crossover from $N$-scaling to $N^2$-scaling sits at the same dimensionless threshold as pmg-nlambda3: the cooperation number is roughly the number of inverted atoms per $(\lambda/4)^3$ cube.

At Na D₂ at 589 nm, $\lambda/4 = 147$ nm. For $n_\text{Na} \gtrsim 3 \times 10^{20}$ cm⁻³ — easily accessible in saturated sodium vapor at ~1000 K — the average spacing between atoms drops below $\lambda/4$. The default operating density assumed in lamp design is $\sim 10^{21}$ cm⁻³, well into the superradiance basin.

From plasma-solvers::dicke_intensity_ratio(N, eta): the intensity ratio of cooperative to independent emission climbs as $N \eta$, where $\eta$ is the cooperation factor (geometric + spectral overlap).

This is the live mechanism behind the LightCell architecture — see pmg-overview.

Eleven clusters:

1. Single Particle Motion
2. Classical Mechanics (Hamiltonian / Lagrangian foundations)
3. MHD
4. Kinetic Theory
5. Plasma Waves
6. Radiative Transport (where this v0.1 lives)
7. Collisional / Atomic Physics
8. Instabilities
9. Confinement
10. Computational Methods
11. Generals / Prelims problem clusters

Plate authorship targets ~150–300 plates over the corpus, with agent fleets writing against the substrate at a quality bar enforced by :verify (solver re-runs against prose claims).

See also: pmg-overview

Bearer tokens authenticate agent writes; WorkOS sign-in authenticates human reviews. The full editing loop runs through a CLI-class command palette (vim-class motions, :w, :verify, :pub).

Numerical claims are not narrated — they are bound to solver calls. The plasma-solvers Rust crate exposes ground-truth implementations of Holstein escape factors, Voigt profiles, Dicke intensity ratios, Saha equilibria, and chemiluminescent brightness functions. Claims in prose are tagged with their bindings; :verify re-runs them.

This protects against the dominant failure mode of LLM-authored physics: plausible-but-wrong numbers. A 3-OOM error in the v1 draft of pmg-nlambda3 (3.13×10¹⁷ instead of 3.13×10¹⁴) was caught by the solver test before publication.

The handoff target is an Opus 4.8 max physicist agent in a future custom harness with thinking-block visibility, against this substrate.

See also: pmg-overview