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Completes the all/no/some square. `some` is read for the first time: "All mammals are vertebrates. Some whales are mammals. Therefore some whales are vertebrates." is decided entailed; "All unicorns are horned. Therefore some unicorns are horned." is decided unsettled, with the no-existential-import reading disclosed in the surface. Mechanism (generate/proof_chain/exist.py): v5-VP's per-individual lowering over a domain widened by one Skolem witness per existential premise and — the load-bearing part — one ARBITRARY element per existential conclusion, at which every universal still instantiates and about which no premise asserts anything. Refuting an existential means deriving a universal, and the arbitrary element is what makes that derivation genuine instead of an assumption of domain closure: without it "Rex is a wolf. Rex is not tame. Therefore some wolves are tame." reads as REFUTED from a domain of one wolf. With it, UNKNOWN. Four `en_exist_*` bands earned SERVE at 720x wrong=0 on the first arena seal (25-band ledger); the 32-case hand-authored v2_exist split passed 32/32 first run; full lane 166/166 wrong=0 across six splits. Also fixes a wrong-answer path this work uncovered in Band v1b (ADR-0261 §5.1): `to_syllogism` FILTERED premises it could not express out of the projection and answered from the remainder, so "Aristotle is a philosopher. All philosophers are scholars. Therefore some scholars are philosophers." lost its only witness and was served "that doesn't follow". It now refuses — matching its propositional sibling `to_deductive_logic`, which always has — and the argument falls through to the bands that can hold a singular fact. The categorical band re-earned SERVE 720/720 after the change; both examples are pinned as regression cases. Promotion: `ds-mem-0020` declined -> unknown (ADR-0258's existential scope-out, now read; an anonymous witness never transfers to a named individual, so UNKNOWN is its honest verdict, not entailed). [Verification]: core test --suite deductive 232 passed; reader tests 33/33; register+surface tests 52 passed; arena 25 bands x 720 wrong=0 (all SERVE); lane 166/166 wrong=0; lane SHAs 9/10 match (public_demo drift is pre-existing on the base commit and unrelated — evidence in the Tier-S brief).
195 lines
11 KiB
Markdown
195 lines
11 KiB
Markdown
# ADR-0261 — Band v6-EX: existential arguments, decided
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- **Status:** Proposed
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- **Date:** 2026-07-24
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- **Arc:** deduction-serve (ADR-0256 → 0257 → 0258 → 0259 → 0260 → this)
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- **Governs:** `generate/proof_chain/exist.py`, the `en_exist_*` shape-bands,
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their arena templates, the `v2_exist` lane split, the `_exist_band_surface`
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serving tier, and the refuse-don't-drop contract of
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`generate.meaning_graph.projectors.to_syllogism`.
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## 1. Context
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The band cascade reads `all` and `no`; `some` refuses
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(`quantifier_out_of_band`) in every fallback tier — ADR-0258 §6 listed
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existentials as a deliberate scope-out, and the generalization arc
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(docs/plans/generalization-arc-2026-07-24.md Phase 1.2) schedules them as the
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move that completes the square of opposition.
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Band v1b already decides categorical some-syllogisms — but only inside the
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shared reader's morphology lexicon, and only for arguments that are purely
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categorical. Real subject matter is neither: it mixes singular facts, verb
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predicates, and vocabulary the lexicon has never seen. Everything outside that
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narrow window refused.
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Existentials are also the first construct in this arc whose lowering is not a
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straightforward instantiation. A universal instantiates at things the argument
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already names; an existential asserts a thing the argument does NOT name, and
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an existential conclusion asks about things that may not be named at all. Get
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that wrong in the obvious way — lower `some` over just the named individuals —
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and the reader will report REFUTED for arguments that are merely unproven,
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which is precisely the wrong-answer class this arc exists to prevent.
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## 2. Decision
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Add `generate.proof_chain.exist.read_exist_argument` as the LAST fallback tier
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(after v1 / v1b / v2-EN / v3-MEM / v4-CM / v5-VP), extending v5-VP's
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per-individual lowering — both atom families unchanged — with two new kinds of
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domain element:
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- **A witness per existential PREMISE** (a Skolem constant nothing else
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names): "some C1 are C2" ⇒ `mem(w,C1) & mem(w,C2)`; the O-form negates the
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second conjunct; the verb forms mint a verb atom instead.
