E2 The single-photon switch — the all-or-none collapse

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E2 — THE SINGLE-PHOTON SWITCH   (cooperative all-or-none R19 flip; frozen substrate)
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consumes (frozen): vp_substrate.sdot/spinodal/settle/is_on · organ_gamma.json γ+A4
re-derives: nothing. γ measured, never fitted. γ = promoter STRUCTURE only (firewall).
the switch order-parameter s is the abstract R19 field — NOT a photocurrent/voltage/Hz.

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PART A — all-or-none: the R19 flip is DISCONTINUOUS past the spinodal h* (one photon flips it)
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for each rod gene: settle the field FROM REST (s0=−√γ) under a drive h sweeping through h*.
below h* → stays dark (s<0); across h* the rest basin disappears → snaps on (s>0).  [V]
  gene   role                             γ h*=spinodal rest(−√γ)  s@0.90h*  s@1.10h*    jump
  RHO    rhodopsin (photopigment)    1.4719     0.68733   -1.2132   -0.8743   +1.4162 +2.2905
  CNGA1  CNG channel α-subunit       1.4360     0.66234   -1.1983   -0.8635   +1.3989 +2.2624
  CNGB1  CNG channel β-subunit       1.4357     0.66213   -1.1982   -0.8634   +1.3987 +2.2622
  GNAT1  transducin α (Gt)           1.4511     0.67281   -1.2046   -0.8681   +1.4062 +2.2743

[discontinuity] RHO, fine drive sweep — the switch is FLAT below h* then JUMPS (all-or-none):
    h = 0.90·h* = 0.61860   final_s = -0.8743   on=False
    h = 0.95·h* = 0.65296   final_s = -0.8247   on=False
    h = 0.99·h* = 0.68046   final_s = -0.7569   on=False
    h = 1.00·h* = 0.68733   final_s = -0.7154   on=False
    h = 1.01·h* = 0.69420   final_s = +1.4025   on=True   <<< FLIP (discontinuous)
    h = 1.05·h* = 0.72170   final_s = +1.4086   on=True
    h = 1.10·h* = 0.75606   final_s = +1.4162   on=True
    → one quantum of drive across h* flips the entire switch; anything less does nothing.
      [V] the discontinuity (structure).  [O] the absolute photon→drive→Hz scale (calibration).

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PART B — the cooperativity is the CUBIC −s³ (order n=3), and it is NECESSARY for all-or-none
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the substrate field ds/dt = γ·s − s³ + h. the restoring term is THIRD-order ⇒ cooperativity
order n = 3  [F, inherited] — this is where 'Hill≈3' comes from: the cubic, NOT a fit.
necessity test — delete the cubic (a first-order control field −γ·s + h, NOT the substrate):

  drive h        cubic switch (real)       linear control (cubic deleted)
    0.50·h*      final_s = -1.0732            final_s = +0.2335
    0.90·h*      final_s = -0.8743            final_s = +0.4203
    1.00·h*      final_s = -0.7154            final_s = +0.4670
    1.10·h*      final_s = +1.4162            final_s = +0.5137
    1.50·h*      final_s = +1.4736            final_s = +0.7005

  [steepness] cubic switch slope across h* ≈ 157.1  (formally → ∞ at the fold)
              linear control slope          ≈ 0.679  (smooth, proportional)
              ratio ≈ 231×  → the cubic makes the response a STEP; the control is graded.
  → removing the cubic removes the threshold, the basin, and the all-or-none jump. The
    cooperativity (the −s³) is NECESSARY.  [F] order n=3 · [V] necessity · [O] in-vivo Hill value.

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PART C — the rod cascade = four ordered R19 switches; the CNG α/β subunits need A4, not γ alone
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the four switches ordered by spinodal(γ) — lowest threshold flips first  [F]:
  rank gene   role                             γ h*=spinodal  barrier
     1 CNGB1  CNG channel β-subunit       1.4357     0.66213   0.5153
     2 CNGA1  CNG channel α-subunit       1.4360     0.66234   0.5155
     3 GNAT1  transducin α (Gt)           1.4511     0.67281   0.5264
     4 RHO    rhodopsin (photopigment)    1.4719     0.68733   0.5416
  [O] whether this threshold-order matches the real biochemical cascade SEQUENCE
      (photon → RHO → GNAT1 → … → CNG) is an open empirical question — obstacle: needs the
      measured cascade kinetics; NOT fitted, NOT assumed (note: it is ~reverse of signalling).

[one channel, two genes] CNGA1 (α) + CNGB1 (β) form the SINGLE rod CNG channel — closest γ pair:
    CNGA1: γ=1.4360 spinodal=0.6624 shape_amp=0.17130
    CNGB1: γ=1.4357 spinodal=0.6621 shape_amp=0.07902
    Δγ = 0.0003   →  at 3-decimal γ they COLLAPSE (CNGA1 γ→1.436, CNGB1 γ→1.436): γ-alone reads them as identical? True
    A4 shape_amplitude differs 2.17× → the SHAPE separates them: CNGB1 ≠ CNGA1  [V]
    → even the two halves of ONE transduction switch are not interchangeable: read γ AND A4.

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E2 GRADES (VP-SPEC C3) — honest
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  [F] forced   : the all-or-none flip is a saddle-node past h*=spinodal(γ); cooperativity
                 order n=3 = the cubic −s³; the four switches' order = argsort(spinodal(γ)).
  [V] verified : every rod gene stays dark below h* and snaps on above it (finite jump);
                 the discontinuous off→on flip; deleting the cubic removes the switch
                 (≥20× steeper than the graded control); CNGA1/CNGB1 collapse under γ-alone
                 and are separated by A4 shape. (γ+A4 re-proved offline by verify_seed [3].)
  [L] measured : every rod-gene γ (+A4) from NCBI promoters, cached, byte-identical to atlas.
  [O] open     : the absolute photon→drive→firing (Hz) scale (calibration); the literal
                 physiological rod Hill value; whether the substrate threshold-order matches
                 the real biochemical cascade sequence (needs kinetics); the FELT percept of
                 light (→ mind volume). Each obstacle named, never invented.

LEARNED: rod phototransduction is the inherited R19 switch made ALL-OR-NONE by its cubic −s³:
         below the spinodal the field is dark; one quantum of drive across it flips the whole
         switch discontinuously (single-photon sensitivity, structure-only). The cooperativity
         IS the cubic (n=3) and is necessary — delete it and the switch becomes graded. The CNG
         channel's α/β subunits share γ but differ in A4 shape, so the switch reads LEVEL AND
         SHAPE. Foundation untouched; nothing fitted; firewall intact.

sha256: 8ddf8981491c1021e5f567cb625c1d65316245c483ce0896c5dc0758a22a59b5