ORBIT Bridge hypothesis

The Rosetta Stone hypothesis.

Can representation, dynamics and constraint connect exact mathematical structures with observed AI behaviour? The Rosetta Stone hypothesis asks for a useful correspondence, not just similar vocabulary or pictures.

A useful general translation has not been established. This page states the candidate connection, the standards a connection would have to meet, and the distinctions it must not collapse.

01Exact and empirical objects

Proof and behaviour start from opposite sides.

Mathematics starts from exact source objects and constructs representations whose logical role can be checked. Behavioural research starts from observations and asks which summaries preserve distinctions useful for prediction, explanation or control.

Those are related questions about representation. They are not evidence that proof-search histories, integer solutions and AI-agent trajectories are the same mathematical object.

02Candidate translation

Three questions for a candidate connection.

Representation

What can be compressed or translated without losing the property required by the conclusion? A mathematical reduction may discard information while preserving a necessary implication. A behavioural summary must retain the distinctions needed for its stated prediction or decision.

Dynamics

Can the evolution of a state or trajectory be represented in a mathematically useful way? Name the state, transitions, time or ordering, and which features of change survive the map. Similar-looking paths alone establish nothing.

Constraint / admissibility

Can formal constraints justify a bounded prediction, theorem or control consequence? State what is admissible, the assumptions and any composition or refinement conditions needed to transfer the conclusion.

For a non-existence proof, a one-way necessary map and an empty target can suffice: reconstruction is not automatically required. A behavioural representation needs evaluation for its intended use; a mathematical analogy does not supply that evidence.

From mathematicsExact problemsStructures where a statement is either proved or it is not.

From behaviourObserved AI interactionsTrajectories recorded across multi-step tasks.

Hypothesis, not a resultRosetta Stone hypothesis

A candidate mathematical description of state, change, constraint and control that both routes could reach. Whether one exists, and what it would preserve, is the open question.

Statisticstests predictions and quantifies uncertainty

Formal methodscheck specified properties and transfer conditions

The arrows stop at the centre on purpose. Nothing here runs from a theorem to a safe agent: a correspondence counts only once it preserves a named property and yields a consequence that can be checked.

03What would count

Map. Invariant. Consequence.

Every proposed correspondence must answer all three questions before it can be more than an analogy.

Map: What objects correspond? Specify the source, target and direction of the map, including any information discarded.
Invariant: What property is preserved? State the exact implication, relation or guarantee and the assumptions it requires.
Consequence: What new prediction, theorem or control result follows? Identify how it can be proved or tested, and what would refute the proposed transfer.

What a useful consequence could look like

Prediction

A mathematical principle fixes a behavioural representation before evaluation, and that representation improves prediction on untouched data against simpler baselines.

Proof

A proved property of an abstract model transfers to a specified implementation through a checked refinement argument.

Control

A stated constraint yields a bounded action consequence under declared operating assumptions, with the empirical and formal claims kept separate.

Any one result would support that particular transfer. It would not establish the whole ORBIT hypothesis.

04Distinctions

Three mistakes would make the bridge look stronger than it is.

A shared language is not a correspondence. Common notation does not establish a preserved property or a useful consequence.
A proof trajectory is not an agent trajectory. It is a sequence of proof-development steps. Any comparison must identify its objects and basis.
Using only the past is not a causal explanation. It is a requirement for prospective measurement, not by itself an account of what caused the behaviour.

05Where this lives

The bridge is one part of ORBIT, not a proof of every programme.

CARF, exact inference and Erdős Basecamp each have independent goals and evidence standards. Their results do not depend on establishing a general bridge. Scientific TDD supplies the discovery and testing process; formal methods check specified propositions, not the hypothesis as a whole.

Programme overviewHow Behaviour, Inference and Theorems relate.CARFThe AI-behaviour programme and its current evidence limits.Exact inferenceThe statistical foundations and released software.Erdős BasecampThe mathematics programme and the E364 worked problem.