core/docs/research/curriculum-premise-scope-2026-07-25.md

Curriculum premise scope, negative rows, and band ceilings — measurements

Date: 2026-07-25 · Arc: curriculum-license-loop Phase A · Decision record: docs/adr/ADR-0264-negative-curriculum-and-premise-scope.md Base: main @ 6ada6f7a

Four probes, run against a clean tree on canonical Python 3.12.13. Each is self-contained and reproducible; probe 2 mutates a corpus file and restores it, asserting byte-identity at the end. Written down because the numbers reverse two decisions in the plan of record, and a claim that reverses a plan needs to be re-runnable by whoever doubts it.

Run from a worktree root with uv run python <file>.

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Probe 1 — negation reaches REFUTED, with correct atom identity

Question. The verb band reads three negation shapes. Does a negated premise mint the same atom as the affirmative question it should refute? If the verb agreement normalizes does not require to a different atom than requires, the ROBDD returns UNKNOWN and every authored negative is silently inert.

from generate.proof_chain.verb import read_verb_argument, VerbArgument
from generate.proof_chain.entail import evaluate_entailment_with_trace

POS = ["conservation requires symmetry", "mass requires force"]
QUERY = "conservation requires asymmetry"

CANDIDATES = {
    "A does-not (base verb)": "conservation does not require asymmetry",
    "B does-not (3sg verb)":  "conservation does not requires asymmetry",
    "C sentential-not":       "it is not the case that conservation requires asymmetry",
}

for label, neg in CANDIDATES.items():
    argument = ". ".join(POS + [neg]) + f". Therefore {QUERY}."
    arg = read_verb_argument(argument)
    if not isinstance(arg, VerbArgument):
        print(f"{label:26s} UNREADABLE -> {arg}")
        continue
    tr = evaluate_entailment_with_trace(arg.premise_formulas, arg.query_formula)
    print(f"{label:26s} outcome={tr.outcome.value:9s} reason={tr.reason!r}")
    print(f"{'':26s} premises={arg.premise_formulas}  query={arg.query_formula!r}")

Result. All three reach refuted / tautological_refutation, with premises=('a0', 'a1', '~(a2)') against query='a2' — same atom, negated. Agreement normalization is not an obstacle; shape B works despite being ungrammatical.

Bearing. ADR-0264 R2 picks shape C, on the grounds that shape A needs a de-inflection table that does not exist and shape B depends on an accident.

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Probe 2 — the premise cap collapses the band at 17 chains, and polarity is ignored

Question. Two at once. (a) What happens to a band when the family exceeds MAX_PREMISE_SENTENCES = 16? (b) What does a row carrying "polarity": "negative" actually serve today?

Appends synthetic-but-admissible negative rows to the real physics corpus — en_physics_v1 lemmas, review_status: reviewed, connective: requires, so they survive load_curriculum admission — then asks the real decision path.

import json, sys
from pathlib import Path

CORPUS = Path("teaching/domain_chains/physics_chains_v1.jsonl")
ORIG = CORPUS.read_text(encoding="utf-8")

sys.path.insert(0, ".")
from evals.curriculum_serve.oracle import vocabulary
vocab = sorted(vocabulary("physics"))
print(f"physics vocabulary = {len(vocab)} lemmas: {vocab}")

def row(n, subj, obj, polarity):
    return json.dumps({
        "chain_id": f"physics-modal-neg-{n:03d}", "domain": "physics",
        "operator_family": "modal", "subject": subj, "intent": "verification",
        "connective": "requires", "object": obj,
        "subject_pack_id": "en_physics_v1", "object_pack_id": "en_physics_v1",
        "review_status": "reviewed", "polarity": polarity,
        "provenance": "probe:phase-a:2026-07-25",
    })

taught = {(r["subject"], r["object"]) for r in map(json.loads, ORIG.strip().splitlines())}
cands = [(s, o) for s in vocab for o in vocab if s != o and (s, o) not in taught]

for n_neg in (1, 7, 8, 20):
    rows = [row(i, s, o, "negative") for i, (s, o) in enumerate(cands[:n_neg], 1)]
    CORPUS.write_text(ORIG.rstrip("\n") + "\n" + "\n".join(rows) + "\n", encoding="utf-8")
    for mod in [m for m in list(sys.modules) if m.startswith(("teaching.", "chat.", "evals."))]:
        del sys.modules[mod]
    from teaching.curriculum_premises import load_curriculum, compile_premises
    from chat.curriculum_surface import decide_curriculum_question
    load_curriculum.cache_clear()
    prem, _ = compile_premises(load_curriculum("physics"), "modal")
    s, o = cands[0]
    d_neg = decide_curriculum_question(f"Does {s} require {o}?")
    d_pos = decide_curriculum_question("Does conservation require symmetry?")
    print(f"\n+{n_neg:2d} negative rows -> modal premises={len(prem)}")
    print(f"    negative pair ({s} requires {o}): verdict={d_neg.verdict!r} reason={d_neg.reason!r}")
    print(f"    taught positive:                  verdict={d_pos.verdict!r} reason={d_pos.reason!r}")

