CVE — seven configurations

Document CVE self-application

ShapeDeclarations {
    purpose: Some(Purpose {
        role: "C/V/E truth-table specification + deciding rule + universal-removal predicate",
        k_min: CveThresholdK.FullWitness,
        v_min: CveThresholdV.NamedCertification,
        e_min: CveThresholdE.StructurallyReady,
    }),
    substrate: Some(CognitiveSubstrate.AnalyticDecompositional),
    anchoring: Some(FormalAnchoring.CurryHowardLawvere),
    e_sense:   Some(ExecutabilitySense.StructuralReadiness),
    self_reference: None,
}

Lifecycle: [T] Theorem of seven-cell closure — the 27-cell configuration space $\mathcal{M}^3$ where $\mathcal{M} = \{\checkmark, \blacklozenge, \times\}$ collapses under the migration map to exactly the seven productive configurations of §1 plus [✗] Retracted. Constructive witness: §9 below enumerates all 27 cells with explicit migration target. Verifier: cross-side pin pin_seven_configurations_closure_exhaustive re-runs the case analysis at build time. Executable: the witness function seven_configurations_closure_witness(c, v, e) in core/architecture/types.vr returns the canonical productive glyph for any input cell.

The three axes C / V / E each take three values (present / partial-or-conditional / absent), producing a 27-cell space. Of those 27 cells, only seven are productive in practice — the rest are either incoherent (a verifiable claim with no constructor is degenerate) or unstable (an executable claim that has no constructor is operationally a stub).

The seven productive cells are the seven canonical CVE configurations. This page lays out the truth-table semantics, shows why the non-productive cells are filtered, and gives a worked example for each productive cell.

1. The seven productive configurations

#	C	V	E	Glyph	Status
1	present	present	present	[T]	Theorem
2	present	trivial	present	[D]	Definition
3	conditional	conditional	conditional	[C]	Conditional
4	present	external	present	[P]	Postulate
5	partial	absent	absent	[H]	Hypothesis
6	absent	absent	absent	[I]	Interpretation
7	n/a	n/a	n/a	[✗]	Retracted

Each productive cell answers a distinct engineering question.

2. Cell 1 — C∧V∧E = [T] Theorem

Question: is this artefact load-bearing?

A [T] Theorem is the strongest possible status. All three axes are positive: a constructor exists, a check exists, and the artefact reduces to executable code. Theorem-class artefacts may be cited from any context and may be extracted to any target.

Worked example: core.collections.list_reverse proves that reversing a list preserves length and inverts order, and the function compiles to a runnable AOT binary that satisfies both properties.

3. Cell 2 — C∧trivial(V)∧E = [D] Definition

Question: is this a boundary or a theorem?

A [D] Definition establishes a boundary by fiat. There is no theorem to prove (the V axis is trivial — the artefact is its own check). The constructor is present (the definition itself). The E axis is present in the trivial sense (definitions reduce to themselves).

Worked example: type Probability is Float { 0.0 <= self && self <= 1.0 };. The refinement establishes the boundary; no theorem is being asserted at this layer.

The "trivial" cell on the V axis is what distinguishes definitions from theorems. A definition's verifier is "the definition matches its declared shape" — a tautology. A theorem's verifier is a non-trivial decision procedure.

4. Cell 3 — cond(C)∧cond(V)∧cond(E) = [C] Conditional

Question: under what assumptions does the artefact hold?

A [C] Conditional is [T]-class relative to listed assumptions. Outside the assumptions, the artefact is undefined. Inside, it reads as a [T] Theorem.

Worked example: fn realpath(path: &Text) -> Result<Text, Error> is a Theorem-class artefact conditional on the host OS satisfying POSIX realpath(3) semantics. Outside POSIX, the artefact is undefined.

The audit chronicle records the conditions verbatim, so an auditor verifying the conditions externally can lift the cog's verdict from [C] to [T] for that audit's specific scope.

5. Cell 4 — C∧external(V)∧E = [P] Postulate

Question: is this internally proved or externally cited?

A [P] Postulate has the C and E axes positive (a constructor exists, the artefact runs) but the V axis is external — the verification is delegated to a trusted external base via citation.

