De Deo, as a picture
Every demonstration in Part I says what it rests on — "(by Prop. vii.)", "This is clear from Deff. iii. and v." Those citations, extracted mechanically from the book pass's committed text (Elwes translation, Project Gutenberg #3800), form the 102-edge graph below. Read it top-down: definitions and axioms across the top, each proposition hanging from its premises, and the two deepest theorems of the book — p32 (will is not free) and p33 (things could not have been otherwise) — at the very bottom, ten steps from the foundations. The green nodes are the four pillars everything leans on: the definition of substance (d3), God's existence (p11), "all is in God" (p15), and p16. And two axioms hang in the corner, cited by nothing.
Part I, complete. □ definitions d1–d8 · □ axioms a1–a7 · ○ the in-degree-7 pillars · ○ the depth-10 theorems · dashed = never cited in any demonstration. Arrows point from each proposition to what its proof cites.
The first axiom is a partition
That is not prose here — it is a partition of being, with substance (def. 3: "in itself") and mode (def. 5: "in something else") hanging off its two cells. The tableau then derives the exclusions Spinoza needs: nothing can be both substance and mode, and a substance-in-another is incoherent, not merely undeclared.
All of Part I, checked in one run
The card below carries the entire demonstrative skeleton of Part I — all 102 citation edges — plus one recursive rule pair for the closure. What Spinoza asserted by construction, the engine now checks: the geometric order is acyclic, every proposition bottoms out in definitions and axioms, axioms 2 and 7 are never used (an observation from the formalization literature — Jarrett 1978 — here a set difference), and the deepest theorems are the denial of free will and necessitarianism.
Necessity: the frame has one world
Where Leibniz's God surveys infinitely many possible worlds, Spinoza's universe is the only world. On a reflexive single-world frame the modalities collapse — □p ≡ p ≡ ◇p — so nothing is contingent (E1p29) and whatever is possible necessarily exists (E1p35). Necessitarianism is a fact about the frame.
Three roads to the number six
Spinoza's own example: given 1, 2, 3, find the fourth proportional. The tradesman answers by a rule "received from a master without any proof" — a bare datum. Reason derives it through Euclid VII.19 — a theorem. Intuition sees 6 at once. Same answer, three epistemic grades — and E2p41 ("knowledge of the first kind is the only source of falsity") becomes the behavior of cancel: the rote answer withdraws; the theorem refuses.
Loving and hating the same thing
Spinoza calls it vacillation of spirit: contrary affects toward one object. That is not an error to purge but a state to represent — the Belnap knowledge-join takes the love-report and the hate-report to the glut ⊤⊥ᵇ, and the glut is designated: the vacillating mind still acts. Ambivalence without explosion.
The therapy of the passions
A passion is a conjecture of the mind — an affect derived defeasibly from a confused idea. Form the clear idea, retract the confused premise, and the passion lifts with its ground; what replaces it is an action of the mind that refuses defeat. Spinoza's remedy is a truth-maintenance system.
Blessedness is not the reward of virtue
…but virtue itself: not two things joined by payment — one state under two names. Coreference, not compensation. (And the value axis beneath this whole study — "good and bad indicate no positive quality in things regarded in themselves", E4 preface — is the same architecture as Tractatus 6.41: see the Tractatus study.)
Go deeper
Six scripts, 119 assertions, all five parts — parallelism as graph isomorphism, mind and body as one thing under two designations, the 48 emotion definitions as a derivation tree — with the full Elwes text and an honest gap ledger beside the code.