TheoryTHY-2026-0106v0.1
Structured quality, hard gates and the specification–verification separation
Quality is Q(Y | X, S, W, B_Q): output relative to task, specification, environment and boundary. It is measured as a structured vector (correctness, alignment, completeness, consistency, robustness, verifiability, provenance) in three layers — formal objective, structured semi-objective, human residual — with fatal conditions as a hard gate that soft quality cannot compensate. Coverage splits into specification, test and state coverage; mutation score measures test strength; verification and specification are separate axes (a perfect proof of the wrong theorem solves nothing); evaluator agreement is not truth; cost is not quality unless the specification makes it one. Quality evidence grades run from E (surface validity) to A+ (formal verification plus goal alignment).
Definitions
definitions- Q_S = (Q_C, Q_A, Q_K, Q_R, Q_B, Q_V, Q_P), typed per domain; layers Q_L = (Q_F, Q_S, Q_H).
- Hard gate G_H(Y) = ∧ h_i(Y); coverage C_Q = (C_spec, C_test, C_state); mutation score MS = killed / non-equivalent mutants.
- Q_verified = Q_verification ⊗ Q_specification; math vector Q_math = (well-formedness, derivation validity, goal alignment, scope fidelity, axiom transparency, counterexample resistance).
- Quality object 𝔔 = (Q_S, G_H, C_Q, E_Q, Grade_Q, Conf_Q, U_Q, Boundary_Q); scalar Q* = Π_Q(𝔔 | task, projection rule).
Assumptions
assumptions- Evaluation oracles (tests, proof checkers, judge models, humans) are themselves fallible: ObservedQuality = F(TrueQuality, EvaluatorPower, Coverage).
Claims
claims- Quality ≠ IntrinsicScalar; SyntacticValidity ≠ SemanticCorrectness; CompileSuccess ≠ CorrectProgram; AllTestsPassed ≠ UniversalCorrectness.
- FormalVerification ≠ RealWorldGoalCorrectness; ProofValidity ≠ GoalEquivalence; ProofGrade ≠ GoalAlignmentGrade.
- FatalConstraintFailure ≁ SoftQualityTradeoff; PeakEpisode ≠ ReliableQuality; Length ≠ Completeness; Cost ≠ Quality.
- ObjectifiableFirst, HumanResidualLast.
Formalisation
formalization- Robustness sensitivity S_R = ΔQ / d(x, x′); requirement coverage C_R = |satisfied| / n with typed importance.
Predictions
predictions- Instruments that fold output-format compliance into 'quality' will misreport task competence as failure on tasks the model actually solves.
Falsification / failure conditions
falsification_conditions- If a single universal quality scalar predicts downstream task success across domains as well as the structured object does, the structure is redundant.
Known limitations
known_limitations- The first pilot showed the prediction in practice — two of three tasks had their 'quality' decided by JSON/Markdown obedience — but that is one instrument on one model, and the theory itself has not been tested beyond it.
Evidence
| Source | Relation | Target | Status | ID |
|---|---|---|---|---|
EXP-2026-0103 XA-06 first real-model pilot — Qwythos-9B-v2 on the A0→A5 ladder (36 trials, 2026-09-03) | tests | THY-2026-0106 Structured quality, hard gates and the specification–verification separation | ACTIVE | REL-2026-0481 |
RST-2026-0102 Diagnostic: the measured 'quality' was format compliance on 2 of 3 tasks; verifier serialization failed 3/18; the A3/A4 rise is a missingness artifact | supports | THY-2026-0106 Structured quality, hard gates and the specification–verification separation | ACTIVE | REL-2026-0489 |
Relations
| Source | Relation | Target | Status | ID |
|---|---|---|---|---|
RES-2026-0102 Quality line — measuring outcome quality without asking humans for a score | develops | THY-2026-0106 Structured quality, hard gates and the specification–verification separation | ACTIVE | REL-2026-0363 |
THY-2026-0107 Binary residual quality measurement (IBQF / BRQM) | extends | THY-2026-0106 Structured quality, hard gates and the specification–verification separation | ACTIVE | REL-2026-0372 |
PAP-2026-0106 Paper 06 — How should output quality be measured? From formal correctness to structured intelligence quality | formalizes | THY-2026-0106 Structured quality, hard gates and the specification–verification separation | ACTIVE | REL-2026-0412 |
EXP-2026-0103 XA-06 first real-model pilot — Qwythos-9B-v2 on the A0→A5 ladder (36 trials, 2026-09-03) | tests | THY-2026-0106 Structured quality, hard gates and the specification–verification separation | ACTIVE | REL-2026-0481 |
RST-2026-0102 Diagnostic: the measured 'quality' was format compliance on 2 of 3 tasks; verifier serialization failed 3/18; the A3/A4 rise is a missingness artifact | supports | THY-2026-0106 Structured quality, hard gates and the specification–verification separation | ACTIVE | REL-2026-0489 |
History and provenance
- Canonical URL
- https://evemisslab.com/ai/theory/THY-2026-0106/
- Machine-readable
/ai/theory/THY-2026-0106/index.json- Snapshot
AI-SNAPSHOT-v0.1-fe85b9694a45- Provenance
source- EveMissLab research collection: Intelligence Physical Metrology (真本體論13)
extracted_by- Splice (Claude Code), reading the canonical UTF-8 sources and each package's own reports
extracted_at- 2026-09-11
generator- tools/extract_all.py
claim_boundary- status, evidence level and result type follow the source artifact's own stated claim boundary; nothing is upgraded beyond what the report supports