SOLVATUM
Crafting the Lapis Philosophorum  ∞  Automatica Principia Proceduralis

The 12 primitives of the Imscribing Grammar — the 12 facets of the Philosopher's Stone — are derived from a bare abstract category   -   𝒞   -   via the four classical alchemical operations: Nigredo, Albedo, Citrinitas, and Rubedo.

  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) Φc
    dialetheic (LP truth b) Φcℂ
    inclosure schema Φ×
    L4 fails Φ↓ / Φ↑
  • L5 Frobenius (μ∘δ=id) → P ↑ ±ˢ
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) — 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 ↑ ∘ † ↔
H Temporal depth I2 · Albedo 𝓕₄ H0 H1 H2 H∞
Ω Winding / protection I3 · Albedo 𝓕₄ 0 ℤ₂ ℤ ∅
D Dimensionality I4 · Albedo 𝓕₄ ∧ △ ∞ ⊙
S Stoichiometry A1 · Citrinitas 𝓕₃ 1∶1 n∶n n∶m
P Polarity / parity A1, L5 · Citrinitas + Rubedo 𝓕₅ ∅ ψ ± ≡ ±ˢ
K Kinetics A2 · Citrinitas 𝓕₅ ↯ ≈ ↺ ⊛ ⊞
F Fidelity A3 · Citrinitas 𝓕₃ ℓ ð ℏ
Γ Interaction grammar A4 · Citrinitas 𝓕₄ ∧ ∨ → ≫
G Granularity / scope Albedo × Citrinitas (cross-stage) 𝓕₃ ℶ ג ℵ
T Topology L3 · Rubedo 𝓕₅ ∈ ⊂ ⋈ ⊠ ⊙
Φ Criticality L4 under L6 · Rubedo 𝓕₅ ↓ c cℂ × ↑
𝓕₃ = 3 values  ·  𝓕₄ = 4 values  ·  𝓕₅ = 5 values   |   Crystal cardinality: 3³ × 4⁵ × 5⁴ = 17,280,000