# VK-IRA v1.0
## Validity-Kernel Iterative Repair Architecture
## 有效核迭代修復架構 — Research Specification

**Status:** Strong Domain-General Architecture Candidate  
**Release meaning:** architecture/specification stabilization  
**Not claimed:** universality, complete correctness, certified global precision/recall

**作者：** Neo.K  
**機構：** EveMissLab／一言諾科技有限公司  
**日期：** 2026-10-07（整理日期；原稿未標註日期）  
**版本：** v1.0  

---

# 0. Core Thesis

An artifact should not be treated as a binary object that is either wholly correct or wholly invalid.

Instead:

$$
\boxed{
\text{Locate what remains valid, identify what fails, model propagation, and apply the least destructive justified intervention.}
}
$$

---

# 1. Universal Object

$$
O
=
\langle
\text{Content},
\text{Representation},
\text{Domain},
\text{Dependencies},
\text{Provenance},
\text{Version},
\text{History}
\rangle.
$$

---

# 2. Validity Domain

$$
\mathfrak D(O)
=
\langle
\text{Type},
\text{Scope},
\text{Time},
\text{Input},
\text{Scale},
\text{Assumptions},
\text{Runtime},
\text{Evidence},
\text{Authority},
\text{Representation}
\rangle.
$$

Domain profiles may add specialized coordinates.

---

# 3. Validity Kernel

$$
K(O\mid\mathfrak D)
\subseteq O.
$$

Candidate kernels may be non-unique:

$$
\mathcal K(O\mid\mathfrak D)
=
\{K_1,\ldots,K_m\}.
$$

Residual:

$$
R(O\mid\mathfrak D)
=
O\setminus K(O\mid\mathfrak D).
$$

---

# 4. Typed Causal Dependency Graph

$$
G_{\mathrm{VK}}
=
(V,E,\tau_V,\tau_E).
$$

Example edge types:

```text
proves
calls
depends-on
derived-from
reported-as
transmitted-by
amends
supersedes
contaminates
amplifies
controls
retains
interpreted-as
represents
converts
```

---

# 5. Representation Adapters

$$
L_i
\overset{A_i}{\longrightarrow}
L_{i+1}.
$$

Each adapter carries:

$$
\Pi_i
=
\langle
\text{Semantics},
\text{Units},
\text{Dimensions},
\text{Scale},
\text{Sign},
\text{Domain},
\text{Identity},
\text{Ordering},
\text{Uncertainty},
\text{Provenance}
\rangle.
$$

---

# 6. First-Failure Localization

$$
j^\star
=
\min
\{
j:
Closure(A_j)=\text{fail}
\}.
$$

Then:

$$
Origin(R)=A_{j^\star}.
$$

Downstream states caused by the same origin are:

```yaml
inherited_manifestation
```

rather than automatically new independent residuals.

---

# 7. Blast Radius

Static:

$$
BR(R,G).
$$

Dynamic:

$$
DBR(R,G,t)
=
\langle
\text{Cone},
\text{Gain},
\text{ThresholdTime},
\text{Recoverability},
\text{Criticality}
\rangle.
$$

$$
\boxed{
\text{LocalError}
\neq
\text{LocalConsequence}
}
$$

---

# 8. Decision Set

$$
\boxed{
\text{Decision}
\in
\{
\text{repair},
\text{restrict},
\text{redefine},
\text{reroute},
\text{replace},
\text{split},
\text{merge},
\text{reclassify},
\text{reattribute},
\text{rollback},
\text{fork},
\text{retire},
\text{defer},
\text{abstain},
\text{reopen}
\}.
}
$$

`abstain` means checked evidence does not justify intervention.

`defer` means a known/suspected residual exists but cannot yet be responsibly resolved.

---

# 9. Minimum-Disturbance Repair

$$
P^\star
=
\arg\min_P
Disturbance(K,P)
$$

subject to:

$$
Resolve(P,R^\star)=1.
$$

$$
\boxed{
\text{Maximum Local Precision}
+
\text{Minimum Global Disturbance}
}
$$

---

# 10. Closure

Generic closure requires:

1. target residual addressed or explicitly deferred;
2. validity kernel rechecked;
3. dependency boundary checked;
4. representation boundaries checked;
5. no new unsupported claim introduced;
6. certificate updated.

Domain profiles add specialized closure.

