The hypothesis space

H(O) attacked directly. Includes a partial retraction of "authority is evidence" — the pushback was right, and testing it splits a regime I had left whole.

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1. Attacking "authority is evidence"

The discriminator

The two claims are separable by a sharp test:

Evidence removes members of H(O). A selector picks a member without removing any.

So: does the authority's act change what is possible, or choose among things that remain equally possible?

Applying it

GitHub renames org/repo → org/repo2, keeping the numeric id. There is a fact here: the object continued, with continuity and lineage. GitHub reports it, and can be wrong — id reuse after deletion, or a delete-and-recreate its id logic conflates. Hypotheses are removed. Evidence.

GitHub forks org/repo. Both copies have complete lineage. Is either "the continuation"? No observation, actual or possible, distinguishes them. GitHub assigns the fork a new id — that act is constitutive, not reportive. Nothing is removed; one branch is chosen. Selector.

A legal registry names a merger successor. There may be causal and economic continuity facts, and the legal answer can diverge from them — which is precisely the mark of a decision rather than a report. Selector.

Pluto. The committee did two separable things: it chose a definition (a convention — and note what it chose: the value space of a dimension, which is the object dimension-algebra.md derived), and then applied it (a derivation). The selection happened at the definition layer, not among hypotheses about Pluto. Membership followed.

The result: the underdetermined regime splits

co-reference.md gave three regimes and left the middle one whole. It has two halves, and they behave oppositely:

Why |H| > 1	Can any observation resolve it?	What authority is
incomplete observation — a sensor gap, an unobserved interval	yes	evidence — an observer with better access
underdetermination in principle — fission, an unobservable swap	no	a selection policy — convention

Partial retraction. "Authority is evidence" is correct for the epistemic half and wrong for the constitutive half. I had one regime where there are two, so the claim was right about the cases I checked and wrong as stated.

The distinction is testable, not stipulative: ask whether a better-placed observer could in principle settle it. If yes, the authority is a witness. If no, it is a legislator. And a legislator's ruling can diverge from every fact without being false — which is exactly what the merger case shows.

Where it belongs. Selection is downstream of inference, as the pushback said. Evidence is inside it. The two must not share a field, and in SubjectRef they currently do.

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2. What is a hypothesis?

Derived, not stipulated. H(O) is the set of things consistent with O:

H(O) = { w : w ⊨ O }

A hypothesis is a complete assignment of truths entailing every observation. For co-reference specifically, it is a partition of the observations into co-reference classes — which is why the count is combinatorial and why crossing objects are the hard case.

Ontology does not disappear under this architecture. It specifies the shape of a hypothesis — what an assignment must assign. The inference layer sits above it, not in place of it.

3. Which observations remove members, and which do not

An observation is informative exactly when it is inconsistent with some member:

o is informative  ⟺  H(O ∪ {o}) ⊊ H(O)

That recovers information-as-elimination, and it is derived here rather than imported.

Observations that leave H unchanged:

• entailed ones (redundant);
• ones on dimensions orthogonal to the question;
• repeated equal observations of a state.

The third is a consistency check that could have failed and did not. Coincident agreeing observations were found in identity-axes.md to be one fact with two evidence entries. Here they are found to be zero information. The episode law and the information law agree — two independent derivations, same answer.

4. Can |H| increase?

Yes — three ways. A naive reading of the architecture would say no, so this is the load-bearing negative result.

1. New subjects appear. Observing a previously unknown entity enlarges the universe of discourse, and the space of partitions grows with it.
2. Contradiction. If two observations conflict, requiring consistency empties H. Recovering means admitting hypotheses in which an observer is wrong — which expands H with faulty-sensor worlds.
3. Retraction. Withdrawing an erroneous observation restores what it removed.

Route 2 is the important one: it is the contested quantity from identity-axes.md, arrived at again. Fact cannot hold a disputed value because it presumes |H| = 1.

5. Can H(O) be represented canonically?

Not extensionally — it is a set of models, generally infinite.

But it has an exact implicit representation:

The observations are the canonical representation of H(O). Store O; H is its model set; canonical truth is the projection of H when |H| = 1.

This retroactively justifies the system's existing shape — store facts, derive views — on grounds it did not previously have. And it condemns one function precisely:

collapse() is an undeclared hypothesis-selection policy. Its order-dependence — the first finding of this entire investigation — is now explained rather than merely observed. When two facts share an identity and differ in value, |H| > 1; collapse picks by array order, which is selection wearing the costume of canonicalization, applied in the epistemic regime where selection is not even licensed.

6. The four states — a correction to the proposed diagram

The proposed architecture is right, and its state table needs a fourth row:

State	Meaning
|H| = 0	contradiction — no assignment satisfies O
|H| = 1	canonical truth exists
|H| > 1	truth is not yet canonical
H undefined	the question is ill-posed

Empty is not meaningless. An empty H is a strong, informative state: the observations are jointly unsatisfiable, so at least one observer is wrong. That is the most actionable state in the table, and it is where provenance earns its place.

Meaninglessness is different — for indistinguishable particles the co-reference question is not unsatisfiable, it is not well-formed, so H is undefined rather than empty. Collapsing the two would file a detected sensor fault and a category error as the same condition.

7. Domain ledger

Domain	Case	Regime
tracking	crossing objects, distinguishable	epistemic
tracking	crossing objects, identical	constitutive
aliasing	two identifiers, one thing	epistemic — a linking observation resolves it
packet routing	fragmentation and reassembly	constitutive — "same packet" is convention
git forks	which is the continuation	constitutive
astronomy	a lost asteroid recovered by orbit computation	epistemic
astronomy	Pluto	definitional — selection at the value space
biology	species identification by genetics	epistemic
biology	amoeba division	constitutive
chemistry	two identical molecules	void — H undefined
chemistry	dissociation	constitutive
transportation	parcel scan gaps	epistemic
organizations	merger successor	constitutive
organizations	rehire — one employment episode or two	definitional

All four states occur, and the split is not domain-aligned: chemistry supplies both a void and a constitutive case, astronomy both an epistemic and a definitional one. The regime is a property of the question, not of the field.

8. Provenance

Three candidates:

"Connector X reported this at time T" is a claim whose subject is a report, whose dimension is source, and whose value is X. That is a truth in the same system, one level up.

Provenance is an observation over observations. Second-order, not metadata.

Not metadata, because metadata is inert annotation and this is truth-bearing and falsifiable. And it is load-bearing exactly at |H| = 0: contradiction expands H with faulty-observer worlds, and provenance observations are what narrow it back. Provenance is the mechanism that makes contradiction tractable rather than fatal.

This separates two things the code fuses. Evidence = { observer, citation, at } serves as both:

	Order	Role
evidence	first-order	attached to a claim; removes hypotheses about the world
provenance	second-order	a claim about a claim; removes hypotheses about observers

9. Standing

Question	Answer
What is a hypothesis?	a complete assignment entailing O; for co-reference, a partition
How is H(O) constructed?	not enumerated — defined as a model set, represented by O
What removes members?	inconsistency; that is informativeness
What leaves it unchanged?	entailed, orthogonal, or repeated-equal observations
Is |H| monotone?	no — new subjects, contradiction, and retraction all increase it
Canonical representation?	the observations themselves
Authority?	evidence in the epistemic regime, a selection policy in the constitutive one
Provenance?	an observation over observations

What is still not established

• The epistemic/constitutive test — "could a better-placed observer settle it?" — is applied here, not derived. It may itself be undecidable in some cases, and I have not shown it is not.
• |H| remains defined and uncounted, unchanged from co-reference.md.
• capability — eight rounds untouched.

Nothing implemented.