CORPUS.write_text(ORIG, encoding="utf-8")
print("\ncorpus restored:", CORPUS.read_text(encoding="utf-8") == ORIG)

Result.

physics vocabulary = 16 lemmas
+ 1 negative rows -> modal premises=10   negative pair='entailed'   taught positive='entailed'
+ 7 negative rows -> modal premises=16   negative pair='entailed'   taught positive='entailed'
+ 8 negative rows -> modal premises=17   negative pair='declined'   taught positive='declined'
                                          reason='compiled_premises_unreadable'
+20 negative rows -> modal premises=29   both 'declined'
corpus restored: True

Bearing, (b) first because it is worse. At +1 row the question the negative was authored to refute answers entailed — surfaced to a user as "Yes — my physics curriculum teaches that acceleration requires charge, directly." The polarity field is read by nothing. evals/curriculum_serve/oracle.py ignores it too, so lane gold agrees with the wrong answer and wrong=0 stays green. This is ADR-0264 Fact 1 and it is the reason Phase A had to precede Phase F.

Bearing, (a). At 17 chains the band stops answering everything, including the taught positive that works today. ADR-0262 §5.1 prescribes ≈219 chains per band; ADR-0262 §6 scopes the cap out as a future contingency. The remedy trips the deferred fix at row 17. ADR-0264 §4.1.

Also confirms physics · modal holds 9 chains, not 8: physics-causal-008 declares operator_family: causal but its connective is requires, and CONNECTIVE_FAMILY is the sole family authority. That is where the plan's n=9 came from.

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Probe 3 — narrowed premise scope is verdict-identical

Question. ADR-0262 §6 proposes compiling "the query's k-hop neighborhood" and argues it is sound because "fewer premises can lose an entailment, never create one." Sound is not the property needed — a narrowing can be sound while silently losing true entailments, which is coverage loss in exactly the class the license counts. Is there a scope that is verdict-identical?

Compares two candidate scopes against full-family compilation over every routable question in all four served domains (philosophy_theology sampled to its first 40 lemmas to stay tractable).

from teaching.curriculum_premises import CONNECTIVE_FAMILY, load_curriculum
from chat.curriculum_surface import SERVED_DOMAINS
from generate.proof_chain.verb import read_verb_argument, VerbArgument
from generate.proof_chain.exist import read_exist_argument, ExistArgument
from generate.proof_chain.entail import evaluate_entailment_with_trace, Entailment

VERDICT = {Entailment.ENTAILED: "entailed", Entailment.REFUTED: "refuted",
           Entailment.UNKNOWN: "unknown", Entailment.REFUSED: "declined"}

def decide(premise_sentences, conclusion):
    if not premise_sentences:
        return "EMPTY_SCOPE"
    argument = ". ".join(premise_sentences) + f". Therefore {conclusion}."
    arg = read_verb_argument(argument)
    if not isinstance(arg, VerbArgument):
        arg = read_exist_argument(argument)
        if not isinstance(arg, ExistArgument):
            return "unreadable"
    return VERDICT[evaluate_entailment_with_trace(arg.premise_formulas, arg.query_formula).outcome]

fam_conn = {}
for c, f in CONNECTIVE_FAMILY.items():
    fam_conn.setdefault(f, []).append(c)

total = mismatch_ti = mismatch_qa = empty_qa = 0
for domain in SERVED_DOMAINS:
    cur = load_curriculum(domain)
    vocab = sorted(cur.vocabulary)
    if len(vocab) > 40:
        vocab = vocab[:40]
    for family, conns in fam_conn.items():
        chains = cur.family(family)
        if not chains:
            continue
        for connective in conns:
            for s in vocab:
                for o in vocab:
                    if s == o:
                        continue
                    concl = f"{s} {connective} {o}"
                    full = [c.sentence for c in chains]
                    ti = [c.sentence for c in chains if c.subject in (s, o) or c.obj in (s, o)]
                    qa = [c.sentence for c in chains
                          if c.subject == s and c.connective == connective and c.obj == o]
                    v_full, v_ti, v_qa = decide(full, concl), decide(ti, concl), decide(qa, concl)
                    total += 1
                    if v_ti != v_full and v_ti != "EMPTY_SCOPE":
                        mismatch_ti += 1
                    if v_qa == "EMPTY_SCOPE":
                        empty_qa += 1
                    elif v_qa != v_full:
                        mismatch_qa += 1

print(f"questions compared        : {total}")
print(f"term-incidence mismatches : {mismatch_ti}")
print(f"query-atom mismatches     : {mismatch_qa}")
print(f"query-atom EMPTY scopes    : {empty_qa}")

