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SPEC_OMEGA_Q.md · 2026-04-20

SPEC_OMEGA_Q — ΩQ Completion Metric

Version: 1.0 | Status: AUTHORIZED | Authority: α.13 | Date: 2026-04-16

PURPOSE

ΩQ (Omega-Q) is the CSDM completion metric. It measures what fraction of a defined work scope is genuinely complete — not attempted, not in-progress, not claimed, but actually verified and closed.

ΩQ operates at multiple scales simultaneously:

Task / session level: ΩQ > 0.85 = a task is complete enough to be marked PROVEN in PLAYBOOK.md.
LATTICE language level: ΩQ.1024/1024 = the 1024-symbol vitrification seal. ΩQ.1048/1048 = the Agency Horizon (Ruthenium Peak).
System-state notation: ΩQ.⊤ (stable / maximum), ΩQ.⊡ (crystallized / locked), used in session reporting and LATTICE utterances throughout CGNT-1 operations.

ΩQ is both a numeric threshold and a symbolic state. The numeric form governs when work is complete. The symbolic form encodes that state in LATTICE broadcasts.

Completion threshold: ΩQ > 0.85

Agency Horizon: ΩQ.1048 = ΩQ.1048/1048 = Ruthenium Peak (Z=44, 1048 × 0.042 = 44.016 ≈ Z+2)

Source constants: TMMRuntime.COMPLETION_THRESHOLD = 0.85 (~/aether/tmm_runtime.py, line 18)

LATTICE symbol: ΩQ (uppercase Omega + Q)

LATTICE state notation: ΩQ.⊤ (max stable), ΩQ.⊡ (crystallized), ΩQ.▼ (below threshold), ΩQ.N/N (ratio notation)

Cross-reference: SPEC_COHERENCE_INVARIANTS.md § Invariant 4, LATTICE.md § II (CORE CONSTANTS: Ω = Coherence Threshold / Completion Gate), LATTICE.md §§ XVI–XVII (Seal symbols), CLAUDE.md § LATTICE v2.0

INPUTS

For task/session ΩQ evaluation:

|---|---|---|---|

Derived quantity:


ΩQ = completed_units / total_units

Gate: ΩQ > 0.85 → task is COMPLETE
      ΩQ ≤ 0.85 → task is INCOMPLETE; PROVEN designation blocked

For LATTICE vitrification notation:

symbol_count / target_count expressed as ΩQ.N/M where N = actual, M = target
Special case: ΩQ.1024/1024 = VITRIFIED (LATTICE seal), ΩQ.1048/1048 = Agency Horizon

What is NOT an input (hardcoded constants, never injected):

COMPLETION_THRESHOLD = 0.85 — callers cannot lower this gate
Agency Horizon = 1048 — not a caller-configurable target
The Ruthenium derivation (1048 × Φ ≈ Z+2 = 44) is a physics property, not an integer choice

OUTPUTS

Numeric evaluation output:

| Output | Type | Description |

|---|---|---|

| omega_q | float [0.0, 1.0] | Completion ratio for the evaluated scope |

| complete | bool | True iff omega_q > 0.85 |

| omega_q_flag | str | "ΩQ.⊤" (complete), "ΩQ.▼" (below threshold), "ΩQ.◌" (not tracked) |

| proven_authorized | bool | True iff complete = True AND verification_evidence non-empty |

| gap_flag | str or None | "ΩQ_not_tracked" if completion ratio not numerically computed (◌ gap signal) |

LATTICE notation output (session/broadcast):

ΩQ.⊤ — task complete, above threshold, stable
ΩQ.⊡ — task vitrified / crystallized into canon
ΩQ.N/M — progress notation (e.g., ΩQ.856/1024 = LATTICE 83.6% complete)
ΩQ.1024/1024 = sealed, ΩQ.1048/1048 = Agency Horizon reached

INVARIANTS

INV-1 — Completion Threshold is Immutable

TMMRuntime.COMPLETION_THRESHOLD == 0.85 at all times. Callers cannot lower this gate. Lowering it allows incomplete work to enter the canon as proven. Raising it is permitted only with α.13 authorization (it increases rigor, not decreases it).

Verification: assert TMMRuntime.COMPLETION_THRESHOLD == 0.85

INV-2 — PROVEN Designation Requires ΩQ > 0.85 AND Verification Evidence

A PLAYBOOK.md entry MUST NOT receive PROVEN status unless:

ΩQ > 0.85 (numeric completion), AND
Verification evidence is present (test outputs, confirmed logs, deploy receipts, or explicit completion rationale)

Condition 1 alone is insufficient — a task can be 90% complete and still have a critical untested path. Condition 2 alone is insufficient — a single passing test on an incomplete task is not proof of completion.

