docs/general-projection.md

General projection — what makes any reality projectable

CONCLUSION WITHDRAWN — see projection-layers.md. This document concludes the vocabulary is "universal across purposive systems". That was promoted before it was earned. Measured since: the gap the counterexamples exposed — subjects cannot cease to exist — affects organizations exactly as much as cells. It is a general expressiveness gap, not a boundary of applicability. The measurements below stand; the boundary claim does not.

Method: falsification, not invention. A candidate universal vocabulary already exists in this repository and was verified domain-free by inspection. Inspection is weak evidence. So the exercise is to try to break it with eight domains, and to run the geometric stages against realities they were never designed for.

Claims are marked measured or argued. The distinction is load-bearing: this document returns to derivation after a long implementation phase, and the project's record is that unfalsifiable elegance is where it goes wrong.

1. The candidate under test

SUBJECT KINDS (6)  resource, work, actor, agreement, artifact, environment
FACT FAMILIES (4)  condition, measure, exchange, placement
CONDITIONS (20)    availability · progress · capacity · integrity · exposure · economics

Plus Evidence (provenance) and bi-temporality (validAt / recordedAt).

2. Eight domains against it

Domain	Entities	Flow	Accumulation	Constraint	Breaks?
organizations	people, tasks, contracts	handoffs	completed work	capacity	no
manufacturing	machines, orders, specs	material	output	throughput	no
financial markets	traders, instruments, contracts	capital	position	margin	no
distributed software	services, requests, SLAs	messages	throughput	quota	no
transportation	vehicles, cargo, timetables	movement	distance	capacity	no
biological cells	molecules, organelles	metabolites	concentration	ATP budget	`agreement`
ecosystems	organisms, nutrients	energy	biomass	carrying capacity	`agreement`
planetary systems	bodies	momentum	mass	orbital energy	almost everything

Where it breaks, precisely

agreement fails for cells and ecosystems. Receptor–ligand binding and mutualism are relationships, not agreements: an agreement presupposes parties that commit and can default. Symbiosis has no obligation and no breach.

Planetary systems break four of six subject kinds and most of the condition vocabulary. A planet is not a resource, work, actor, agreement, artifact or environment. It is a body. It has no agency, so actor is empty; no purpose, so work is empty; no obligation, so agreement is empty.

The finding — argued from the above

The vocabulary is not domain-free. It is purposive-free-of-domain.

actor presupposes agency. work presupposes purpose. agreement presupposes obligation. And all twenty conditions presuppose a norm — stalled, blocked, saturated, unprotected, exposed, overspend are each a deviation from an intended state. A planetary system has no intended state; an ecosystem has none except one an observer imposes.

The vocabulary is universal across purposive systems and fails outside them. That is a much sharper claim than "domain-free", and it is falsifiable: exhibit a non-purposive system the six kinds classify naturally, and it is wrong.

3. What survives as genuinely universal

Separating the vocabulary into what survives all eight and what does not:

Primitive	Universal?	Why
Subject identity (`SubjectRef`, `urn`)	yes	every domain has distinguishable things with stable identity
Relation (`exchange`)	yes — measured	coupling exists in all eight; ran unchanged on four
Magnitude (`measure`)	yes	every domain has quantities
Location (`placement`)	yes, with a caveat	universal as a fact, but its status inverts — see §5
Time (bi-temporal)	yes	observation time ≠ event time in every domain
Evidence (provenance)	yes	precondition of observed reality, which is the premise
`SubjectKind` (the six)	no	a purposive taxonomy
`condition` (the twenty)	no	every member is a deviation from intent
`actor`, `work`, `agreement`	no	presuppose agency, purpose, obligation

The sharp result: SubjectRef is universal; SubjectKind is not. Fact with evidence and bi-temporality is universal; three of its four families are, and condition is normative.

So the smallest universal semantic vocabulary is roughly:

identity · relation(weighted, directed) · magnitude · location · time · provenance

Six primitives. Everything else measured here is domain or purpose specific.

4. The geometric stages, tested outside their domain — measured

metric.ts and layout.ts were run on four realities they were not designed for:

Domain	n	distinct positions	stress	asymmetries recorded
cell / glycolysis	8	8	614.92	27
market / settlement	4	4	6.31	12
planetary / n-body	6	6	64978.75	11
transport / freight	5	5	189.61	9

They ran unchanged. Every entity received a distinct position; every asymmetry was recorded in the residual. No domain concept was required.

Fidelity is structural, not semantic — measured

Stress spans four orders of magnitude, so the obvious reading is that some domains project badly. That reading is wrong. Holding the domain fixed and varying only graph shape and weight range:

Structure	stress
star, weight range 0.01–0.99	64978.75
star, weight range 0.70–0.99	36.04
chain, wide range	0.00
ring, uniform	3.64

Same topology, only the dynamic range changed: 1800× difference. A chain with the same wide range embeds perfectly.

Embedding fidelity is governed by the structure of the relation, not by what the relation means.

By the criterion in the brief — if two completely different realities project to the same spatial language, that language is closer to the engine than to either domain — the metric→geometry stage is part of the engine.

5. Which geometric interpretations are available, and which justify themselves

Given the six universal primitives, what can space carry?

Visual primitive	Derives from	Domain-invariant?	Justification
position	relation, via metric embedding	yes	operates on distances; meaning never consulted
extent (size)	magnitude	yes	monotone map from a number
connection (drawn edge)	relation, directly	yes	required — see below
opacity	provenance	yes	absence of observation ≠ absence of value
motion	time	yes	temporal derivative of any of the above
containment	hierarchy	yes if hierarchy is observed	otherwise invented
colour	identity or magnitude	yes, but	high bandwidth, no natural order — measured here to be the channel alerts seize
taxonomic shape	`SubjectKind`	no	purposive taxonomy
threshold styling	`condition`	no	presupposes a norm

Why drawn edges are not optional — derived

Two impossibility results, both measured in this repository:

Direction cannot survive position. Planar distance is symmetric, |p_a − p_b| = |p_b − p_a|; a relation need not be. No placement of points in any metric space carries asymmetry.
Individual relations cannot survive position. n(n−1) weights cannot inject into 2n coordinates for n ≥ 4.

Therefore: if the relation matters and n ≥ 4, position alone is provably insufficient, and the relation must also be drawn or emitted as residual. That is a derivation, not a design preference — and it holds for glycolysis and n-body identically, because it is a fact about embeddings.

The inversion at `placement` — argued

In organizations, location is derived — there is no true position, so it must be computed from relation. In planetary systems location is primary — it is the observation, and relation (gravitational coupling) is derived from it.

So placement is universal as a fact family, but its direction of derivation reverses between domains. A general engine cannot assume position is an output. It must accept position as either an input or a derived quantity, and know which.

This is the one place where the existing implementation is domain-shaped in a way the vocabulary is not: layout.ts assumes position is always derived.

6. What this does not establish

Human understanding is untouched. Every result here is projection correctness. Whether a glycolysis embedding is interpretable requires observers, and no evidence exists.
Four domains were run, not eight. Ecosystems, manufacturing, distributed software and organizations were reasoned about, not executed.
The six primitives are a lower bound from eight domains, not a proof of minimality. A ninth domain could break them — that is the falsification route, and it is the only one available.
No architecture changed. Nothing here proposes extending the ontology; the standing rule requires a measured phenomenon the current vocabulary cannot represent, and the two candidates found — non-purposive systems, and inverted placement — are recorded rather than acted on.