Worked example: the trusted-base kernel rule K-Universe-Ascent is a [P] Postulate cited under @framework(verum_internal_meta, "K-Universe-Ascent"). The verification is external in the sense that the rule's soundness is admitted from the meta-theory rather than internally re-derived.

The external/internal V distinction is real. A claim verified internally by an SMT cert replay is [T]; a claim verified externally by citation is [P]. The two have different audit chronicle treatments.

6. Cell 5 — partial(C)∧absent(V)∧absent(E) = [H] Hypothesis

Question: is this speculation, draft, or production?

A [H] Hypothesis has only partial C — the artefact is formulated but not realised. The V and E axes are absent. A Hypothesis MUST carry a maturation plan (@plan(...)) or the cog triggers AP-034 HypothesisWithoutMaturationPlan.

Worked example: a research cog my_app.experimental.zk_proof formulates a future zero-knowledge-proof feature but has no implementation, no tests, and no proof. The cog is [H] Hypothesis(High) with a @plan(target: "v0.5", ...).

7. Cell 6 — absent(C)∧absent(V)∧absent(E) = [I] Interpretation

Question: is this anything more than prose?

A [I] Interpretation has all three axes absent. It is descriptive prose only — written down, but not realised, checked, or extracted.

[I] Interpretations are transitional only. Mature corpora contain zero [I] entries; in strict: true mode, declaring a cog [I] triggers AP-035 InterpretationInMatureCorpus.

Why the status exists at all: during exploration, some artefacts are written down before any of C/V/E is realised. Naming the status [I] rather than "todo" or "draft" forces explicit transition rather than silent decay.

8. Cell 7 — n/a = [✗] Retracted

Question: what was tried and rejected?

A [✗] Retracted is not a CVE configuration; it is the negation of the configuration space. The artefact has been deliberately withdrawn — refuted, deprecated, scope-removed. The record is preserved as a negative example in the audit chronicle.

Citing a [✗] cog is AP-033 RetractedCitationUse.

Worked example: a cog implementing legacy DES encryption is retracted with reason "weak primitive — deprecated by NIST SP 800-131A" and replacement my_app.crypto.aes256_gcm.

9. Closure theorem — exhaustive case analysis

Theorem (CVE seven-cell closure). Let $\mathcal{M} = \{\checkmark, \blacklozenge, \times\}$ denote the per-axis modes (positive, partial, absent). The configuration space $\mathcal{M}^3$ has 27 cells. Every cell migrates uniquely to one of the seven productive configurations of §1, plus a special-case eighth glyph [✗] Retracted that lies outside $\mathcal{M}^3$ by being a meta-state (deliberate withdrawal).

The proof is by exhaustive case analysis on $\mathcal{M}^3$. Case modes:

• $\checkmark$ — axis positive (constructor present, verifier present, executable);
• $\blacklozenge$ — axis partial (formulated witness, conditional verification, external delegation, or trivial-by-definition);
• $\times$ — axis absent.

The migration map is operational: each cell either coincides with a productive cell or migrates to one when the artefact is matured (per the deciding rule §10).