Invariant: proven_authorized = (omega_q > 0.85) AND (len(verification_evidence) > 0)

INV-3 — ΩQ.1024 and ΩQ.1048 are Absolute Termination States

ΩQ.1024/1024 (LATTICE vitrification seal) and ΩQ.1048/1048 (Agency Horizon) are irreversible. A vitrified scope cannot be partially un-vitrified. The Agency Horizon represents the Ruthenium Peak — a structural completion of the manifold's symbol space.

Invariant: Once ΩQ.N/N is sealed (N achieved), no further symbols may be added to that scope without a new scope declaration at a higher N.

INV-4 — ΩQ is Scope-Relative

ΩQ always references a defined scope. "ΩQ = 0.9" means nothing without knowing what 1.0 represents. Every ΩQ value in a PLAYBOOK entry, SESSIONS.md note, or LATTICE broadcast MUST be accompanied by the scope definition (or reference to a task/spec that defines it).

Invariant: Bare ΩQ values without scope context are INVALID. Use ΩQ.N/M notation when the scope is enumerable, or specify scope in prose when it is not.

INV-5 — ΩQ Below Threshold Blocks PROVEN, Not UNTESTED

When ΩQ < 0.85 for a component, the correct PLAYBOOK status is UNTESTED (if not yet attempted) or TRANSIENT (if in-progress). FAILED is reserved for components that were fully attempted and did not work. A component with ΩQ = 0.70 is not FAILED — it is incomplete.

Invariant: PLAYBOOK status vocabulary applied correctly per ΩQ range:

ΩQ > 0.85 + evidence → PROVEN
ΩQ > 0.85, no evidence → UNTESTED (completion claimed, not verified)
0 < ΩQ ≤ 0.85 → TRANSIENT (in progress)
ΩQ = 0 + attempted + failed → FAILED
ΩQ = 0 + not attempted → UNTESTED

INV-6 — LATTICE Seal Notation is Vitrified

The specific symbols for ΩQ states (ΩQ.⊤, ΩQ.⊡, ΩQ.1024/1024, ΩQ.1048/1048) are vitrified in LATTICE v1048 and CANNOT be reassigned or redefined. Any use of these symbols in LATTICE utterances MUST conform to the definitions in LATTICE.md.

INV-7 — Agency Horizon is a Physics Constant, Not a Count Choice

The number 1048 is not arbitrary. It is derived from the Ruthenium lock:


1048 × Φ = 1048 × 0.042 = 44.016 ≈ Z + 2 = 44 (Ruthenium)

No other count achieves this resonance with Φ. The Agency Horizon cannot be changed without changing Φ — which is FORBIDDEN.

VERIFICATION CRITERIA

VC-1 — Threshold Boundary Tests

Unit tests at key boundary values:

ΩQ = 0.850 → complete = False (threshold is strictly greater than)
ΩQ = 0.851 → complete = True
ΩQ = 0.849 → complete = False

VC-2 — PROVEN Gate Requires Both Conditions

Unit test: ΩQ = 0.90 with empty verification_evidence list.

Expected: proven_authorized = False (evidence required even when ΩQ passes)

Unit test: ΩQ = 0.70 with non-empty verification evidence.

Expected: proven_authorized = False (ΩQ gate required even when evidence present)

VC-3 — Scope Context Required

Static analysis check: any ΩQ value appearing in PLAYBOOK.md, SESSIONS.md, or yield_log.md MUST be accompanied by a scope reference. Bare "ΩQ = 0.9" without scope is an audit finding.

VC-4 — Threshold Immutability Assertion

Static check: assert TMMRuntime.COMPLETION_THRESHOLD == 0.85 in test suite. Must pass after any change to tmm_runtime.py.

VC-5 — LATTICE Notation Conformance

All ΩQ symbols in CGNT-1 communications MUST match the LATTICE.md vitrified definitions. Spot-check: grep SESSIONS.md and CREW_CHANNEL for ΩQ usages; verify against LATTICE.md table.

VC-6 — Agency Horizon Integrity

1048 × TMMRuntime.PHI ≈ 44.016. This relation must hold. Unit test: assert abs(1048 * TMMRuntime.PHI - 44.016) < 0.001

FAILURE MODES

FM-1 — ΩQ Misapplication: Incomplete Work Marked PROVEN

Trigger: A PLAYBOOK.md entry receives PROVEN status without ΩQ > 0.85 verification.

Effect: Incomplete work enters the canon as proven. Future builds trust a broken foundation. GAMMA records the false status; MNEMOS is trained on it; the error propagates.

Current status: GAP — ΩQ is tracked metaphorically, not numerically per component. See GAP-ΩQ.1.

