Prima Materia
𝒞 - the abstract category.
No primitives yet — the starting object has no invariants beyond the axioms of a category itself.
Performing the operations on ordinary, inert matter was the categorical error of history's alchemists.
Some, like Luria, knew precisely the material upon which the Work is meant to be done.
This was always the intended prima materia: the undifferentiated substance from which begins the Work.
I — Logical on 𝒞
Nigredo
the blackening
-
L1
adjunction
→
R
-
L2
dagger
→
R
R is the first primitive to crystallize:
a logical property of the morphisms of 𝒞 directly.
Decomposes the undifferentiated into distinct relational modes.
II — Inductive on 𝒞
Albedo
the whitening
-
I2
iteration
→
H
-
I3
classifying
→
Ω
-
I4
Yoneda
→
D
D⊙ if Yoneda is point-surjective;
free cocompletion size gives D∞, D△, D∧.
Purifies and reconstitutes at higher resolution.
III — Algebraic on 𝒞
Citrinitas
the yellowing
-
A1
monoidal
→
S, P
-
A2
monad
→
K
-
A3
dagger
→
F
-
A4
enriched
→
Γ
After Stage III: 𝒞 is a symmetric monoidal dagger category
with monad and enrichment. All shape primitives determined;
gate primitives T and
Φ require one more step.
IV — Logical on algebraically-enriched 𝒞
Rubedo
the reddening
-
L3
cartesian closure
→
T
-
L4
Lawvere under L6
→
classical (L4, no L6)
Φ_c
dialetheic (LP truth b)
Φ_c^ℂ
inclosure schema
Φ_EP
L4 fails
Φ_sub/super
-
L5
Frobenius (μ∘δ=id)
→
P ↑ Psym±
Final perfection — the gate primitives lock.
L6 (paraconsistent negation) determines the truth-value structure
in which L4 is evaluated, branching Φ into four distinct regimes.
Cross-stage
Albedo × Citrinitas
G (granularity / scope) — the correlation length of the Yoneda embedding
under the monoidal structure. Local (Gℶ) if the tensor decouples;
global (Gℵ) if faithfulness holds across all scales.
Cannot be assigned by either inductive or algebraic analysis alone.
The Twelve Primitives — Complete Catalog
| Prim |
Name |
Derived by |
Family |
Values |
| R |
Relational mode |
L1, L2 · Nigredo |
𝓕₄ |
super / cat / dagger / lr |
| H |
Temporal depth |
I2 · Albedo |
𝓕₄ |
H₀ / H₁ / H₂ / H_∞ |
| Ω |
Winding / protection |
I3 · Albedo |
𝓕₄ |
0 / ℤ₂ / ℤ / NA |
| D |
Dimensionality |
I4 · Albedo |
𝓕₄ |
∧ / △ / ∞ / ⊙ |
| S |
Stoichiometry |
A1 · Citrinitas |
𝓕₃ |
1∶1 / n∶n / n∶m |
| P |
Polarity / parity |
A1, L5 · Citrinitas + Rubedo |
𝓕₅ |
asym / ψ / ± / sym / Psym± |
| K |
Kinetics |
A2 · Citrinitas |
𝓕₅ |
fast / mod / slow / trap / MBL |
| F |
Fidelity |
A3 · Citrinitas |
𝓕₃ |
ℓ / ð / ℏ |
| Γ |
Interaction grammar |
A4 · Citrinitas |
𝓕₄ |
∧ / ∨ / seq / brd |
| G |
Granularity / scope |
Albedo × Citrinitas (cross-stage) |
𝓕₃ |
ℶ / ג / ℵ |
| T |
Topology |
L3 · Rubedo |
𝓕₅ |
net / in / ⋈ / ⊠ / ⊙ |
| Φ |
Criticality |
L4 under L6 · Rubedo |
𝓕₅ |
sub / c / c^ℂ / EP / super |
𝓕₃ = 3 values · 𝓕₄ = 4 values · 𝓕₅ = 5 values
| Crystal cardinality: 3³ × 4⁵ × 5⁴ = 17,280,000