Process-Relational Ontology

The question. Can a category-theoretic / sheaf-theoretic framework formalise process-relational ontology in a way that produces falsifiable statistical methodology — and does it unify the relational ontologies in QBism, Mesoamerican cosmology, and modern decision science?

Reading as

What if reality is made of relations and processes, not things? Here's that idea, kept honest with a falsifiable first step on real data.

Status — Early. An open, exploratory thread — shared here for the questions and the method, not for results. Findings are kept off the public site until they're earned and vetted. Tools: Category theory · Gudhi · LaTeX.

The bet

Reality modelled as relations and processes (morphisms) rather than substances and objects (elements): category theory as the language, sheaf cohomology as the statistical tool, decision-under-uncertainty as the applied domain. The same relational move shows up in Whitehead's process philosophy, in QBism (experience over wavefunction), and in topology (shape of change over static state).

This is a synthesis, and a synthesis is OPEN until its pieces are proven. What keeps it honest is that every component is established, peer-reviewed work — Abramsky–Brandenburger's sheaf model of contextuality, the contextual fraction as an effect size, Pearl's causal hierarchy, the QBism of Fuchs–Mermin–Schack, Urton's topological reading of quipu knots. The contribution would be the connecting methodology, not any single brick. Nothing here claims the synthesis is true; it claims the question is worth making testable.

The setup

Definitions first — the part that has to be precise before any computation is allowed to mean anything.

The wedge (do this first)

Not the grand synthesis — one computable question. Dataset: the Harvard Khipu Database (~650 digitised quipus: knot type, position, colour, cord structure).

The method

Reuse the P5 TDA pipeline: a feature vector per quipu (knot positions + types) → persistent homology → H₀/H₁ signatures.

The falsifiable claim (C1)

Do those signatures cluster quipus into numerical vs. narrative classes, matching Urton's manual classification? Publishable if yes (TDA recovers encoding structure); publishable as a methodology note if no. Either way, one VERIFIED entry earned.

The method — what actually gets run

Pull the open Khipu Database; build per-quipu knot-configuration point clouds.
Run the existing persistence pipeline; compute H₀/H₁ and compare clusters to Urton's classification.
Report the result honestly — positive or null — as the first VERIFIED brick before any larger claim.
Only then reach for C2 (contextual fraction as an outlier-robust effect size) and C3 (nonzero first Čech cohomology of a sheaf of local policies = a coordination obstruction).

Open questions (honestly open)

These aren't rhetorical. Each is a place the project could still be a metaphor instead of a result.

C1 — quipu knot configurations carry persistent-homology signatures distinguishing numerical from narrative encoding.
C2 — the contextual fraction defines a dimensionless, outlier-robust effect size for multi-observer data.
C3 — a sheaf of local decision policies has nonzero first Čech cohomology exactly when local choices can't be glued into a globally consistent policy.
Q1 — is there a functor from process-relational ontologies to statistical models? Q2 — do Maya cyclic-time structures want p-adic probability (ties to P6)? Q3 — is forward-deployed distributed decision-making a gluing problem over a sheaf of local policies?

On care. Indigenous mathematical systems (Inca quipu, Maya/Aztec cosmology) are studied here through established scholarship — Urton, León-Portilla, the digitised primary archives — with citation and respect, as living intellectual traditions, not raw material to mine. The anomalous-cognition thread stays strictly in the methods frame of the contested-claims work: this is about effect sizes, contextuality, and bias-robust inference, and it makes no claim that the phenomena are real.

Key formulas

β_{k} = dim H_{k} (X) = dim (ker \partial_{k} / im \partial_{k + 1})

Betti numbers: H₀ counts connected components, H₁ counts loops; persistence tracks them across scale.

\overset{ˇ}{H}^{1} (U, F) \neq = 0

Nonzero first Čech cohomology of a sheaf of local policies = a global gluing obstruction (conjecture C3).

Reading the work rests on

Phenomenology and QBismAn Introduction to Knot TheoryAn Interactive Introduction to Knot TheoryComputational TopologyInformation Theory

This is an in-progress thread, not a finished claim. If you work near it — TDA, phenomenology, phonetics, the foundations of inference — I'd genuinely like to compare notes: research@backporch.studio.