docs/external-calibration.md

Independent calibration, modality, and the projection grammar

The typing instrument tested against concepts it was not derived from, modality attacked, and the grammar built and executed.

Outcome: the instrument matches three established results in philosophy of biology it was not shown, and fails one case — configuration — because warrant is not one of its three components. The failure is recorded and not fixed, per the standing instruction. Modality is overloaded: at least four distinct modal logics, and convention is not one of them. The grammar rejects eight classes of encoding across three domains, tests/projection-grammar.test.ts, 11 tests.

Task 1 — external calibration

Sixteen concepts, four domains, none of them the source of the instrument.

Mathematics

Reduction	Alg	Role	Layer	Verdict	Correct?
function → relation	✓	✓	✓	accept	✓ a function is a functional relation
equivalence relation → partition	✓	✓	✓	accept	✓ genuinely the same object
equivalence relation → tolerance relation	✗	✓	✓	reject	✓ transitivity differs
vector space → set	✗	✓	✓	reject	✓ structure is lost

Physics

Reduction	Alg	Role	Layer	Verdict	Correct?
force → field	✓	✗	✓	reject	✓ a field gives rise to forces; it is not one
mass → number	✓	✗	✗	reject	✓ a property is not a value
probability → measure	✓	✗	ambiguous	flagged	✓ — see below

The probability row is the interesting one: the instrument cannot assign a layer, because probability is epistemic under one reading and ontological under another. It independently flags the same concept that Task 2 and semantic-typing.md found contested. Flagging rather than deciding is correct behaviour, not a failure.

Biology — the strongest evidence

Reduction	Alg	Role	Layer	Verdict	Correct?
species → set of organisms	✓	✗	✓	reject	✓
adaptation → trait	✓	✗	✓	reject	✓
capability → state	✓	✗	✓	reject	✓
organism → collection of cells	✓	✗	✓	reject	✓

All four match established positions in philosophy of biology that the instrument was never shown. Species are not sets — a species persists through complete membership turnover, which is the Ship-of-Theseus structure the subject round found for teams and nations. Adaptation carries a historical role a trait does not: a trait that happens to be useful was not thereby selected for.

And biological capability produces the same verdict as organisational capability, from a different domain, on the same role mismatch — modal versus actual. That is the retraction reproduced independently.

Software — where it fails

Reduction	Alg	Role	Layer	Verdict	Correct?
interface → type	✓	✓	✓	accept	✓
implementation → interface	✓	✗	✓	reject	✓
permission → state	✓	✗	✓	reject	✓ deontic, not actual
configuration → state	✓	✓	✓	accept	✗ WRONG

Configuration is a convention-warranted state. Its algebra, role and layer all match an evidence-warranted state, so the instrument accepts a reduction that discards the thing that matters — a configured threshold is stipulated, not measured, and by semantic-typing.md that difference is exactly what nothing downstream can detect.

The instrument is blind to warrant, because warrant is not one of its three components.

Not fixed. Adding warrant as a fourth component is the obvious repair and it is precisely the tuning-against-observed-failure that was forbidden. The instrument's calibration is now: 15 of 16 correct, one systematic blind spot, one correct flag. A repair should be justified from derivation, not from this table.

Also worth recording: permission → state is rejected, and permission is deontic modality — a fourth independently-sourced instance of the capability shape, alongside biological capability, organisational capability, and dependence.

Task 2 — modality is overloaded

Six candidates, tested by which modal axioms hold. That is the discriminator algebra alone cannot supply, and it is decisive.

Modality	`□p → p`?	Closed under consequence?	Layer
logical necessity	yes	yes	semantics
physical possibility	yes	yes	ontology
legal / deontic	no	yes	convention
computational feasibility	yes	no	computation
statistical probability	graded	—	contested
human intention	no	no	—

Two axioms separate four groups. What is legally required is frequently not actual — the deontic T failure is the whole reason law exists. What is provable is not thereby feasible: computational modality is bounded by resources, so it is not closed under logical consequence. Intention fails both — intending does not achieve, and one does not intend every consequence of what one intends.

