E9 Red-green colour vision — the angle map with one sample lost (theoretical, non-clinical)
Colour is the propagation angle, so the three cones are three angle-samples and the three discrimination axes are their pairwise margins; the green-red (M-L) margin is the smallest ⇒ the angle map forces red-green as the most fragile colour axis, and coincident λmax gives an exactly-zero margin — dichromacy (lose a sample) and anomalous trichromacy (peaks converge) are one continuum, stated direction-only behind a machine-checked magnitude firewall.
What this rung establishes
Colour, in this volume, is the light's propagation angle χ(λ) (E1) — not a frequency the receptor could track. So the three cone opsins are three angle-samples, and the three colour-discrimination axes are simply their pairwise angle margins. Read this way the angle map answers a question it was never tuned to: which colour axis is the most fragile. The three cones land at 89.7497° (S), 89.8006° (M) and 89.8428° (L), and the green-red (M–L) margin is the smallest of the three — so red-green is the structurally most fragile axis. This is forced by the measured peaks and the frozen law, and it matches that red-green is the most common inherited colour-vision difference. [F][L]
Key results
- Invariant quantum size
- D = 4.852620 pm (χ depends on λ alone)
- S / M / L cone angles
- 89.7497° / 89.8006° / 89.8428°
- Blue-green (S–M) margin
- 0.0509°
- Green-red (M–L) margin
- 0.0421° ← smallest (most fragile)
- Blue-red (S–L) margin
- 0.0931°
- How much tighter green-red is
- 1.208× tighter than S–M, 2.208× than S–L
- Coincident λmax ⇒ margin
- 0.000000° (exact — same angle)
The fragility ordering is geometry, not a clinical severity claim (which would be firewall-blocked): the green-red axis simply has the least angular room on the map. [F]
Dichromacy and anomalous trichromacy are one continuum
Because χ is a function of λ alone, two opsins with the same peak map to the same angle, so their margin is exactly 0.000000°. That single fact joins the two pictures. Dichromacy removes one of the three angle-samples — lose L and the samples left are S and M (surviving margin 0.0509°), lose M and they are S and L (surviving margin 0.0931°); in both the tight green-red axis vanishes and one chromatic axis survives. Anomalous trichromacy is two peaks converging: held inside one m-band, where χ is locally smooth-monotone (sawtooth-proof), the margin falls monotonically — 0.199367° → 0.073276° → 0.032565° → 0.010231° → 0.000000° — as the gap closes. The limit of convergence is the loss. [F][V]
The lever is therefore a pure direction: peaks toward each other shrink the margin (to zero at coincidence); peaks apart widen it. How anomalous, the real hybrid peak, any clinical severity — all are the firewall-blocked [O]; nothing is quantified or named. Honest caveat: χ(λ) is hypersensitive and distributional (a sawtooth, inherited from E1/E6), so the margin is a property of the committed peaks, not a smooth response to an arbitrary nanometre-scale shift; only the coincidence limit and the local within-band sense are forced — stated, not hidden.
Why it is colour-blindness, not loss of acuity
The three channels carried on one wave are orthogonal: colour is the angle χ (E1, the WHAT), position is the image geometry (E3, the WHERE), and brightness/detection is the R19 switch magnitude (E2). Removing a cone removes one angle-sample but neither a position-sample nor the switch — so the loss is confined to a single colour axis while spatial acuity and the light/dark response stay intact. That is forced by the channel orthogonality, and it is why the condition is specifically colour vision, with acuity preserved. The felt experience of colour confusion is the mind volume's. [F]
γ is read read-only; the genomics is measured, not γ
The opsin genes' γ (LEVEL) and A4 (SHAPE) are read as a structural excitability offset — read-only, byte-equal to the frozen atlas: OPN1LW γ = 1.4820 (spinodal 0.6944, A4 amplitude 0.09028) and OPN1MW γ = 1.4058 (spinodal 0.6415, A4 amplitude 0.12596), a level offset of Δγ = 0.0762 with shapes differing 1.40×. This chapter makes no claim that γ predicts the opsin peak — the optical layer (peak → angle) and the DNA-structural layer (γ/A4 → excitability) are kept separate. The genomic architecture that makes red-green X-linked and male-prevalent — the OPN1LW/OPN1MW tandem array on the X chromosome — is measured genomics [L], not derivable from the promoter-γ this package reads: a named [O].