#	C	V	E	Migrates to	Reason
1	$\checkmark$	$\checkmark$	$\checkmark$	[T] Theorem	full closure — coincides with cell 1 of §1
2	$\checkmark$	$\checkmark$	$\blacklozenge$	[C] Conditional	partial E lifts to E-conditional under stated environment, the trio reads as $\blacklozenge \blacklozenge \blacklozenge$
3	$\checkmark$	$\checkmark$	$\times$	[C] Conditional with E="not extractable"	pencil-and-paper proof; condition records the missing extractor
4	$\checkmark$	$\blacklozenge$	$\checkmark$	[D] Definition (V trivial) or [P] Postulate (V external) or [C] Conditional (V conditional)	partial V triages by the kind of partiality — see the V-partial sub-classification below
5	$\checkmark$	$\blacklozenge$	$\blacklozenge$	[C] Conditional	both V and E partial; the conjunction reads as conditional closure
6	$\checkmark$	$\blacklozenge$	$\times$	[C] Conditional with E-condition	dropped to conditional; the conditions record the V-partial and E-absent state
7	$\checkmark$	$\times$	$\checkmark$	[C] with V="TODO: prove" (transitional only) or downgrade to [H] Hypothesis with @plan(...)	code that runs but has no spec; transitional cell, must mature into [T] or be downgraded
8	$\checkmark$	$\times$	$\blacklozenge$	[H] Hypothesis	constructor present, no V, partial E — speculative implementation with no spec
9	$\checkmark$	$\times$	$\times$	[H] Hypothesis	constructor without V or E — bare formulation that compiles
10	$\blacklozenge$	$\checkmark$	$\checkmark$	[C] Conditional	partial C reads as conditional construction (typed schema or bounded reference impl)
11	$\blacklozenge$	$\checkmark$	$\blacklozenge$	[C] Conditional	all three axes partial — canonical conditional
12	$\blacklozenge$	$\checkmark$	$\times$	[C] Conditional	partial C, present V, absent E — proof with no execution
13	$\blacklozenge$	$\blacklozenge$	$\checkmark$	[C] Conditional	partial C and V, present E — running prototype
14	$\blacklozenge$	$\blacklozenge$	$\blacklozenge$	[C] Conditional	all-partial = canonical conditional state
15	$\blacklozenge$	$\blacklozenge$	$\times$	[H] Hypothesis	partial C+V, no E — the artefact is a bet with maturation plan
16	$\blacklozenge$	$\times$	$\checkmark$	[H] Hypothesis	partial C, no V, present E — running prototype without spec, bet with plan
17	$\blacklozenge$	$\times$	$\blacklozenge$	[H] Hypothesis	partial C, no V, partial E — canonical hypothesis state
18	$\blacklozenge$	$\times$	$\times$	[H] Hypothesis	partial C alone — canonical hypothesis state, coincides with cell 5 of §1
19	$\times$	$\checkmark$	$\checkmark$	[I] Interpretation (transitional only) — must mature: add C-witness or downgrade	V and E without C is operationally a runtime assertion (@verify(runtime)) that does not produce a witness; the assertion is a degenerate cell on the path to [T] or removal
20	$\times$	$\checkmark$	$\blacklozenge$	[I] (transitional only)	same as cell 19, with weaker E — must mature or be removed
21	$\times$	$\checkmark$	$\times$	[I] (transitional only)	V alone is empty operationally; transitional
22	$\times$	$\blacklozenge$	$\checkmark$	[I] (transitional only)	E without C is a black-box artefact; must mature into [H] (with C-plan) or be removed
23	$\times$	$\blacklozenge$	$\blacklozenge$	[I] (transitional only)	partial V and E without C — descriptive only
24	$\times$	$\blacklozenge$	$\times$	[I] (transitional only)	partial V alone — descriptive
25	$\times$	$\times$	$\checkmark$	[I] (transitional only)	running code without spec or witness — must mature into [H] with @plan(...)
26	$\times$	$\times$	$\blacklozenge$	[I] (transitional only)	partial E alone — descriptive
27	$\times$	$\times$	$\times$	[I] Interpretation	empty cell — coincides with cell 6 of §1
⊥	n/a	n/a	n/a	[✗] Retracted	meta-state outside $\mathcal{M}^3$: deliberate withdrawal; record preserved as negative example

V-partial sub-classification (used in cell 4):

V-partial mode	Migrates to
trivial (definition by fiat)	[D] Definition (cell 2 of §1)
external (delegated to a trusted citation)	[P] Postulate (cell 4 of §1)
conditional (under stated assumptions)	[C] Conditional (cell 3 of §1)

Closure (proof end). Every cell of $\mathcal{M}^3$ has been assigned a unique productive migration target (column "Migrates to"). Cells coinciding with productive ones are stable attractors (cells 1, 3, 5, 9, 14, 17, 18, 27 of the case analysis); the remaining 19 cells are transitional and the deciding rule (§10) drives them either to a productive cell (via Action A — replenishment) or to retracted state (via Action C — deletion). The seven configurations of §1 plus [✗] are the stable attractors of the entire configuration space. ∎

The Verum-side closure witness is the function seven_configurations_closure_witness(c, v, e) declared in core/architecture/types.vr (returns the canonical Lifecycle glyph for any input cell), cross-side mirrored at crates/verum_kernel/src/arch.rs::seven_configurations_closure_witness, pin-tested by pin_seven_configurations_closure_exhaustive in crates/verum_kernel/tests/k_arch_v_alignment.rs.