"Possible" is an overloaded word, not one semantic role. Four distinct logics, five layers.

The typing test says the same thing from the other side — six items, five layers, so not one concept. Two independent routes, same verdict, and the modal-logic route was not derived from this investigation.

They vary independently in both directions: "it is physically possible that X" can be asserted on weak evidence (strong modal claim, weak warrant), and "it is certain that X is merely possible" is a strong warrant about a weak modality. So semantic-typing.md's repair holds.

But the repair was under-specified. It added modal force to the relation tuple as a single field. It must be a pair:

relation = (domain, codomain, algebra, layer, (modality kind, force))

Convention is not a modality — a correction

Convention was listed among the modal appearances. It does not belong.

Modality concerns what could or must be. Convention constitutes — it does not constrain possibility, it creates a category. By semantic-typing.md's criterion, asserting makes it so, which no modality does.

So of the four appearances — capability, dependence, probability, convention — the first three are modal and distinct from one another (dispositional, counterfactual, graded), and the fourth is not modal at all. Four appearances, three modalities, one misfiling.

Task 3 — the projection grammar

Built: src/lib/grammar/index.ts. Tested: tests/projection-grammar.test.ts, 11 tests, all passing. Eight rejection rules, each citing the finding it derives from.

Rule	Rejects	Derived from
R1 order-invented	categorical → ordered channel	geometry is derived, never chosen
R2 proximity-invented	categorical → spatial, no metric	`metric.ts`
R3 order-destroyed	ordered → categorical channel	projection conservation
R4 direction-invented	symmetric → arrow	separation-audit.md
R5 persistence-mismatch	occurrence → persistent mark	minimal-ontology.md
R6 channel-overloaded	two meanings, one channel	visual channel separation
R7 constraint-as-state	a limit drawn like a level	`core/fact.ts`
R8 warrant-unencoded	convention with no warrant channel	semantic-typing.md

Three rules reproduce decisions already in this codebase — R2 the coupling metric, R7 the "a limit that nothing enforces may not be drawn as a capacity meter" comment, R6 the channel separation work. The grammar was derived from the ontology and lands on choices made earlier for local reasons. That is the evidence it is describing the system rather than decorating it.

It made a prediction, and the prediction is uncomfortable

If persistence must match, then of ten channels exactly one can carry a zero-extent truth. The test asserts it and it holds:

occurrences are drawable on 1/10 channels —
the renderer's vocabulary for events is one channel wide

That was not built in; it falls out. And it says something about the renderer: this system is far better equipped to draw states than events, which is the visual counterpart of the finding that exchange is the only occurrence family and cannot express a unary occurrence.

And the grammar separated a conflation without being told

shipment was found in truth-kinds.md to name two truths — a parcel and an act. The grammar takes them apart from their types alone: the location is a state and takes position; the dispatch is an occurrence and is rejected from position, admitted only to flash.

Standing

Question	Answer
Does the instrument survive external calibration?	15/16, with one systematic blind spot
What is the blind spot?	warrant — configuration is a stipulated state and types identically to a measured one
Was it fixed?	no — that is tuning against observed failure
Is "possible" one role?	no — four modal logics, separated by two axioms
Is convention modal?	no — constitutive, and it was misfiled
Does typing predict visual validity?	yes — 8 rules, 3 domains, 11 tests, 3 rules reproducing existing decisions

What is still not established

The calibration set is 16 concepts chosen by one party, and the reductions attempted were ones I selected. A set chosen adversarially would be stronger.
The biology results agree with established positions, but I supplied both the reduction and the judgement of correctness. That is weaker than an independent adjudicator.
The grammar is tested on encodings I wrote. It has not been run against WorldScene, which is the real test and would likely find violations — R6 in particular, given the span.style overload recorded as unresolved.
The modality kind refinement is derived and not implemented.

npm test 154 → 165, all passing.