Result.

questions compared         : 8520
term-incidence mismatches  : 0
query-atom mismatches      : 0     (over non-empty scopes)
query-atom EMPTY scopes    : 8463
max premises, full-family  : 9
max premises, term-incidence: 8

Bearing. Verdict-identity holds for any scope that is a superset of the query-atom rows, because every compiled premise mints one independent propositional atom and no other atom appears in the query formula. That exact condition is ADR-0264 R5 — stronger than §6's soundness argument and the reason narrowing here is not the ADR-0261 §5.1 premise-dropping failure.

8,463 of 8,520 (99.3%) have an empty query-atom scope. Those must return UNKNOWN, not the current empty_curriculum refusal — ADR-0264 R6. The same 99.3% is the quantified UNKNOWN-padding exposure that Phase B's mix floor has to bound.

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Probe 4 — band ceilings against the licensing threshold

Question. A question routes only if exactly one served subject's vocabulary contains both terms. So honest volume is bounded by vocabulary, not corpus size. Which bands can reach n ≥ 657?

from collections import Counter, defaultdict
from teaching.curriculum_premises import CONNECTIVE_FAMILY, load_curriculum, compile_premises
from chat.curriculum_surface import SERVED_DOMAINS

fam_conn = defaultdict(list)
for c, f in CONNECTIVE_FAMILY.items():
    fam_conn[f].append(c)

vocab = {d: load_curriculum(d).vocabulary for d in SERVED_DOMAINS}
owner = Counter(t for d in SERVED_DOMAINS for t in vocab[d])

routable = {}
for d in SERVED_DOMAINS:
    excl = {t for t in vocab[d] if owner[t] == 1}
    routable[d] = sum(1 for s in excl for o in excl if s != o)
    print(f"{d:22s} |V|={len(vocab[d]):4d} exclusive={len(excl):4d} routable={routable[d]:6d}")

for d in SERVED_DOMAINS:
    cur = load_curriculum(d)
    for f in sorted(fam_conn):
        n_chains = len(compile_premises(cur, f)[0])
        if not n_chains:
            continue
        cap = routable[d] * len(fam_conn[f])
        print(f"curriculum_{d}_{f:12s} chains={n_chains:3d} max_honest_n={cap:6d} "
              f"{'reachable' if cap >= 657 else 'IMPOSSIBLE'}")

Result. 8 of 11 bands are structurally unable to reach 657 — including curriculum_physics_modal (480), the plan of record's chosen first content target. Full table in ADR-0264 §4.2.

physics              |V|=  16 exclusive=  16 routable=   240
mathematics_logic    |V|=  16 exclusive=  15 routable=   210
systems_software     |V|=  16 exclusive=  15 routable=   210
philosophy_theology  |V|= 151 exclusive= 149 routable= 22052

Bearing. physics · modal was chosen for having the most ratified chains. Chain count is not the constraint. Its 480 ceiling counts every possible question and still falls short, and no amount of authoring raises it — only growing en_physics_v1 would. philosophy_theology · modal has the same 8-chain start and a 44,104 ceiling. ADR-0264 §4.2 retargets Phase F accordingly.

Cross-check against ADR-0262 §5.1, which computed the question space as |V|² − |V| and got physics 240 (identical) and philosophy_theology 22,650 (vs 22,052 here). The difference is that this probe excludes lemmas taught by more than one served subject, which resolve_domain refuses as ambiguous_reading. 22,052 is the tighter and correct figure; §5.1's arithmetic was right and its bound slightly loose.

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What these four probes jointly establish

A taught edge yields exactly one entailed question, so entailed cases available = chains in the family. The cap holds that to ≤16. Against n ≥ 657 committed, a license therefore needs a ledger ≥ 97.6% non-entailed — which ADR-0262 §5.1 already rules unacceptable, and its ⅓-entailed target caps committed volume at 48.

So no curriculum band can earn a SERVE license as the architecture stands, and the blocker is engineering (premise scope), not content. That inverts the conclusion two arcs closed on. Probe 3 is the unblock: it shows the narrowing that removes the ceiling costs nothing in verdict fidelity.