Grades (VP-SPEC C3 — honest)
| [F] | Colour is the propagation angle ⇒ the three cones are three angle-samples and the three discrimination axes are their pairwise margins; the green-red (M–L) margin is the smallest; coincident peaks give an exactly-zero margin (so dichromacy = remove one sample, anomaly = peaks converge — one continuum); colour (angle) is orthogonal to position (image) and brightness (switch), so the loss costs exactly one colour axis. |
| [V] | Three distinct cone angles; M–L is the smallest of the three margins; the coincidence margin is exactly 0; the within-m-band convergence is monotone to 0; the remaining cones' R19 switch is unchanged; the cone γ is byte-equal to the atlas. The magnitude firewall is machine-checked. |
| [L] | Every cone γ (+A4) from NCBI promoters, cached, byte-identical to atlas; the cone peaks (S420/M530/L560, literature); red-green is the most common inherited colour-vision difference (epidemiology); the X-linked OPN1LW/OPN1MW tandem-array architecture (genomics). |
| [O] | The magnitude of any anomalous shift / the real hybrid peak / any clinical severity (firewall-blocked — none produced); the sawtooth, distributional χ(λ) (only the coincidence limit + local sense forced); the X-linked genomic architecture (needs the feature table, not the promoter-γ); the felt percept of colour and of colour confusion (→ mind volume). |
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/E9-red-green-dichromacy/run.pysha256 2e6eb1649c60d3ca9846189f…
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E9 — RED-GREEN COLOUR VISION (the angle map with one sample lost or two converged)
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SCOPE: theoretical, NON-CLINICAL. Structure-only / direction-only behind the magnitude firewall.
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; adds no γ. γ measured, never fitted; γ = promoter STRUCTURE only (firewall).
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PART A — three discrimination axes; the GREEN-RED axis is the tightest (most fragile)
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each cone opsin at its MEASURED λmax (literature [L]), mapped by the inherited law:
OPN1SW (S/blue ) λmax= 420nm → χ=89.7497°
OPN1MW (M/green) λmax= 530nm → χ=89.8006°
OPN1LW (L/red ) λmax= 560nm → χ=89.8428°
the three colour-discrimination axes are the three pairwise angle MARGINS:
S-M (blue-green) margin = 0.0509°
M-L (green-red) margin = 0.0421° ← SMALLEST
S-L (blue-red) margin = 0.0931°
green-red is the tightest axis? True (M-L is 1.208× tighter than S-M, 2.208× tighter than S-L)
→ FORCED by the measured λmax + the frozen angle law (no fitting). This MATCHES that
red-green is the most common inherited colour-vision difference [L]: the angle map
NAMES which axis is structurally most fragile. [F]↔[L]
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PART B — coincidence ⇒ collapse (exact): dichromacy and anomaly are ONE continuum
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χ is a function of λ ALONE, so two opsins with the SAME λmax map to the SAME angle ⇒ margin = 0.
[exact endpoint] hypothetical L′ placed AT λ(M): χ(L′)=89.8006° = χ(M) ⇒ margin = 0.000000° (EXACT zero)
[dichromacy] remove one of the three angle-samples (the cone is absent/non-functional):
lose OPN1LW (L/red ) → samples left: OPN1SW (89.7497°) + OPN1MW (89.8006°); surviving axis margin = 0.0509°
lose OPN1MW (M/green) → samples left: OPN1SW (89.7497°) + OPN1LW (89.8428°); surviving axis margin = 0.0931°
in BOTH cases the within-red-green (M-L) axis VANISHES; exactly one chromatic axis survives.
[anomalous trichromacy] two peaks CONVERGE; inside one m-band (χ locally smooth-monotone,
sawtooth-proof) bring a hypothetical L′ down toward λ(M); the margin falls monotonically to 0:
gap fraction 1.00 of one m-band → margin = 0.199367°
gap fraction 0.60 of one m-band → margin = 0.073276°
gap fraction 0.30 of one m-band → margin = 0.032565°
gap fraction 0.10 of one m-band → margin = 0.010231°
gap fraction 0.00 of one m-band → margin = 0.000000°
monotone fall to exactly 0 as the gap closes → the LIMIT of convergence IS the loss. [F]
[direction-only lever] peaks TOWARD each other ⇒ margin shrinks (→ 0 at coincidence);
peaks APART ⇒ margin grows. This is the DIRECTION only.
MAGNITUDE (how anomalous / the real hybrid λmax / any clinical severity): [O], firewall-
blocked — no quantity, agent, or clinical effect is named.