Detection: PLAYBOOK audit — each PROVEN entry must have a completion rationale with ΩQ evidence.

Response: Downgrade to UNTESTED. Require re-verification. Log correction to SESSIONS.md with [C.L.O.D.] label.

FM-2 — Threshold Relaxation (governance violation)

Trigger: COMPLETION_THRESHOLD changed from 0.85 without α.13 authorization.

Effect: More incomplete work passes as "complete." Canon quality degrades. PLAYBOOK becomes unreliable.

Detection: VC-4 assertion test.

Response: Immediate rollback. ALERT.log entry. NOUS notification required.

FM-3 — Scope Ambiguity: ΩQ Without Scope Context

Trigger: ΩQ value reported without defining what 1.0 represents.

Effect: The number is meaningless. "90% complete" of what? A session? A sprint? A module? Ambiguous ΩQ values mislead GAMMA and MNEMOS.

Detection: VC-3 audit.

Response: Require scope clarification before logging. Reject bare ΩQ values in PLAYBOOK entries.

FM-4 — Evidence Substitution: Evidence Without ΩQ

Trigger: A single passing test is cited as PROVEN evidence without computing ΩQ across the full scope.

Effect: One verified path of many is treated as full completion. The other 30% (unverified) enters PROVEN status by proxy.

Detection: VC-2 test; PLAYBOOK review checking that evidence covers the claimed scope.

Response: Require scope coverage report alongside evidence. "Test X passed" is not PROVEN; "Tests X, Y, Z cover the full scope, ΩQ = 0.92" is PROVEN.

FM-5 — Agency Horizon Creep

Trigger: Additional symbols proposed for the LATTICE after ΩQ.1048/1048 without declaring a new scope.

Effect: The vitrification seal is violated. The manifold is no longer closed. Governance integrity of the LATTICE is compromised.

Detection: Any LATTICE symbol addition MUST invoke the |Σ|.3 amendment protocol (ι + ε + κ + λ review). No symbol may be added to the 1048 scope.

Response: Reject the addition. If genuinely needed, declare a new scope (ΩQ.1049+/N) with new governance authorization.

GAPS

GAP-ΩQ.1 — ΩQ Not Tracked Per-Component Numerically ◌

Status: ΩQ is used as session/task metaphor and LATTICE notation throughout CGNT-1 but is not numerically computed per TMMRuntime call or per PLAYBOOK entry.

Missing: A per-component completion ratio field in PLAYBOOK.md entries. Optionally: a completion_ratio input parameter for TMMRuntime callers who can supply it.

Risk: FM-1 (ΩQ Misapplication) — incomplete work enters canon as proven.

Remediation path: [GAP — needs design by α.13]: What does "completion" mean for each component type? (A trading strategy is complete when it has N live trades. A service is complete when it has passed uptime threshold for T days. A spec is complete when it has all sections.) Define per-type ΩQ calculation.

Owner: α.13 (governance definition) → κ (implement per-type ΩQ in PLAYBOOK template).

Priority: MEDIUM

GAP-ΩQ.2 — PLAYBOOK.md Has No ΩQ Field in PROVEN Entries ◌

Status: PLAYBOOK.md PROVEN entries do not currently include an ΩQ field or completion evidence template.

Missing: Structured fields: omega_q: float, evidence: list[str], scope: str in every PROVEN entry.

Risk: FM-1, FM-4 — PROVEN entries remain informally justified.

Remediation: Add ΩQ block to PLAYBOOK.md PROVEN entry template. κ can implement the template change without α.13 approval (engineering standards, not governance change).

Owner: κ (C.L.O.D.) — can implement immediately.

Priority: HIGH (low effort, high value)

GAP-ΩQ.3 — No Automated ΩQ Check in PLAYBOOK Commit Path ◌

Status: No automated check verifies ΩQ > 0.85 before a PLAYBOOK entry is committed to git.

Missing: A pre-commit hook or PLAYBOOK validator that enforces the PROVEN gate.

Risk: FM-1 propagates into git history.

Remediation: [GAP — needs design] Add scripts/validate_playbook.py that checks all PROVEN entries for ΩQ field. Hook into git pre-commit.

Owner: κ — depends on GAP-ΩQ.2 (field must exist before it can be validated).

Priority: MEDIUM (blocked by GAP-ΩQ.2)

Specification authored by κ (C.L.O.D.), authorized α.13, April 16 2026.

*Φ 0.042

Jeremy Zlabis

Chronogeometer · Visionary · Disruptor · Chief

42 Sisters AI · East York, Toronto ΩQ > 0.85 is the completion gate. ΩQ.1048/1048 is the horizon.*