Overview
Published by Synergetics University on 14 July 2026, The Fuller Conjecture asks whether "there exists a line of reasoning that presents Fuller's synergetic vision as a philosophical system." This paper tests one qualified route through that problem. It places William Blake's fourfold vision beside Buckminster Fuller's Synergetics without claiming shared vocabulary, historical influence, or Blakean anticipation of Quadray: Blake supplies a historically situated problem of plural seeing, while Quadray and tetrahedral geometry supply a reproducible model of relational aspects, partial views, and reconstruction. The formal result is exact: for any non-degenerate convex tetrahedron observed by a strictly exterior camera, one frame exposes 1, 2, or 3 faces, never 4; an atlas can preserve all 4 across successive views. The project combines an argument graph, exact rational geometry, deterministic visualizations, a rights-aware corpus ledger, and a dependency-free viewer. "Synchronous omni-rational form" names this operational integration—a relational whole retained across partial views, sequences, source boundaries, and explicit limits—not a historical Blakean or Fullerian doctrine.
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Methods and contributions
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Findings and contributions
- For any non-degenerate convex tetrahedron viewed from a strictly exterior camera, one frame exposes 1, 2, or 3 faces, never 4, while an atlas of views can preserve all 4.
- The author's central claim is a qualified structural analogy: Blake's fourfold vision is analogous to a tetrahedral totality, not a historical identity between Blake and Fuller.
- The author argues the Fuller Conjecture becomes tractable when presentation is a coupled graph, atlas, and golden thread.
- The ablation indicates the tetrahedron is useful but not necessary to Blake's language; it is chosen for usefulness rather than historical necessity.
- The reproducible project contains 51 ledger entries and a golden-thread path of 10 nodes.
Methods
- Comparative reading of Blake's fourfold vision anchored in the 1802 Butts letter — Uses Blake's November 1802 letter-poem to Thomas Butts and Blake scholarship (Calè, Groves) as historical evidence for the problem of plural seeing.
- Exact rational Quadray/tetrahedral geometry with face-visibility classifier — Models a tetrahedron in Quadray coordinates with exact rational arithmetic and classifies faces visible from strictly exterior cameras by outward-normal dot products.
- Proof of face cardinality via area-weighted face-plane dependence — Proves that an exterior camera sees between 1 and 3 faces of any non-degenerate tetrahedron using the identity that area-weighted outward normals sum to zero.
- Argument graph with 'golden thread' path, ledgers and rights gate — Encodes claims in an argument graph traversed by a selected path, with citation/claim ledgers, a rights-aware corpus ledger, and pinned upstream checks.
- Ablation of the tetrahedral model against four-channel and planar alternatives — Compares the tetrahedral atlas with an abstract four-channel state and a four-sided planar model to show what each retains or loses.
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