docs/inference-operations.md
Reducing the five operations
Observe, Compare, Eliminate, Select, Project — attacked as the ontology was.
⚠️ Corrected by constraint-floor.md. The surviving verb is named wrongly below. Observation is one value of the warrant parameter, not the verb — pure mathematics, cellular automata and physical law carry constraints with no observer at all. The reduction stands; the name does not.
Outcome: none of the five survives as an independent operation except one. Compare is supplied by ontology. Eliminate is a definition, not an act. Project and Select are both Observe under different parameters. One verb remains, and its parameter space predicts a cell this project deliberately leaves empty.
1. Are Compare and Eliminate independent?
No — and they are not peers.
Elimination removes a member of H because its predicted value differs from the
observed one. So elimination invokes comparison; comparison is a component, not a
stage beside it.
But comparison does not reduce into elimination either, because it appears elsewhere: in separation (is this value different from the last?), and in projection (rendering a difference, an ordering, a rank). Something used by three operations is not a stage in a pipeline containing them.
What is comparison, minimally? Applying an equality or ordering relation over a value space. And dimension-algebra.md already established that equality is absorbed into the value space, and that ordering is optional structure carried by the dimension.
Compare is not an operation. It is the value space's equality relation, and it is supplied by ontology.
Compare is a noun the pipeline mistook for a verb. It reduces out of the operation list entirely, into the dimension.
2. Is Projection merely Observation in reverse?
No — the symmetry is real but the direction is wrong.
An inverse restores information. Observation is lossy; projection is lossy. Two lossy maps do not compose into an identity — they compose into a lossier map. Reality → facts → geometry → pixels loses information at every arrow, in the same direction throughout. Projection cannot be observation reversed, because nothing in the chain runs backwards.
But something stronger than reversal is available. Both operations are:
- information-losing maps,
- from a richer domain to a poorer representation,
- carrying a traceability obligation — the ability to run the map backwards as an audit, which is not the same as inverting it.
And in this repository those obligations are already stated twice, independently: connectors must never invent facts, and the renderer must never invent information. Two disciplines derived separately, and identical. That is empirical support, not analogy.
So:
Project = Observe, applied to a model rather than to reality.
The observer of reality produces facts; the renderer "observes" the model and produces pixels; the human observes the pixels. One operation, iterated down a chain, with a different thing on the input side each time.
The expected asymmetry — that observation is evidence-bearing while projection is design-laden — does not survive inspection. Connectors make design choices too (what to emit, at what resolution), and this project's renderer is required to be evidence-bearing. Neither side has the property the other lacks.
3. Is Selection primitive, or policy over H(O)?
Neither, exactly. Selection is Eliminate with a different warrant.
hypothesis-space.md defined selection as picking a member
without removing any. Mechanically, though, both operations end with a smaller
H. Run the two side by side and the mechanism is identical; what differs is
what licenses it:
| Warrant | |
|---|---|
| eliminate | evidence — an observation inconsistent with the discarded members |
| select | convention — a rule that no observation supports |
Selection is elimination without evidence.
This is why six rounds went by without the distinction surfacing, and it is why conflating them is dangerous rather than merely untidy: the two are indistinguishable at the mechanism level and distinguishable only by warrant — and warrant is not in the type.
collapse() is the live instance. It performs selection (picking by array order)
while presenting as canonicalization. Nothing in its signature could reveal the
difference, because the difference is not mechanical.
4. Eliminate is not an operation either
The reduction goes one step further than expected.
H(O) is defined declaratively:
H(O) = { w : w ⊨ O }
Adding an observation does not perform an elimination. It changes O, and
H(O) is whatever the definition then yields. All elimination is already
contained in the set-builder.
Elimination appears to be an operation only because an implementation would compute it incrementally. That is an artifact of evaluation strategy, not a fact about inference — the same category error as treating memoisation as arithmetic.
Eliminate is a definition, not an act.
And this recasts §3: selection cannot be "elimination with a different warrant"
if elimination is not an operation. What selection actually does is add a
constraint to O that is not an observation. Which is the same thing observing
does, with a different warrant.
5. The reduction
| Operation | Verdict |
|---|---|
| Observe | survives — the only operation |
| Compare | not an operation — the value space's equality, supplied by ontology |
| Eliminate | not an operation — the definition of H(O) |
| Project | Observe, with a model as target |
| Select | Observe, with convention as warrant |
One verb: assert a constraint on
H. Everything else is a parameter, a definition, or ontology.
Two parameters remain, and they are exactly the two things this project already spends its discipline on:
| Parameter | Values |
|---|---|
| target — what is examined | reality, model |
| warrant — what licenses the assertion | evidence, derivation, convention |
The five-operation model was concealing that there is one operation and a warrant. That the reduction lands on warrant-tracking — which is what provenance is — is the confirmation: the operational analysis and the provenance discipline were derived independently and meet.
6. The parameter space predicts an empty cell
Six combinations. Five are occupied:
| evidence | derivation | convention | |
|---|---|---|---|
| reality | observation — a connector reporting | — empty — | definition — "a planet is…" |
| model | instrumentation — the mutation harness, which observes the source tree and rendered DOM as objects | projection — the renderer | selection — collapse() picking by order |
The empty cell is reality × derivation: asserting about reality on
derivational warrant. That is prediction — simulation, extrapolation,
forecasting.
This system has none. And the reason is not oversight:
"The renderer must never invent information" is exactly the prohibition of
reality × derivation.
The project's founding rule turns out to be a cell exclusion in this space. It was stated as a discipline; it is derivable as a structural choice.
That also sharpens what the rule costs. Excluding the cell forbids fabrication — and it equally forbids prediction, which is a legitimate operation the system therefore cannot perform. The exclusion is correct for this system's purpose and it is not free, and those are different statements that the rule as written does not separate.
7. Standing
| Question | Answer |
|---|---|
| Compare and Eliminate independent? | no — Compare is ontology, Eliminate is a definition |
| Projection = Observation reversed? | no — both lossy in the same direction; Projection is Observation on a model |
| Selection primitive or policy? | neither — Observe with a convention warrant |
| Smaller set? | one operation, two parameters |
What is still not established
- The claim that Observe is irreducible is a failure to reduce, one round old, and by this investigation's own standard that is not promotion.
- The 2×3 parameter space is derived from the operations that survived, so its completeness is inherited from theirs. A seventh combination would falsify it.
- Whether
warranthas exactly three values is untested — it is the same question, one layer up, as whether persistence is binary, and that one took a dedicated round. capability— nine rounds untouched.
Nothing implemented.