docs/co-reference.md
Co-reference
The phenomenon at which every reduction of Subject terminated, attacked directly.
⚠️ Partially retracted by hypothesis-space.md. The underdetermined regime splits in two. "Authority is evidence" holds where more observation could settle the question, and fails where none could — there authority is a selection policy, downstream of inference rather than inside it.
Outcome: co-reference is partially derivable, and the boundary is exactly characterizable — it is a data-association bound, not an open/closed-system bound. A third regime exists where the question is void. Authority is evidence bundled with convention and presented as ontology. The URN prediction survives, with its failure mode refined.
1. The five reductions
1. Spatiotemporal continuity — necessary sometimes, never sufficient
| Attack | Result |
|---|---|
| teleportation | no continuous path; identity survives by convention |
| tracking loss | continuity holds in reality, is absent from the record |
| temporary disappearance | same — an unscanned parcel is not a discontinuous parcel |
| packet routing | fragmentation and reassembly leave no single continuous entity |
| animal migration | continuity holds unobserved; re-identification is done by tags — an import |
Two distinct failures, and separating them matters. Teleportation and packet reassembly show continuity is not necessary. Tracking loss and migration show only that it was not observed — the absent-evidence rule from truth-reduction.md, applied at the subject layer.
And continuity is not independent. Continuity is a predicate over a placement series, and placement is a state whose subject is the thing whose identity is in question. Stating "it moved continuously" presupposes "it."
The escape is to track unlabelled observations by proximity — real technique, and it fails precisely when two objects come close enough that the association is ambiguous. That failure has a name and it is the whole problem: data association.
2. Attribute similarity — insufficient, and in one domain the target does not exist
| Attack | Result |
|---|---|
| identical twins | same attributes, two individuals |
| cloned repositories | byte-identical, distinct |
| duplicate packets | identical, distinct |
| identical molecules | no fact distinguishes them |
The molecule case is not another failure of the same kind. Two H₂O molecules are not merely hard to tell apart — in quantum mechanics identical particles are fundamentally indistinguishable, and this is not epistemic: boson and fermion statistics differ because the particles cannot be labelled. Swapping two of them does not produce a different physical state.
There are domains where co-reference is not underdetermined but absent. Individual identity is not a universal feature of reality.
That is an ontological result, and it means any theory asserting that every observation has a determinate subject is false.
3. Causal lineage — necessary, not sufficient
Fission, fusion, mergers, git forks, amoeba division, molecular dissociation: in every case lineage is intact and identity is still not determined. Confirmed from subject-reduction.md: lineage gives a many-to-many graph, and identity requires collapsing it to a one-to-one thread. No fact performs the collapse.
Git is the informative case because the lineage is fully recorded — perfect information, and the fork's name is still assigned by fiat. That isolates the gap: it is not missing data.
4. Structural position — neither necessary nor sufficient
| Attack | Shows |
|---|---|
| role reassignment | new individual, same position |
| employee transfer | same individual, new position |
| network rewiring | same node, different edges |
| planetary capture | same body, new structural position |
Individual and position vary independently, demonstrated in both directions. This reduction fails faster and more completely than the others.
But it fails usefully. Position is exactly what distinguishes otherwise identical things — two identical bolts in two holes, or identical particles by lattice site. So position substitutes for identity precisely where individual identity is absent (§1.2). The two results are complementary, not merely adjacent.
5. Observation history — a container, not a criterion
| Attack | Result |
|---|---|
| intermittent sensors | gaps |
| observer disagreement | two observers, incompatible co-reference judgements |
| aliasing | two identifiers, one thing — fusion at the identifier layer |
| duplicate identifiers | one identifier, two things — fission at the identifier layer |
The last two are symmetric, and they are the fission/fusion pair one level up.
Repeated observation establishes co-reference only if observations carry labels — which is importing — or by inferring from continuity, attributes, lineage or position, all of which failed above. Observation history contributes no independent criterion.
2. The criteria are complementary — which is what makes the boundary derivable
Each criterion fails, but they do not fail on the same cases:
| Criterion | Fails on |
|---|---|
| continuity | gaps, teleportation, crossings |
| attributes | duplicates |
| lineage | fission, fusion |
| position | reassignment |
So combinations cover more than any single one. Twins are separated by continuity; crossing objects are separated by attributes. This is not a theoretical observation — multi-object tracking combines a motion model with an appearance model for exactly this reason.
The residue is where all of them fail at once, and it is a single, precisely statable case:
Two candidates indistinguishable in every observed dimension, whose continuity is unobserved across an interval containing a possible swap.
There, no observation anywhere distinguishes swap from no-swap.
The boundary, stated
Let O be the observation record and H(O) the set of association hypotheses
consistent with it.
| Condition | Status | |
|---|---|---|
| derivable | |H(O)| = 1 |
co-reference is computed, no import needed |
| underdetermined | |H(O)| > 1 |
must be imported or assumed — no fact in O decides |
| void | the candidates are fundamentally indistinguishable | there is nothing to decide (§1.2) |
The boundary is not open-versus-closed system. A closed system with two identical objects and a sensor gap is equally undecidable; an open system with distinguishable objects is decidable. The real variable is observational resolution against object density — whether the record separates the alternatives.
