Constitution as Colimit

What is this? An early-stage research program — a philosophical framework with mathematical vocabulary and physical ambitions. It is not a finished theory of physics. It produces no novel quantitative predictions in its current form. What it offers is a structural reorganization of known physics using category theory, with some genuine mathematical results and several honest open problems.

What is a colimit? A colimit is a construction from category theory that captures how parts constitute a whole. Given a diagram of objects and their relationships, the colimit is the universal object that “glues” the diagram together while preserving only the relationships visible from outside. Internal structure is compressed away. A proton, in this framework, is a colimit of its quarks — the quarks’ individual identities are lost, but their shared relationships (color charge closure) persist in the composite.

Two layers. Each page has a main text written for a general reader and a formal section written for mathematicians. Both audiences read the same pages. The formal sections can be skipped without losing the main argument.

Verification status. This work is authored in collaboration with Claude (Anthropic). No human mathematician has independently verified the proofs. The formal results are stated with proof sketches; full proofs are in the GitHub repository. Independent verification is invited and would be the most valuable contribution anyone could make to this research. See How This Work Is Done for details.

Epistemic status. Claims are labeled: Established means standard physics or mathematics the framework relies on. Proposed (formalized) means the framework’s own contribution with a mathematical chain behind it — not yet independently verified, but the formal steps are stated. Proposed (conceptual) means a conceptual account without formal content — a direction, not a result. Structural means a reorganization of established physics using the framework’s vocabulary. Open means the framework acknowledges it does not know. The Questions page lists every open problem the framework has identified — read it alongside the main pages.

There is no stuff. No thing at the bottom holding everything up. There is only the process of constitution — and what it is constituted from is more constitution. Three axioms define this process. They are not descriptions of reality. They are what constituting means. This page introduces them, explains why binary distinction is physical, and addresses the immediate objection: the process of what?

Every particle is a combination of yes-or-no answers to a small number of questions. Does it have mass? Does it spin? Does it couple to electromagnetism? The answers map to binary configurations — and the configurations that survive pruning match the Standard Model particle table. Shell capacity (2, 8, 18, 32 electrons) follows from three rules (which import their quantum numbers from standard physics). Three generations of matter fall out of one branch event.

The Standard Model has three forces with three different symmetry groups — SU(3), SU(2), and U(1). The fork taxonomy develops all three from a single operation: a binary fork, differentiated by two parameters. Whether the “neither” outcome is physically accessible determines U(1) vs. SU(2). Whether the force reaches into the sub-grain determines 1 fork vs. 2. One mechanism. Three force state-counts — the gauge groups themselves require additional mathematical steps.

Only non-existence is exact. Any non-zero value — any correlation, any coherence, any measurement — is constituted from the full web: infinite, noisy, always in motion. This single principle provides an ontological account of the Tsirelson bound (2√2), argues against PR-boxes on constitutional rather than information-theoretic grounds, and identifies a common ontological principle underlying both the Tsirelson bound and decoherence.

The universe expands because the process generates more constitutional events. But what does that mean? Two framings are under active investigation — one treats configuration space as something that grows, the other dissolves space entirely into a relational measurement. Both make the same core claim: the cosmological constant is a growth rate, not an energy density. The 10¹²⁰ discrepancy may be the right answer to the wrong question.

There are exactly three ways an emergent system can fail: it fragments, it condenses, or its rate of change exceeds its capacity to adapt. These three modes have distinct topological signatures — measurable, predictable, and structurally identical whether the system is an ecosystem, a cancer network, or a democracy. An ecological food web actively resists what its own degree sequence would predict. The political work on this site documents one of these modes in action.

Five formal theorems in Coalg(G_ℂ). Cocompleteness, ℂ-enrichment, the discrete path sum identity, phase invariance, and the tensor product via ℂ[x] bialgebra structure. The F vs. G functor distinction. The enrichment/colimit separation. Written for mathematicians. No accessible layer — equations throughout.

Everything the framework does not know. Mass ratios, the Schrödinger equation, inflation, the continuous path integral limit, interaction dynamics, dark matter specifics. Presented not as admissions — as the research frontier. A framework that admits its edges grows. These are ours.

This research is authored in collaboration with Claude (Anthropic). The methodology, the role of AI in the work, and the question of independent mathematical verification.