Coverage — Spectral Brand Theory

The chain is not ours, and that is the point

The chain below belongs to the media and marketing-measurement tradition, not to this work. Every row is measured against it, so you can hold each verdict against the paper behind it: every key links to the paper, through a DOI that always resolves to the current version.

budget → media units bought → impressions delivered → attention → perception → memory → behaviour → revenue

The reading key

Owned — a paper makes a defended claim about this stage. Touched — a claim exists but is partial, or is about a neighbouring object. Ceded — deliberately not ours, by a recorded decision. Empty — nothing.

Evidence grades. A executed pre-registered study with public logs · B executed but single-case or interpretive · C calibrated simulation, labelled by its own paper as not a test · D formal result, no data · — nothing.

A paper counts as coverage; an article, a post or a seed does not.

The eight stages

#	Stage	Verdict	Papers	What is actually claimed	Evidence
0	Budget	touched	2026k 2026aj	A shadow-price allocation rule across perceptual dimensions — not across media — on hypothetical weight profiles; and paid media treated as a flow-dependent organizational function under a cited depreciation calibration.	D
1	Media units bought	empty	—	Nothing. The corpus says it in its own voice: we do not buy media.	—
2	Impressions delivered	empty	—	Nothing. Impressions occur once in the whole corpus as a chain quantity — as the denominator of a spill cost, under an assumed linearity. There is no delivery model, no reach curve, no frequency distribution.	—
3	Attention	ceded	—	Ceded by decision, and the decision is worth stating because a settled position reads as a hole. Every occurrence of "attention" in this corpus is one of three other constructs — the encoding bandwidth of an AI observer, the observer weight vector, or a competitor mechanism being distinguished from ours. Ad attention is handed to the external tradition by name.	—
4	Perception	owned	2026a 2026d 2026e 2026f 2026r 2026v 2026as 2026az 2026ba 2026ax	The home ground, and the only stage with executed, pre-registered, publicly logged campaigns behind it: a theory of what a perception is, an instrument that reconstructs cohort-resolved eight-vectors from public artifacts, two independently measured noise floors, a version floor separating apparatus drift from brand signal, and a discipline of abstaining rather than manufacturing a difference.	A
4b	Perception — valence sub-layer	owned	2026ax	Per-reflection valence in [−1, +1] per dimension, with its own operator floor.	B
5	Memory	empty	—	Nothing. Priors are described as stored in memory inside a profile definition, and mental availability appears only as a rival framework the corpus argues against. There is no recall measure, no salience measure and no memory model.	—
6	Behaviour	touched	2026bf 2026bb	Model behaviour only. Stated choice propensity of LLM cohorts, which that paper says plainly is not behaviour; and a revealed pick by an LLM agent, which is a real behaviour of a model rather than of a person. There is no human behavioural data anywhere in the corpus.	A
7	Revenue	empty	2026p 2026k	Effectively nothing. One single-case interpretive mapping of revenue milestones onto dimensional-activation events, author-scored without inter-rater reliability; plus an assumed increasing concave willingness-to-pay function, taken rather than derived.	B

The seven arrows

Of the seven arrows in the chain as specified, this corpus owns none. Five are unclaimed outright.

Arrow	Status
budget → media units	Unclaimed.
media units → impressions	Unclaimed. No reach curve, no delivery model, no frequency distribution — handed to the external media-planning tradition.
impressions → attention	Unclaimed and explicitly ceded. Two untested hypotheses sit in a research agenda; they are tests to run, not claims.
attention → perception	Not this arrow. The corpus owns a substitute that skips attention rather than bridging it — no paper conditions perception on attention having occurred.
perception → memory	Unclaimed.
memory → behaviour	Unclaimed.
behaviour → revenue	An analytic bridge only, and to shares rather than revenue: a closed-form switching matrix under a cited external parameterisation. It fails its own consistency check in one of three categories, and shares are not revenue.

What is owned instead: a substitute arrow and a collapsed one

Four papers formalise a route from an emitted signal straight to a perceptual state, bypassing impressions and attention entirely: a campaign as a forcing vector on a forced Ornstein-Uhlenbeck process with a recoverable decay constant, a resonance over-index for a dimension-strong creative on a dimension-sensitive cohort, a coherence-emission threshold inequality, and order dependence with absorbing states. Every one is theory plus a calibrated demonstration; not one is a field measurement, and each paper says so in its own text. Their precise-looking numbers are model properties, not measured advertising response, and should never be quoted without that qualifier.

Two executed studies reach further, on a collapsed arrow the classic chain does not contain: perception straight to behaviour, with attention and memory skipped. They disagree informatively. The perceptual layer carries choice propensity where perception separates the brands, and stops carrying it exactly where it does not. Bounded, replicable, and about LLM cohorts rather than people.

The warning that matters most

Two ladders, meeting at one node

The chain in this corpus's own head is not this chain. The instrument's ladder runs perception → valence → desire → demand. The advertising ladder runs impressions → attention → perception → memory → behaviour. One is a transmission chain, tracking how a signal reaches a person; the other is a construction chain, tracking what a decision-maker builds on top of a read. They intersect at exactly one node — perception — and nowhere else.

So results from this work, laid over the advertising chain, imply coverage of two stages and three arrows that are completely empty. If you see them presented that way, the presentation is claiming more than the papers do.

The count

Of 8 stages this corpus owns 1 — perception, with its valence sub-layer — and touches 2 more. Of 7 arrows it owns 0 as specified. Attention is ceded by decision, not empty — it was handed to the external models that already measure it, and is not waiting to be filled in.

Where to go instead. For delivery, reach and frequency, the media-planning tradition. For attention, the attention-measurement vendors and the published models this corpus differentiates from rather than competes with. For recall and mental availability, the memory and salience literature. For attribution and incrementality, the experimental and econometric marketing-measurement literature. A map that only says no is not useful; these are real questions with real answers elsewhere.

The organizational side has its own map, and three chains rather than one: orgschema.com/coverage. The two meet at exactly one node, the rendered artifact.