core/docs/research/curriculum-volume-quantification-2026-07-24.md

Curriculum-Volume Quantification — ADR-0262 §5.1

Tier S6 (generalization-arc-2026-07-24 §6). Evidence only. This document does not propose ratifying curriculum content or flipping curriculum_serving_enabled — both are Shay's decisions (project-curriculum-serving-ratified doctrine: a flag flips on earned evidence, not proximity to it). It answers one question precisely: how short of a SERVE license is each served (subject × relation family) band today, measured against the actual ratified corpora, not an estimate.

Method: teaching.curriculum_premises.load_curriculum(domain) — the same loader the curriculum composer uses in serving — run against each of the four subjects chat.curriculum_surface.SERVED_DOMAINS currently routes to. Counts below are chain counts (ratified, vocabulary-resident, review_status == "reviewed"), i.e. exactly the population compile_premises would draw premises from; nothing here touches unmounted or unratified content.

1. The floor, restated precisely (§1.2 of the ratification packet)

Action.SERVE needs a one-sided Wilson lower bound ≥ θ=0.99 (core/reliability_gate/ceilings.py, core/reliability_gate/floor.py). For a perfect record this reduces to committed / (committed + z²) with z = 2.576, which crosses 0.99 at committed ≥ 657.

657 committed cases alone is not sufficient — the plan (§6) and the ratification packet both require a genuine outcome mix, not 657 restatements of the same fact padded with paraphrase (repetition-padding was already considered and rejected as dishonest earlier in this arc: conservative_floor cannot distinguish "657 independent facts" from "16 facts asked 41 times each," but a ledger that gamed the floor that way would not have earned anything). Treating "genuine mix" as roughly a three-way split across entailed / refuted / unknown (the plan's own working assumption, not a formally ratified policy — flagged here as an assumption, not fact) puts the entailed bucket's floor at ≈219 distinct taught relations — ⌈657 / 3⌉. That is where the plan's "≈219 per subject × family" figure comes from; this document supplies the measured n for every currently-served band to compare against it.

2. Measured ratified-chain counts, per subject × family (2026-07-24)

domain	family	ratified chains (n)	657÷n	219÷n
physics	causal	7	94×	31×
physics	modal	9	73×	24×
mathematics_logic	modal	4	164×	55×
mathematics_logic	sequence	4	164×	55×
mathematics_logic	contrast	8	82×	27×
mathematics_logic	evidential	8	82×	27×
systems_software	causal	7	94×	31×
systems_software	modal	6	110×	37×
systems_software	sequence	3	219×	73×
philosophy_theology	modal	8	82×	27×
philosophy_theology	contrast	8	82×	27×

11 bands are live (a subject × family pair with ≥1 ratified chain routes questions today, per chat.curriculum_surface.band_for); every one is between 24× and 73× short of the entailed-bucket floor alone, before even authoring the matching refuted/unknown volume. No served subject has a family close enough to flag as "next." Systems-software sequence (n=3) is the thinnest; mathematics_logic modal/sequence (n=4 each) are tied for second-thinnest; physics modal (n=9) is the closest of the eleven, still 24× short.

Total ratified chains per subject (all families, informational context — not a band-level floor since bands are scored per family, not per subject): physics 16, mathematics_logic 24, systems_software 16, philosophy_theology 16.

3. Vocabulary is not the constraint

Curriculum.vocabulary (every lemma the subject's mounted packs teach) is 16 lemmas for physics/mathematics_logic/systems_software and 151 for philosophy_theology — an order of magnitude more vocabulary than chains in every subject. The gate untaught_vocabulary (§4.6) is not what is holding any band back; the terms are taught, the relations between them are not authored in ratified volume. This confirms ADR-0262 §5.1's framing: the blocker is curriculum content authorship, not reader/vocabulary coverage — see also S3's mechanism-vs-coverage instrument (docs/research/vocab-trigger-instrument-2026-07-24.md), which finds the curriculum path's own refusals are overwhelmingly coverage-class for a different reason (relation, not term, absent) while carrying zero untaught_vocabulary refusals in the committed lane corpus.

4. What one subject fully reaching the floor would look like

Taking physics modal (the closest band, n=9) as an illustration only: it would need roughly 210 more ratified requires/enables relations, authored and reviewed through the existing curriculum ratification pipeline, before an entailed bucket alone could support a 657-committed band — and that is before authoring the matching refuted/unknown volume this document is not attempting to size (refuted questions need explicit negative curriculum content the corpora do not currently carry at all; unknown questions are comparatively cheap to author from in-vocabulary-but-untaught pairings, so they are not expected to be the binding constraint).

5. Non-goals of this document

• Does not recommend which subject or family to grow first — that is content strategy, Shay's call.
• Does not estimate authoring effort/time (no clock-time estimates per standing convention).
• Does not touch curriculum_serving_enabled or any corpus file.

Relates to project-curriculum-grounded-serving, project-generalization-arc, docs/adr/ADR-0262-curriculum-grounded-serving.md §5.1.