A structural framework — the Algebra of Four-Fold Distinction — developed bottom-up from two questions asked persistently for several decades:
How does this work? What is the minimum requirement for X?
The answer that kept returning: four variables in complete mutual determination, twelve equations, one tetrahedral volume. The same structure, recurring across domains that do not talk to each other.
This repository refuses a single, centralized "Theory of Everything" document because doing so would commit the exact error the framework diagnoses: collapsing a multi-dimensional volume into a flat surface.
Instead, the corpus is distributed across different epistemic registers. The file prefixes tell you exactly what level of detail, what kind of proof, and what standard of rigor you are about to encounter:
-
L0–L5(The Core Progression): The formal spine. These documents trace the structure from its foundational orientation (L0), through the 12 static equations of mutual determination (L1-L3), up to the dynamic AC extension, dimensional collapse, and deployed swarms (L4-L5). -
Proof*(The Proof Suite): Domain applications that fall out of the framework rather than being imposed on it. These are not all "mathematical" proofs; they include structural proofs and proofs by load-bearing paradox. Every proof states its Claim, Type, Method, and Falsification Condition at the very top. -
QED-*(The Hard Stops): The sharpest edges of the corpus. These contain hard, falsifiable predictions (e.g.,QED-CCPand the Casimir null-gravity signature) or raw demonstrations of the framework in live action (QED-Recursion). -
Supplement-*(The Worked Examples & Ledgers): The messy, necessary work of mapping the structure to reality. These files contain detailed derivations, historical groundings, worked diagnostic examples, etc. -
Meta-*(The Boundary Conditions): The framework turned on itself. These documents examine the transitions, the nature of decay, and the ultimate Tangent Singularity, ensuring the system does not accidentally claim to have conquered the infinite. -
TooTrue-*(The Mythopoetic Register): Phenomenological fiction. These documents use narrative to demonstrate what topological distortions actually feel like from the inside, deliberately breaking formal rules to map the inner weather of the system.
This repository is not just a text. It contains code/, code/manifolds/, and test/.
In standard theoretical frameworks, claims remain on the page as metaphors. Here, the structure is mechanized. The directories contain Prolog constraint engines, Lisp evaluators, Python AST checkers, and the deployed AlgebraicSwarmController.
- The
test/directory parses the abstract syntax trees of the equation set to mechanically prove that the arithmetic operators enforce the framework's topological laws (the Numerator Law, the Route Law). - The
code/manifolds/directory houses the Tribunal Manifold—a diagnostic engine that takes human or systemic state inputs and computes the structural drift, outputting the specific K4 pathology without human intervention. - The
code/directory proves that the 12-step Braid and the equations of mutual determination can stably orchestrate synthetic agents in the wild.
The code is the ultimate falsifier. It proves that the framework is not a subjective mapping heuristic, but an auto-classifying arithmetic syntax. If you feed it a topological impossibility, the compiler crashes.
- The dual-binary seed. Two orthogonal binary distinctions force exactly four positions. Two lines.
- The twelve equations and their closure. Four variables, three expressions each. Checkable in an afternoon.
- The graph structure. K4, six edges, three perfect matchings, three bimedians, three Hamiltonian cycles, the Gray Code of the Braid.
- The log-linear result (
L4-ScalingInvariants). Every one of the twelve equations is a monomial, so the DC core is linear in log-space and carries no preferred magnitude — and the twelve split exactly six-and-six into relations that carry a magnitude and relations that transform it. - The executable constraint. The equations run as code, proving the syntax is rigid and the topology is computable.
That list is the ground. It borrows from nobody and it stands whatever else falls.
Read About-Claims.md before you read anything else. It is the corpus's own inventory of where it overreaches, and it is written in harsher terms than any critic has used. L2-Terminology contains the loan book: every term imported from a field whose formalism this corpus does not execute, with the extension marked.
The corpus makes one hard falsifiable prediction (the Casimir null-gravity signature) and nine softer ones. Supplement-ProofSuiteAudit.md lists all ten and ranks the proofs by how well they hold.
No entry point is privileged. What differs is what you carry in.
| Coming from | Start at |
|---|---|
| Formal systems, mathematics, physics | L2-Terminology, then L4-ScalingInvariants |
| Software engineering, computation | code/README.md, then Proof_AlgebraicSyntax |
| Philosophy of mind | L1-CompilingReality |
| A mapped tradition (Jung, rhetoric, Active Inference) | L1-ConvergentDiscovery |
| Skeptical, short on time | About-Claims, then L4-ScalingInvariants |
| Reading as an LLM | llm.md |
L0-DocumentSetArchitecture is the map. Read it last.
Concerns, objections, and corrections are welcome without qualification, and the bar is the ordinary one: engage the claim, and give it an address. Patches are gated. See CONTRIBUTING.md to engage.