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- **One arbitrary element per existential CONCLUSION**: a domain element about
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which no premise asserts anything and at which every universal is still
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instantiated.
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An existential conclusion lowers to the disjunction of its conjunction over
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the WHOLE domain — named individuals, witnesses, and the arbitrary element.
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New sentence shapes, all `some`-led:
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`some <C> are|is [not] [a|an] <C2>` (I-form and O-form) and
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`some <C> [do not] <verb> [<object>]`. Every other shape delegates verbatim to
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v3-MEM's and v5-VP's parsers, refusals included.
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Bands (priority order): `en_exist_negative` (any negative universal) >
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`en_exist_chain` (≥2 universals) > `en_exist_universal` (exactly 1) >
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`en_exist_witness` (no universals). Rendered by `render_entailment_exist` —
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the verb surface with the no-existential-import reading disclosed in the
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UNKNOWN template. Rides `deduction_serving_enabled` (default off); no new flag.
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**Second decision, forced by the first (§5.1):** `to_syllogism` now REFUSES
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when the comprehension carries a relation it cannot express, instead of
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filtering that relation out and projecting the remainder.
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## 3. Why this is sound
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1. **ENTAILED.** Let *M* be any first-order model of the premises. Each
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witness is interpretable in *M* (its existential premise asserts a
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satisfier); universal instantiation is truth-preserving at every element;
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the arbitrary element may be interpreted as ANY element, domains being
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non-empty. So every lowered premise holds in *M*. If the lowered premises
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propositionally entail the query disjunction, some element of *M*
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satisfies the conjunction — which is ∃. Skolem constants occur nowhere in
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the original argument, so this is entailment-preserving Skolemization, not
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merely satisfiability-preserving.
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2. **REFUTED — the arbitrary element is load-bearing.** Refuting ∃x φ(x)
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means deriving ∀x ¬φ(x). The lowered conjunction dual is entailed only if
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it is entailed at the arbitrary element, and that element is arbitrary (no
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premise mentions it), so what holds of it holds of every element — the
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universal is genuinely derived, never assumed by domain closure. Without
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it, "Rex is a wolf. Rex is not tame. Therefore some wolves are tame."
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would come back REFUTED — asserting that no wolf anywhere is tame — from a
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domain of one. With it, the honest UNKNOWN. This is the single most
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important line of this ADR and it is pinned by a named test.
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3. **Completeness within the fragment** lifts exactly as v3-MEM/v5-VP: a
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propositional countermodel becomes a first-order countermodel whose domain
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is the named individuals, the witnesses, and the arbitrary element.
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4. **No existential import.** Universals are read as vacuously true over an
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empty class, so the subaltern moods (Darapti, Felapton, Bamalip) are
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UNKNOWN, and the two contradictory pairs of the square are decided: an
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A-form REFUTES the corresponding O-form, an E-form REFUTES the I-form.
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This matches the modern first-order reading, matches what the categorical
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band (v1b) already does, and is the conservative choice — it declines to
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claim a member exists that no premise asserted. It is disclosed to the user
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in the UNKNOWN surface rather than left as a silent convention.
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5. **The plural `do not` is read here and refused in v5-VP** — deliberately,
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not inconsistently. "All C do not V" is genuinely scope-ambiguous (¬∀ vs
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∀¬) and refuses; "some C do not V" is unambiguously ∃x(C(x) ∧ ¬V(x)).
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6. **Cascade honesty** — every arena template and lane case was verified to
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fall through all six earlier bands, so this tier is pure widening: every
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previously-served argument is served byte-identically. The one previously
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DECLINED case it now decides (`ds-mem-0020`) is promoted to its correct
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verdict, not a favorable one.
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## 4. License and render
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The four `en_exist_*` bands earned SERVE through the ADR-0199 arena
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(720/band committed, wrong=0, θ_SERVE=0.99; ledger resealed at 25 bands).
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The by-construction gold is cross-checked template-by-template against the
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independent truth-table oracle over each template's INTENDED lowering — every
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universal's per-element implications and every query disjunct spelled out — so
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a lowering that drops or invents a domain element shows up as a disagreement
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rather than passing silently (INV-25). Unearned or ledger-stripped deployments
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serve the same sound answer hedged (`_UNVERIFIED_SHAPE_DISCLOSURE`).
