docs/separation-audit.md
Separation audit
Prompted by a methodological failure, not a domain one: the asymmetry round over-collapsed by inferring identity from shared algebraic shape.
Outcome: the over-collapse is measurable — the algebraic profile is 4-to-1 ambiguous, so that inference was guaranteed to fail. The relation hypothesis is falsified as stated, repaired, and turns out to be diagnostic: it identifies three concepts that are bundles. Convention is a warrant value whose layer differs from its siblings, which derives the sixth layer rather than merely noting it.
1. The audit
| Concept | Reflexive | Symmetric | Transitive | Other | Semantic role | Layer |
|---|---|---|---|---|---|---|
| distinction | no | yes | no | — | difference | ontology (property) |
| indistinguishability | yes | yes | no | tolerance | sameness-in-practice | ontology |
| equality | yes | yes | yes | equivalence | sameness | convention |
| precedence | no | no | yes | asymmetric | before | ontology |
| dependence | no | no | yes | asymmetric, counterfactual | determines | ontology |
| causation | no | no | contested | = precedence + dependence | produces | ontology |
| lineage | no | no | yes | not functional (fission) | descends from | ontology |
| justification | no | no | roughly | defeasible | supports | epistemology |
| provenance | no | no | yes | second-order | came from | epistemology |
| naming | no | no | no | many-to-many | denotes | representation |
| co-reference | yes | yes | no in practice | tolerance | same subject | spans three |
| constraint | — | — | — | over configurations | restricts | semantics |
| warrant | — | — | — | — | licenses | spans two |
What the audit shows
The over-collapse is measurable. The profile {irreflexive, asymmetric, transitive} is shared by precedence, dependence, lineage and provenance —
four concepts, three semantic roles, two layers, one profile.
Algebraic profile is 4-to-1 ambiguous on the surviving concepts. Inferring identity from it was not a near-miss; it was guaranteed to over-collapse.
That is the methodological finding stated as a measurement rather than a caution.
Defeasibility is a second, independent separator of epistemic from ontological arrows. Justification is non-monotonic — adding a premise can destroy it. Nothing else in the table is: adding an observation never destroys a causal fact.
And this recovers an earlier result from a new direction. |H| was found to
increase under contradiction and retraction. That is non-monotonicity, and it
appears here as an algebraic property of justification. Two findings, arrived at
separately, are the same one. The anti-parallel argument from
asymmetry.md is now not the only support for that separation.
Co-reference is a tolerance relation, not an equivalence. Data association is approximate, so in practice A matches B, B matches C, and A does not match C. That is the aliasing problem in algebraic form — and it gives co-reference the same profile as indistinguishability, which is consistent, since co-reference is distinction at the subject layer.
2. Is "relation" the right abstraction boundary?
Hypothesis: a relation is a typed assertion with domain, codomain, algebraic properties, warrant, layer.
Falsified as stated
Precedence has no warrant. It obtains or it does not. What carries a warrant is the claim that A precedes B — not the precedence itself.
The 5-tuple conflates a relation with an assertion about a relation. That is the same split already derived twice:
| Layer split | Where found |
|---|---|
| truth / record | minimal-ontology.md |
| relation / assertion-about-relation | here |
Third instance of one structural separation.
Repaired
relation = (domain, codomain, algebraic properties, layer)
assertion = (relation, warrant)
Warrant moves out. And that yields a criterion that was not available before:
A relation is conventional iff asserting it makes it so.
It discriminates correctly. Naming and selection: asserting makes it so. Precedence and dependence: no. Justification: no — there are bad justifications, and asserting one does not create it. So the criterion does not over-generate into the epistemic layer, which was the risk.