10. The deciding rule — three actions

When CVE-closure is violated relative to the artefact's declared purpose (see audit termination) the audit applies one of three deciding actions. If the declared purpose is satisfied and there is no defect relative to it, no action is applied — the artefact is preserved as-is and the audit closes (the fourth resolution: preservation without change).

Action A — Replenishment of the missing component

If the missing component can be built in reasonable time, it is built.

• Mathematics example. "There exists a fixed point of the operator $\mathcal{T}$" with contracting $\mathcal{T}$ satisfies axis V (Banach's theorem) but not axis C (no explicit witness). Replenish: state the iterative procedure $x_{n+1} = \mathcal{T}(x_n)$ and prove convergence; the limit point is the constructive witness, and axis E follows automatically. Configuration V → CVE⁺.
• Software engineering example. A specification asserts an API without a reference implementation: axis C is violated. Replenish: write a reference implementation, validate via the test battery. Configuration V → CVE⁺.
• Legal system example. A statute declares a right without a procedure of realisation: axis E is violated. Replenish: develop an application procedure, ratify via subordinate legislation. Configuration CV → CVE⁺.

Action B — Status downgrade

If replenishment is not possible in reasonable time, the artefact's status is downgraded to one that reflects the actual configuration. A hypothesis without proof or counterexample goes to status [H] (or its domain analogue: a backlog item, an open scientific question, a pending bill).

Action C — Deletion

If neither replenishment nor downgrade yields a sensible outcome, the artefact is deleted. The canonical case: a metaphysical assertion "X is Y" without specifying the category in which the identification occurs and without a formal functor between the concepts has no CVE configuration. Delete.

Universal removal of unclear-status assertions

Every CVE-L5 corpus claiming [T]-mature aggregate status eliminates assertions without a definite CVE-L0 configuration. The mechanism specialises by domain: in mathematical theory, CVE-L0 assertions of status [I] are removed before the canonical edition; in software engineering, "TODO: figure out" comments are cleared before release; in legal systems, norms lacking a definite application procedure are removed at codification; in standards, vague phrasings are removed at finalisation. The CVE-L5 maturity predicate is: every CVE-L0 artefact in the corpus has a precisely determined CVE configuration, fixed by an explicit status from the seven-symbol taxonomy.

Solving rule, in tabular form

Per the audit protocol's §14.2 deciding table:

Configuration of K₁/V₁/E₁ answers	Action
All three "yes"	CVE-closed, mature status, preserve
Two "yes" + one "no" or "partial"	Action A (replenish) or Action B (downgrade)
One "yes" + two "no" or "partial"	Action B (downgrade to hypothesis) or Action C (delete)
All three "no"	Action C (delete)

The deciding rule is uniform across domains; only the "yes" / "partial" / "no" criteria for each axis vary by domain.

11. The truth-table is closed

Adding a new productive configuration would require either a new combination of C/V/E modes or a new mode on one of the axes (beyond present / partial / conditional / external / absent). Verum's design constraint is that the seven configurations are closed: no new variant is admitted without a corresponding extension to the C/V/E modes.

This closure is the frame's C-positiveness at L6 — the CVE framework, asked of itself, answers "the seven canonical configurations are exactly the productive cells of the truth table". A new configuration would falsify the answer.

12. Cross-references

Relation markers per the convention introduced in three-axes §5:

• frame: CVE overview — the universal frame.
• frame: Three axes — the C / V / E dimensions whose truth-table this page enumerates.
• specialisation: Seven canonical symbols — glyph reference for the seven cells.
• refinement: Seven layers — layered application of CVE through the same configurations.
• refinement: Articulation hygiene — CVE-L6 register-prohibition discipline.
• operationalisation: Lifecycle primitive — the ATS-V primitive that carries the seven glyphs.