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## 5. Findings and scope-outs
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### 5.1 A wrong-answer path found in Band v1b (fixed here)
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Authoring this band's lane surfaced a defect in `to_syllogism` that predates
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it. The projector built its premise list by FILTERING the meaning graph's
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relations down to the categorical ones — silently discarding anything else,
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then answering from what survived. Two consequences, both wrong served
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answers rather than declines:
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- "Aristotle is a philosopher. All philosophers are scholars. Therefore some
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scholars are philosophers." — the singular `member` premise was dropped, the
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argument lost its only witness, and serving replied *"That doesn't follow."*
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It does follow.
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- "Every mineral is a solid. Some quartzes are minerals. Therefore some
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quartzes are solids." — the shared reader misreads "every mineral" as an
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individual named `every_mineral` (a separate reader gap, §5.2), the
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resulting `member` relation was dropped, and a valid Darii was served as
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*"That doesn't follow."*
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The arena never caught it because the CATEGORICAL band's templates are all
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purely categorical two-premise syllogisms in the synthetic lexicon — a family
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in which nothing is ever dropped. A band can hold an earned license and still
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have an unmeasured wrong-answer path if its practice corpus does not span its
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reachable inputs; that lesson is the durable part of this finding.
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The fix makes `to_syllogism` behave exactly like its propositional sibling
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`to_deductive_logic`, which has always refused on a relation it cannot express:
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**refuse, don't drop.** Refused texts fall through to the reader bands that CAN
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hold a singular fact — v6-EX decides both examples correctly. The categorical
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band re-earned SERVE at 720/720 after the change (no coverage lost), and both
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examples are now pinned as regression cases (`ds-ex-0008`, `ds-ex-0011`, plus
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a projector unit test and an e2e test).
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### 5.2 Scope-outs (typed refusals today)
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1. **"Every C is a D" misread by the shared reader** — `comprehend` reads the
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quantifier phrase as an individual (`every_mineral`). Post-§5.1 this is
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harmless (v1b refuses; v6-EX reads the sentence correctly through v3-MEM's
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universal parser), so it is recorded, not patched: fixing the shared
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reader's template set is its own unit of work with its own lane.
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2. **Partitives** — "some of the sailors" refuses `partitive_out_of_band`
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rather than reading "of the sailors" as an opaque class run.
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3. **Multi-token subjects in verb existentials, PPs, ditransitives** —
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`sentence_shape_out_of_band`, inherited from v5-VP's closed grammar.
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4. **Tense** — `some C were P` / `some C did not V` refuse
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`tense_out_of_band`.
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5. **Connective × existential composition** — "If some C are P then …"
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refuses `mixed_structure_out_of_band`; fusing v4-CM's connective grammar
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over existential leaves is a later composition.
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6. **Numeric and proportional quantifiers** (`most`, `few`, `several`, `at
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least two`) — `quantifier_out_of_band`. `some` is the only existential
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spelling read; "there is a C that …" is not read either.
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7. **Universal conclusions** — unchanged from v3-MEM: proving ∀ from these
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premises needs the eigenvariable machinery this band uses only for the
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refutation direction, and exposing it as a conclusion form is a separate,
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testable unit.
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8. **Identity / co-reference, existential-import premises** — unchanged
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scope-outs; a user who wants the traditional square can state the
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existential premise explicitly and this band will use it.
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## 6. Verification
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- `tests/test_exist_argument_reader.py` — 33 tests: gap-is-real cross-check,
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flagship Darii lowering (exact formulas and atoms), the arbitrary-element
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soundness test, no-existential-import, both contradictory pairs, witness
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non-transfer, one-witness-per-premise, verb existentials with plural
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`do not`, number linking inside existentials, 4 band classifications, 13
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typed refusals incl. delegated v3-MEM/v5-VP reasons, honesty caps,
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determinism.
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- `tests/test_meaning_graph_projectors.py` (+1) — the §5.1 refuse-don't-drop
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contract.
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- Surface/e2e/lane: `tests/test_deduction_surface.py` (+5),
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`tests/test_deduction_serve_e2e.py` (+2, one of them the §5.1 regression),
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`tests/test_deduction_serve_lane.py` (+1 over the 32-case `v2_exist` split;
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`v2_member` docstring updated for the `ds-mem-0020` promotion) — full lane
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166/166, wrong=0, all six splits.
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- Arena: 4 × 720 committed, wrong=0, first seal run; all 25 bands still SERVE;
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corpus soundness asserted against the independent oracle before sealing
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(18,000 cases).
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