[honest caveat] χ(λ) is hypersensitive and DISTRIBUTIONAL (a sawtooth, inherited E1/E6): the
margin is a property of the COMMITTED peaks, not a smooth response to an arbitrary nm-scale
shift. Only the coincidence LIMIT and the local within-band sense are forced — stated, not hidden.
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PART C — orthogonality: removing a cone costs ONE colour axis, not acuity, not the switch
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the three channels carried on one wave are ORTHOGONAL:
colour = the propagation ANGLE χ(λ) (E1, the WHAT)
position = the image GEOMETRY (E3, the WHERE)
brightness = the R19 SWITCH magnitude (E2, detection)
[angle channel] removing one cone: colour angle-samples 3 → 2 (one axis lost).
[switch channel] the remaining cones' R19 switch is untouched (spinodal stable: True) ⇒ the light/dark response (E2) is intact.
[position channel] the image geometry (E3) consumes no cone identity ⇒ spatial acuity is intact.
→ the loss is confined to ONE colour axis; acuity (WHERE) and detection (the switch) survive.
This is why it is *colour*-blindness — FORCED by the channel orthogonality, and it matches
the preserved-acuity phenomenology. The felt experience of colour confusion → mind volume. [F]
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PART D — γ read READ-ONLY (structural offset); genomics is [L], NOT γ (firewall)
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the opsin genes' γ (LEVEL) + A4 (SHAPE) are read as a STRUCTURAL excitability offset — READ-ONLY,
byte-equal to the frozen atlas. E9 makes NO claim that γ predicts λmax (optical vs DNA-structural
layers kept separate, E1 firewall):
OPN1LW (L/red ): γ=1.4820 spinodal=0.6944 A4_amp=0.09028 stiffest_off=2150bp
OPN1MW (M/green): γ=1.4058 spinodal=0.6415 A4_amp=0.12596 stiffest_off=2200bp
Δγ(L,M) = 0.0762 (a structural offset, NOT λmax); A4 shapes differ 1.40× (level and shape stay orthogonal).
[no-drift] cone γ byte-equal to frozen atlas (no fitting): True
[O] the genomic architecture making red-green X-linked / male-prevalent (the OPN1LW/OPN1MW tandem
array on the X chromosome) is [L] genomics — NOT derivable from the promoter-γ this package
reads. Obstacle named; not invented. The felt percept belongs to the mind volume.
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E9 GRADES (VP-SPEC C3) — honest
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[F] forced : the three discrimination axes are the pairwise angle margins, and the M-L
(green-red) margin is the smallest; coincident λmax ⇒ exactly-zero margin;
dichromacy = removing one angle-sample; anomaly = peaks converging (margin→0);
the colour/position/brightness channels are orthogonal (loss = one colour axis).
[V] verified : three distinct cone angles; M-L is the smallest of the three margins; the
coincidence margin is exactly 0; the within-m-band convergence is monotone to 0;
the remaining cones' R19 switch is unchanged; cone γ byte-equal to the atlas.
(The magnitude firewall is machine-checked every run.)
[L] measured : every cone γ + A4 (NCBI promoters, cached); the cone λmax (S420/M530/L560, lit.);
red-green is the most common inherited colour-vision difference (epidemiology).
[O] open : the MAGNITUDE of any anomalous shift / the real hybrid λmax / any clinical
severity (firewall-blocked — none produced); the sawtooth, distributional χ(λ)
(only the coincidence limit + local sense are forced); the X-linked genomic
architecture (needs the feature table, not the promoter-γ); the felt percept of
colour and of colour confusion (→ mind volume). Each obstacle named.
LEARNED: colour is the propagation ANGLE, so the three cones are three angle-samples and the
three discrimination axes are their pairwise margins. The GREEN-RED margin is the
smallest — the angle map FORCES red-green as the most fragile colour axis (matching the
epidemiology). Coincident peaks give an exactly-zero margin, so dichromacy (lose a
sample) and anomalous trichromacy (peaks converge) are ONE continuum whose endpoint is
coincidence. Because colour (angle) is orthogonal to position (image) and brightness
(switch), the loss costs exactly one colour axis while acuity and detection survive.
Foundation untouched; no γ added; nothing fitted; firewall intact and machine-checked.
sha256: 3e5c4eb1d9dbc812740511ee7d91c17f581d5fd090144908d31a383ce76f1caf