---

# 11. Oracle Governance

A benchmark oracle must pass:

```yaml
temporal_validity:
artifact_layer_relevance:
semantic_change:
interpretable_correction_target:
blind_phase_independence:
```

$$
\boxed{
CommitMessage="fix"
\neq
\text{QualifiedOracle}
}
$$

$$
\boxed{
\text{ChangedFile}
\neq
\text{ChangedExecutableSemantics}
}
$$

---

# 12. Blindness Levels

```text
B0 fully blind
B1 structure-qualified blind
B2 target-known semi-blind
B3 mechanism-partially-known
B4 open oracle
```

Metrics from different blindness levels must not be silently pooled.

---

# 13. Validation Coverage

$$
\Gamma_{\mathrm{val}}
=
\langle
\text{Source},
\text{Data},
\text{Model},
\text{Specification},
\text{Inference},
\text{Runtime},
\text{Reporting},
\text{ExternalValidity},
\text{Representation}
\rangle.
$$

Each coordinate may be:

```yaml
checked_pass
checked_fail
blocked
not_checked
unknown
not_applicable
```

$$
\boxed{
\text{NotChecked}
\neq
\text{CheckedPass}
}
$$

---

# 14. Provenance

VK-IRA distinguishes:

- artifact provenance;
- source provenance;
- wording lineage;
- idea lineage;
- authority/version lineage;
- incident provenance;
- root-cause provenance;
- signal provenance.

---

# 15. Core Invariants Learned by v1.0

$$
\boxed{ErrorExists\neq CoreDestroyed}
$$

$$
\boxed{HistoricalMention\neq ActiveResidual}
$$

$$
\boxed{Interpretation\neq OntologicalIdentity}
$$

$$
\boxed{BrokenProof\neq FalseTheorem}
$$

$$
\boxed{ParsedRepresentationError\neq SourceError}
$$

$$
\boxed{PublicDomain\neq AuthorityToRewriteVersionHistory}
$$

$$
\boxed{BugDetection\neq PatchEquivalence}
$$

$$
\boxed{UnableToReplay\neq FailedReplication}
$$

$$
\boxed{NoKnownCorrection\neq NoError}
$$

$$
\boxed{Superseded\neq HistoricallyFalse}
$$

$$
\boxed{DimensionallyCorrect\neq PhysicallyValid}
$$

$$
\boxed{LoadCompleted\neq DataLoadedCompletely}
$$

$$
\boxed{HighScore\neq Generalization}
$$

$$
\boxed{ComponentSize\neq Criticality}
$$

$$
\boxed{DetectedSignal\neq BiologicalOrigin}
$$

$$
\boxed{LexicalSimilarity\neq SemanticEquivalence}
$$

$$
\boxed{ResidualOrigin\neq ResidualManifestation}
$$

---

# 16. Benchmark Integrity

All attempted benchmark cases remain visible:

- successful detections;
- negative controls;
- abstentions;
- misses;
- blocked cases;
- partial oracles;
- invalid oracles.

---

# 17. v1.0 Pipeline

$$
\boxed{
O_t
\rightarrow
\text{Parse}
\rightarrow
\mathfrak D
\rightarrow
\text{Adapters}
\rightarrow
K
\rightarrow
R
\rightarrow
G_{\mathrm{typed}}
\rightarrow
BR/DBR
\rightarrow
\text{Decision}
\rightarrow
Patch/Abstain
\rightarrow
\text{Sandbox}
\rightarrow
\text{Closure}
\rightarrow
\text{OracleGovernance}
\rightarrow
\text{Certificate}
\rightarrow
O_{t+1}
}
$$

---

# 18. v1.0 Claim Boundary

## Supported

$$
\boxed{
Strong\ Domain\text{-}General\ Error\text{-}Governance\ Architecture\ Candidate
}
$$

## Not supported

The first campaign does not establish:

- universal applicability;
- completeness;
- optimality;
- guaranteed correctness;
- known global precision/recall;
- superiority to all domain-specific validation systems.

---

# 19. Open Requirements for v1.x / v2.0

1. Clean external empirical full-replay positive oracle.
2. Preregistered benchmark corpus.
3. Independent third-party/model reproduction.
4. Adversarial false-positive benchmark.
5. Multi-residual interactions.
6. Conflicting validators/oracles.
7. