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Eigenius

Domain bridges

Crossing between two domains happens in two stages. The first stage is declarative and data-shaped: formulate the entities and propositions of a specific domain, and state the implications that link them to a neighbouring vocabulary. This is what a domain bridge does. A domain bridge is a chain-resident, citable, refutable artifact that says what holds between two vocabularies as a matter of definition. The type-checker confirms it is well-formed, the layer stores it, and every downstream user cites it.

The second stage is where institutions earn their keep: they take that declarative material and lift it into live computation and reasoning — actually running the analysis, actually composing the proof. The bridge says what follows from what; the institutions do the work.

A statistician says “the sample’s mean is below 100 nM”; a medicinal chemist says “the compound has low IC₅₀”. These are different statements in different vocabularies, and the move from one to the other is normally hidden in author judgement — exactly where reproducibility failures and AI hallucinations hide. The domain-bridge primitive forces that move onto the record as a first-class object.

What a domain bridge is

A domain bridge is a chain-resident DeclaredResource whose canonical_proposition is an implication from one user-defined vocabulary into another. In the drug-screening example, the bridge formulates the medicinal-chemistry predicate HasLowIC50 and states the implication that links it to the statistics vocabulary:

∀ (s : sample-set, c : compound),
  sample_for(s, c)
  → stats:lt(stats:mean_of(s), 100 nM)
  → screen:HasLowIC50(c)

The left of the implication is the language of the statistics institution: “the sample’s mean is below 100 nM”. The right is the language of medicinal chemistry: “the compound has low IC₅₀”. These are different statements; nothing in the chain connects them by default. The bridge is that connection, on the record as a first-class object.

Domain bridges are authored at the domain layer, by users — they are how a research team writes down its own methodology. They are distinct from the institution-level analogue (comorphisms) which mediate between runtimes and are declared at institution registration time, not by domain users.

Why it matters

Three structural consequences fall out of making the translation a typed chain object:

  1. The translation becomes audit-separate. A reviewer who disputes the bridge edits the bridge — without disputing the statistics or the literature rule that uses the translated claim. Three independent disputes instead of one tangled one.

  2. One bridge serves the whole campaign. The bridge above is universal over both sample sets and compounds. A single methodology resource is referenced by every screening sentence in the campaign; specialisation to a particular (sample-set, compound) pair happens at certificate-author time.

  3. AI agents cannot route around it. The kernel’s type discipline rejects any composition that takes a statistical conclusion to a domain claim without a typed translation artifact. An AI agent that wants to make the leap must either cite a chain-resident bridge or commit a new one as a Declared resource — at which point the bridge is on the record, the agent is the declarer, and a reviewer can examine the asserted methodology directly.

Where domain bridges sit in the stack

A domain bridge is declarative: it states a relationship between vocabularies as data. No computation runs at the moment the bridge lands on the chain — the kernel only confirms that the implication is well-typed against the entities each side mentions. The runtime stage, in which the statistical claim actually gets computed and the translated domain claim actually gets composed with a literature rule into a final conclusion, is mediated by institutions.

Together the two stages are the typed integration protocol:

  • Domain bridges declare what holds between vocabularies, as flat data the chain stores and the type-checker checks.
  • Institutions run the procedures within each vocabulary and dispatch the typed crossings between them.

The drug-screening walkthrough exercises both stages end-to-end: the statistics institution emits a statistical claim; the chain-resident domain bridge translates it into the medicinal-chemistry vocabulary; the reasoning institution composes the resulting domain claim with a literature rule.

In practice

The full drug-screening example uses a polymorphic domain bridge with both the sample_for premise and the threshold built in. Walking the worked example end-to-end shows how the bridge composes with the verifier’s result, the literature rule, and the per-pair sample-for witness to produce a chain-checkable conclusion.