The bulb map

One receptor → one glomerulus is a bijection, so the combinatorial capacity 2^N = 128 is carried intact into a spatial odour map. The organisers emerge as R19 Organs in spinodal(γ) order (EBF1 → EMX2 → LHX2). Which glomerulus a receptor targets is axon-guidance chemistry — a named [O].

The 3 OSN organisers emerge as R19 Organs in spinodal(γ) order (EBF1 → EMX2 → LHX2); one-OR→one-glomerulus convergence is a bijection, preserving capacity 2^N = 128 as a spatial map. The targeting coordinate is a named [O].

The map's developmental order is forced by measured γ

Smell's substitute for a spatial image is the bulb map: axons of the same receptor converge onto specific glomeruli, turning the receptor-space code into a spatial odour map. The organisers that lay it down (the OSN-identity transcription factors) emerge as R19 Organs in spinodal(γ) order.

The 3 OSN-identity organisers in spinodal(γ) order; dwell ∝ γ^1.5 sets relative size. Lowest γ clears its presence threshold first.
organiser	order	γ	h* = spinodal	dwell ∝ γ^1.5	role
EBF1	1	1.4097	0.64423	1.52159	OSN differentiation (early B-cell factor)
EMX2	2	1.4574	0.67720	1.59947	OR expression regulation
LHX2	3	1.5172	0.71930	1.69891	OSN differentiation / OR gene choice

The emergence order is EBF1 → EMX2 → LHX2 — monotone in measured γ. Each Organ is absent below 0.9·h* and present above 1.1·h*: an intact downstream pathway with the master switch off still yields absence, a real organ rather than parts.

Convergence is a bijection — it preserves the capacity 2^N

One OR → one glomerulus is an injective relabelling of the 7 receptor channels onto 7 bulb positions. A bijection on N channels induces a bijection on their 2^N subsets, so the combinatorial capacity is carried into bulb space intact: 2^N = 128 distinct spatial images.

Because a bijection preserves chains, the receptor-space nested thermometer maps to a nested spatial thermometer — 4 patterns, glomeruli lighting in the same order. The map inherits the code's order and capacity from the frozen switch and measured γ.

The honest [O] — the targeting coordinate is not in γ

The substrate fixes the map's order and capacity, but not which physical glomerulus a given receptor targets. That coordinate is axon-guidance chemistry — the receptor's own signalling shaping a Neuropilin-1/Sema3A gradient — in its coding sequence, not its promoter γ. This is the same kind of molecular [O] as the odorant key: structure is substrate-derived, specificity is not.