E1 Angle → cone — trichromacy as three angle-bands
The three cone opsins sit at three distinct propagation angles χ(λmax) ⇒ trichromacy; the cone/rod lineage emerges from the R19 switch ordered by spinodal(γ), with A4 shape breaking γ-ties.
What this rung establishes
Colour is sampled as three angles. The three cone opsins are placed on the inherited angle map by their measured peak wavelength (literature, not γ, not fitted), and land at three distinct near-transverse angle-bands — OPN1SW (S/blue) at 89.7497°, OPN1MW (M/green) at 89.8006°, OPN1LW (L/red) at 89.8428° — so the eye reads colour as three angles: trichromacy. The committed 633/532 anchor (red 89.9378° ≠ green 89.8248°, separation 0.1130°) is the falsifier, asserted with no fitting. [F][L]
Key results
- S–M angle separation
- 0.0509°
- S–L angle separation
- 0.0931°
- M–L angle separation
- 0.0421°
- Lineage order key
- argsort(spinodal(γ)) — lowest-threshold switch first
- First cone (OPN1SW)
- γ = 1.3663, spinodal = 0.6147
- Stiffest rod gene (PDE6B)
- γ = 1.5354, spinodal = 0.7323
The cone/rod lineage emerges from the shared R19 Organ primitive: emergence
order is the substrate's forced key argsort(spinodal(γ)), and relative size is dwell ∝ γ^1.5.
Whether this substrate order matches real retinal developmental time is an open empirical
question — reported, not fitted. [F][O]
A4 breaks γ-ties: equal-γ genes are not interchangeable
The order key is a total order: primary spinodal(γ), tie-break the A4 shape. The rod CNG channel's α/β subunits CNGA1 and CNGB1 are the closest γ pair in the whole eye atlas (Δγ = 0.0003); at three-decimal γ resolution they collapse to an identical value, exactly the failure mode of reading γ alone. Their A4 shape amplitudes differ (0.17130 vs 0.07902, a factor of 2.17×), so the shape tie-break orders them deterministically. The full key gives 19/19 unique ranks — no collapse. [V]
Grades (VP-SPEC C3 — honest)
| [F] | The angle law λ→χ and the 633/532 anchor; three distinct angle-bands; the R19 order argsort(spinodal(γ)); dwell ∝ γ^1.5; the A4 tie-break rule. |
| [V] | Organ spinodal == measured atlas for all genes; the (spinodal, A4) key is a strict total order; CNGA1/CNGB1 collapse under γ-alone and are broken by A4 shape. |
| [L] | Every γ (+A4) from NCBI promoters, cached; the cone λmax (S420/M530/L560, literature). None fitted. |
| [O] | Absolute angle→firing scale (→ E2); whether the substrate order matches developmental time; the felt colour percept (→ mind volume). Each obstacle named. |
Reproducibility
Every number on this page is the code’s own output. The transcript below is the verbatim, hash-pinned stdout of the listed module(s); tools/gate_volume.py re-runs them and asserts HTML↔code drift 0.
research/E1-angle-to-cone/run.pysha256 d2a46872d3756b83abca29de…
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E1 — ANGLE → CONE (the first emergence; built on the frozen inherited foundation)
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inherited invariant quantum size D = 4.852620 pm (χ depends on λ alone)
consumes (frozen): vp_color_by_angle.chi_deg/D · vp_substrate.Organ · organ_gamma.json γ+A4
re-derives: nothing. γ measured, never fitted. γ = promoter STRUCTURE only (firewall).
