The combinatorial odour code
Smell has no wave, so odour identity is a combinatorial pattern over the receptor bank. N = 7 all-or-none R19 switches give 2^N = 128 patterns; the measured γ sets only the threshold order. The odorant→receptor key is molecular recognition, not in γ — a named [O].
A bank of N = 7 olfactory-receptor R19 switches has capacity 2N = 128 combinatorial patterns; a uniform drive reaches a nested thermometer of 4 of them. The odorant→receptor key lives in the binding pocket, outside γ — the central [O].
Smell breaks the wave→place skeleton — honestly
Vision and hearing read a wave as a single physical place (propagation angle, basilar position). Smell has no wave: the stimulus is a molecule, so identity is a combinatorial pattern over a large olfactory-receptor repertoire — each odorant lights a subset of receptors, each receptor answers to many odorants.
The one thing the promoter γ supplies here is each receptor's excitability: the spinodal threshold orders the 7-gene panel from most to least trigger-happy. That is an expression layer, never which odorant binds which receptor.
| gene | rank | γ | h* = spinodal | A4 amp | odorant note |
|---|---|---|---|---|---|
| OR2J3 | 1 | 1.2224 | 0.52020 | 0.08098 | OR — cis-3-hexen-1-ol (green) |
| OR2W1 | 2 | 1.2412 | 0.53224 | 0.08711 | broadly-tuned OR |
| OR51E2 | 3 | 1.2427 | 0.53321 | 0.08267 | OR — short-chain acids / steroids |
| OR5AN1 | 4 | 1.2637 | 0.54678 | 0.09210 | OR — muscone (musk) |
| OR1D2 | 5 | 1.2714 | 0.55179 | 0.09530 | OR — bourgeonal / lily-of-the-valley |
| OR7D4 | 6 | 1.2945 | 0.56689 | 0.12418 | OR — androstenone (perceptual variation) |
| OR6A2 | 7 | 1.3036 | 0.57288 | 0.11104 | OR — aldehydes (cilantro) |
The code is combinatorial: capacity 2N ≫ N
A bank of N = 7 all-or-none switches has up to 2N = 128 distinguishable ON/OFF patterns — far more than the 7 receptors. That is why the genome carries hundreds of OR genes: a combinatorial code, not one receptor per odour.
A uniform drive swept up flips the frozen switches in spinodal order, yielding a nested thermometer readout of 4 patterns (ON counts {0, 3, 5, 7}, all ≤ N+1 = 8). The readout is fully substrate-derived from the measured thresholds.
The thermometer reaches only 4 of 128 patterns; the rest need an odorant-specific drive vector. An abstract vector driving only the 1st- and 3rd-ranked receptors hard reaches the non-nested ON set (OR2J3, OR51E2), unreachable by any uniform drive — but that vector is not in γ.
The honest negative — smell's identity is not a substrate quantity
Vision's "what" (colour) is a substrate quantity, the propagation angle χ. Smell's "what" (odour) is not: it is a combinatorial pattern whose key — the odorant↔receptor match — is molecular recognition in the receptor's binding pocket, outside both γ and A4. This is the volume's central [O], named throughout and never fitted.