Epistemology Infrastructure: Relational Dynamical Network and Spinfoam

The refusal, and what follows from it

What a party holds is reconstructed from the representations available to it, under the interpretation it holds. Nothing content-like crosses between parties; what crosses is a perturbation, which the receiving party's own law consumes. That is a familiar enough claim to state. The consequence is less familiar, and it is formal rather than rhetorical:

A model adequate to that account may not assume a space in which the states of distinct parties are located — because distances in a common medium are what a signal traverses, and the picture returns as a property of the mathematics no matter what the prose says.

Most models of communication smuggle the transmission picture back in through their mathematics: a shared state space, a common metric, a global clock, a scalar that orders one party's quantity against another's. Each is a place where a distance can be measured, and a measurable distance is a channel a content can traverse. This project is an attempt to build the models without any of them, and to make the absence checkable.

Two models, and where they meet

They meet at exactly one function — rdn.correspond.induce_history(run, party, identification). Everything the paper claims about the correspondence is a property of that function, which is what makes those claims testable rather than asserted.

Why the core carries no domain word

The package is called rdn and not epistemic, and the reason is a claim in the paper rather than a matter of taste. A model of this kind is a formalism: it fixes what kinds of object there are and how they compose, and asserts nothing about the world until an interpretation is assigned. The definitions of knowledge and of emergence hold under one particular design — and hold in no form for the models alone.

So knowledge is not a core function. It is one interpretation's name for a core computation, and a musical reading of the same computations names them differently and is equally entitled:

A package named epistemic whose core module was epistemic.network would assert in its own import path the thing the paper denies. Hence four strata, of which only the first is the formalism: formalism (rdn.structure, .network, .history, .correspond), strategy (how a design advances state at all), interpretation (which formal quantity gets which domain word), and design (the state sets, laws, couplings and admissible classes of a particular case). Dependencies run downward only, and a test — not a review convention — enforces it per source file.

Four figures, all generated from the code

Every figure below is produced by figures/make.py under a single recorded seed; deleting the output directory and re-running reproduces them. Resolution order is fixed in the figures because reproducibility is what matters there, and randomised in the tests because order-independence is the property under test.

The removal test, and its three outcomes

Emergence is not asserted; it is tested by deleting a component and asking whether a capacity of the whole survives. Running it on the news design gives three distinct outcomes, and the third is a control the paper itself does not run:

  delete archive     -> FAILS
  delete reader      -> INEXPRESSIBLE
  delete editor      -> HOLDS

The analysis parameters travel with the answer rather than being hidden — how many trials must succeed, and how many perturbations to skip before judging — because a warmup chosen to make a result appear is exactly the failure the discipline is meant to prevent. And which of a design's parameters carry a substantive claim about the case, rather than merely making a contrast legible, is machine-readable in the design module.

The refusals, and what enforces each

Each of these corresponds to a claim that fails if it fails; none is a matter of house style. Every one is held by a test, so that the discipline survives the next contributor.

The last of the refusals deserves a note of its own. A utility function anywhere in the core would turn the epistemic results into results about a utility-maximising system, and the paper's claims would stop applying. So goals, preferences and rewards live behind a policy interface, on the far side of a seam: the epistemic update never calls the action layer, and a decision procedure added tomorrow changes which emissions occur and never how reconstruction works.

What is deliberately absent

These are marked as open problems in the test suite, so the absence appears in the test report rather than in a document nobody opens.

• A single history for a whole network. The correspondence is per node, and the resulting histories are joined by nothing. Inventing a joined object would be inventing a result, so the test records the absence as a strict expected failure.
• Amplitudes. A generative account would need a configuration space, a functional determining weights, and an interpretation of those weights; no candidate is supplied for any of the three. The deeper obstacle: a weight presupposes recurrence, while an account holding interpretive conditions to be historically produced is committed to the singularity of a trajectory. A design could supply an algebra by fiat and could not supply a repeated trial.
• Distance or similarity between structures. What is supplied is a reformulation rather than a solution: a common-subcomplex comparison up to isomorphism, requiring no shared vocabulary, returning a correspondence and a count — never a fraction.
• Inference of a reconstruction map from data. The map is not observable; what another node can see is what this one emits.

The package

pip install -e ".[test,figures]"

pytest                   # 124 passed, 1 xfailed
python tour.py           # the whole apparatus in one screen, public API only
python figures/make.py   # regenerates every figure, seeded

Python 3.12 and numpy; matplotlib for the figures only. Nothing else in the core — because a dependency in the core is a dependency the formal claims inherit. Three reference designs ship with it: the paper's news instance (eight nodes, two of them generalised couplings), a music design with no network at all and no knowledge in it anywhere, and a domain-neutral toy against which the conformance tests stand — so that nothing about the formalism is tested only through the example it was written for.

What this does not establish