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PART A — three cone opsins on the angle map → trichromacy as three angle-bands
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[falsifier] committed anchor: red 633nm → χ=89.9378°, green 532nm → χ=89.8248°, sep=0.1130° [F]
[place] each cone opsin at its MEASURED λmax (literature [L]), mapped by the inherited law:
OPN1SW (S/blue ) λmax= 420nm → χ=89.7497° (γ=1.3663 read separately; NOT used to place the angle — firewall)
OPN1MW (M/green) λmax= 530nm → χ=89.8006° (γ=1.4058 read separately; NOT used to place the angle — firewall)
OPN1LW (L/red ) λmax= 560nm → χ=89.8428° (γ=1.4820 read separately; NOT used to place the angle — firewall)
[bands] pairwise angle separations (each colour is a BAND, not a sharp line):
OPN1SW vs OPN1MW: Δχ=0.0509°
OPN1SW vs OPN1LW: Δχ=0.0931°
OPN1MW vs OPN1LW: Δχ=0.0421°
three distinct angle-bands? True · S<M<L monotone at these peaks? True
→ the eye reads colour as three angles (trichromacy). Globally χ(λ) is hypersensitive/distributional
(inherited honesty: not a smooth monotone lookup); the felt colour percept is the mind volume's. [F]/[O]
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PART B — emerge the cone/rod lineage via the R19 Organ (order = argsort(spinodal(γ)))
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the cone/rod lineage (nodes: cone_color_angle, rod, rod_phototransduction, photoreceptor),
emerged by the substrate rule — lowest spinodal flips first: [F] order · [F] dwell∝γ^1.5 (abs [O])
rank gene node γ spinodal rel.dwell
1 OPN1SW cone_color_angle 1.3663 0.6147 1.0000 ← cone
2 OPN1MW cone_color_angle 1.4058 0.6415 1.0437 ← cone
3 OTX2 photoreceptor 1.4217 0.6524 1.0614
4 CRX photoreceptor 1.4233 0.6536 1.0632
5 NRL rod 1.4271 0.6562 1.0675
6 CNGB1 rod_phototransduction 1.4357 0.6621 1.0772
7 CNGA1 rod_phototransduction 1.4360 0.6624 1.0775
8 GNAT1 rod_phototransduction 1.4511 0.6728 1.0945
9 RHO rod_phototransduction 1.4719 0.6873 1.1181
10 OPN1LW cone_color_angle 1.4820 0.6944 1.1297 ← cone
11 PDE6B rod_phototransduction 1.5354 0.7323 1.1913
cone ranks in the lineage: OPN1SW=1, OPN1MW=2, OPN1LW=10
[O] whether this substrate order maps onto real retinal developmental TIME is an open
empirical question — obstacle: needs developmental-timing data; NOT fitted, NOT assumed.
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PART C — A4 tie-break: equal-γ genes are NOT interchangeable (DNA v1.13)
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order key (TOTAL): primary = spinodal(γ); tie-break = A4 shape (amplitude → stiffest_offset → symbol).
the A4 key acts ONLY as a tie-break — for distinct γ, γ alone decides; it is a stated
derived convention, not a fit.
[total order] full key gives 19/19 unique ranks → no two genes collapse.
[real near-degeneracy] CNGA1 vs CNGB1 — the rod CNG channel α/β subunits, closest γ pair in the atlas:
CNGA1: γ=1.4360 spinodal=0.6624 shape_amp=0.17130 stiffest_off=1900
CNGB1: γ=1.4357 spinodal=0.6621 shape_amp=0.07902 stiffest_off=1775
Δγ = 0.0003
at 3-decimal γ resolution: CNGA1 γ→1.436/spinodal→0.662, CNGB1 γ→1.436/spinodal→0.662
γ-ALONE collapses them to one value? True ← the failure mode (genes read as identical)
A4 shape_amplitude differs 2.17× → shape tie-break orders them: CNGB1 before CNGA1 [V]
→ two genes with equal γ but different A4 shape are NOT interchangeable: the emergence
reads LEVEL (γ) AND SHAPE (A4), never γ alone.
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E1 GRADES (VP-SPEC C3) — honest
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[F] forced : the angle law λ→χ and the 633/532 anchor; the three distinct angle-bands;
the R19 order = argsort(spinodal(γ)); dwell ∝ γ^1.5; the A4 tie-break rule.
[V] verified : Organ spinodal == measured atlas for all 16 genes; the full (spinodal,A4)
key is a strict total order; CNGA1/CNGB1 collapse under γ-alone and are
broken by A4 shape. (γ+A4 themselves re-proved offline by verify_seed [3].)
[L] measured : every γ + A4 (NCBI promoters, cached); the cone λmax (S420/M530/L560, lit.).
[O] open : absolute angle→firing and photon→Hz scale (E2 / calibration); whether the
substrate order matches real developmental TIME (needs timing data); the
full A4 anchor/loop/anchor-phase (needs the NCBI feature table); the FELT
colour percept (→ mind volume). Each obstacle named, never invented.
LEARNED: the eye reads colour as the light-propagation ANGLE χ(λmax) — three cone opsins at
three distinct angle-bands = trichromacy — and the cone/rod lineage EMERGES from the
R19 switch ordered by spinodal(γ), with the A4 SHAPE breaking γ-degeneracies (equal-γ
genes are not interchangeable). Foundation untouched; nothing fitted; firewall intact.
sha256: 64622f7a5a641b7693a7e9ed63e361e677238debbef1ad4f0fa3273ad4da7a09