And it is the same law as everywhere else
At the value layer: two observations are one truth iff no differing value intervenes. At the subject layer: two observations are one subject iff no distinguishing observation intervenes.
Co-reference is episode separation, one layer up. The persistence law governs both.
Fourth time this investigation has arrived at the same separation principle by an independent route — after missing-versus-zero, absent-evidence semantics, and idempotent occurrences.
Verdict: co-reference is partially derivable. Not primitive, not necessarily imported, and in one regime not a question.
3. Authority
Five candidates, tested.
subject.ts documents authority as "the system of record that owns this
identifier." When a connector emits authority=github, path=org/repo, it
asserts that these observations co-refer. That assertion has a source, and it
can be wrong — identifier reuse after deletion, renames, and merges all falsify it.
| Candidate | Verdict |
|---|---|
| evidence | yes — testimony about co-reference, from an observer, falsifiable |
| convention | partly — it also carries the post-fission selection rule (a forked repo gets a new id by GitHub's decision) |
| provenance | no — provenance records where a claim came from; this is the claim |
| external oracle | no — an oracle is infallible; this is not |
| ontology | no — but it is presented as ontology, and that is the defect |
Authority is co-reference testimony bundled with a selection convention, and presented as ontology.
The empirical finding
Every other claim in this system carries evidence — an observer and a citation —
and can be disputed, collapsed and graded. SubjectRef is
{ kind, subtype, authority, path }: no evidence, no validAt, no observer.
Subject identity is the only claim in this system with no provenance.
A project whose entire discipline is provenance has exactly one unprovenanced claim, and it is the one that resisted six rounds of reduction. Those facts are related: an assertion that cannot be recorded cannot be disputed, and one that cannot be disputed cannot be found wrong.
This also locates the aliasing gap correctly. It is not that the system lacks an alias mechanism. It is that co-reference claims have nowhere to live, so two claims about one subject cannot be brought into contact to disagree.
4. The URN prediction — falsification attempted
The prediction: embedding kind in the URN is the same error as
conditionIdentity and placement@at — a mutually exclusive classification
placed in a key, so a change of classification breaks identity.
Falsification attempt: perhaps kind is constitutive rather than
classificatory. If a resource and a work are genuinely different things
rather than one thing under two labels, then a kind change is a subject change,
and including it in identity is correct.
This is the strongest available defence, and it does not fully succeed.
Against it: Pluto. Reclassification did not change the object; it changed the
scheme. If kind is classificatory, the defect is exact. The module's own
comment — "Six abstract kinds, deliberately domain-independent" — describes a
classification scheme, which leans classificatory.
But grant the constitutive reading anyway. Then kind must be functionally
determined by (authority, path), and including it is redundant. Redundancy in
a key is not harmless: two connectors reporting the same (authority, path) with
different kind mint two subjects. That is dual ownership, and it is the
failure this project already names.
| Reading | Failure mode |
|---|---|
| classificatory | reclassification splits a subject's history |
| constitutive | observer disagreement mints a duplicate subject |
The prediction survives under both readings. What changes is the failure mode, not whether there is one.
Refined from the previous round: I classified this as certainly the same defect. It is more precisely a defect under either reading, with different consequences, and the code does not settle which reading was intended.
One correction to how I framed it. subtype is explicitly excluded from
identity — "carries display and provenance and never identity semantics." The
author drew a line between subtype and kind deliberately. This is therefore a
design decision to challenge, not an oversight, and I should not have implied
otherwise.
Classified as the third instance of one underlying error — a value in the key — rather than a new defect, per the objective.
5. Layers
| Layer | Co-reference |
|---|---|
| ontology | lineage is real; the one-to-one thread is not; for indistinguishables, neither is |
| observation | continuity, attributes, position — each partial, jointly stronger, jointly bounded |
| canonicalization | |H(O)| = 1 → compute; > 1 → must import; void → refuse |
| projection | subtype, correctly excluded from identity |
| presentation | the name; the post-fission selection rule |
6. Standing
| Question | Answer |
|---|---|
| Is co-reference primitive? | no |
| Derivable? | partially — exactly when observations separate the hypotheses |
| Necessarily imported? | no — imported only in the underdetermined regime |
| Is there a regime with no answer? | yes — indistinguishable particles |
| What is authority? | evidence + convention, presented as ontology |
| Is the boundary open/closed system? | no — observational resolution vs object density |
| Does the URN prediction survive? | yes, under both readings |
What is still not established
- The three regimes are characterized but the middle one is not quantified.
|H(O)|is defined, not computed, and nothing here says how to count it for a real record. - The claim that the four criteria are jointly bounded rests on exhibiting the residue case, not on proving no fifth criterion exists. A fifth criterion covering the swap case would falsify the boundary — that is what to attack.
capabilityremains untouched — seven rounds.
Nothing implemented.