And the framework is diagnostic
The repaired form survives every surviving relation except three, and the
exceptions are the finding: a concept that cannot take a single layer value is
a bundle.
| Concept | Spans | Verdict |
|---|---|---|
| co-reference | ontology (lineage) + epistemology (data association) + convention (selection) | bundle of three |
| dimension | semantics (value space) + ontology (persistence) | bundle of two |
| warrant | epistemology (evidence, derivation) + constitutive (convention) | bundle of two |
Two of these three were found independently, before this framework existed —
dimension in constraint-floor.md's layer audit,
co-reference in subject-reduction.md. The framework
retroactively predicts findings that were made without it, and then finds a third
that was not.
That is the strongest form of support available here, and it is the reason to stop reducing and record the relation layer as it stands.
3. Convention
Three candidates were offered: irreducible, a special case of warrant, or projection-level policy.
It is a warrant value — warrant ∈ {evidence, derivation, convention} was
already derived in inference-operations.md. Equality
thresholds and fission naming are both assertions carrying a conventional
warrant, so no new machinery is needed to place them.
But it is not epistemic, and its siblings are. Evidence and derivation track a truth that obtains independently. Convention constitutes the truth — by the criterion in §2, asserting makes it so. That is a different relationship to its object, not a different degree of confidence in it.
So warrant spans two layers, and the sixth layer is real:
Constitutive. Not a peer layer of concepts, but the layer of one warrant value — which is why the five-layer scheme had nowhere to put it.
constraint-floor.md noted the scheme could not hold the selection rule. This derives what it is, via a criterion rather than by elimination. That is an improvement on the earlier claim, not a retraction of it.
Is convention irreducible? Within this framework, yes: constitutive assertion does not reduce to evidence (which tracks an independent fact) or to derivation (which follows from premises). Reducing it further would require attacking stipulation itself — i.e. agency — which is outside everything attacked so far and is the honest boundary of the claim, not a demonstration of irreducibility.
Not projection-level. Projection is representational; convention operates at canonicalization, before any projection exists. Equality thresholds decide what is true, not how it is shown.
4. The safest surviving statement
The proposed formulation:
"Systems contain distinctions and structured dependencies, but the dependency semantics are layer-specific."
This is better than "two properties and a set of relations," because it does not
reify relation as a universal. But it is still slightly too strong, and the
counterexample is in this repository's own vocabulary.
An undirected graph has structure and no dependency. Nodes differ; edges are
symmetric. Nothing depends on anything. So structured dependency is not
universal either — symmetric structure exists and carries no direction at all.
distinction itself is such a relation.
Weakened accordingly:
Systems contain distinctions and relations among them. Whether a relation is symmetric or asymmetric, and what it means, is layer-specific.
Direction is demoted from part of the claim to one of the things that varies — which is the same demotion the asymmetry round performed on direction, applied one level further out.
The category error, restated
The diagnosis is right and generalises:
| Round | Error |
|---|---|
| earlier | this thing has a value, therefore value is the thing |
| asymmetry | this relation has direction, therefore direction is the relation |
Same shape. And sufficiency-test.md already reduced the first to functionality violated. The second is not a functionality violation — it is inferring identity from a shared property. So these are two distinct error classes, and the temptation to unify them by shared shape is the very error under discussion. Recorded separately, deliberately.
Standing
| Question | Answer |
|---|---|
| Does algebra determine identity? | no — 4-to-1 ambiguous, measured |
| Is "relation" the right boundary? | not as proposed — warrant belongs to assertions |
| Repaired form? | (domain, codomain, algebra, layer) + separate assertion |
| Does it survive? | yes, and it is diagnostic — three bundles found, two of them retroactively |
| Is convention irreducible? | within this framework, yes; reducing it means attacking stipulation |
| Is convention a warrant value? | yes — and its layer differs from its siblings |
| Is convention projection-level? | no — it operates at canonicalization |
What is still not established
- Modal force — still unattacked, still what separates dependence from precedence, now two rounds outstanding.
- Whether the three bundles are the only ones. The framework finds bundles it is pointed at; nothing here enumerates candidates.
- The bundle criterion — cannot take a single layer value — depends on the layer scheme being right, and that scheme has now grown once under pressure.
capability— thirteen rounds untouched.
Nothing implemented.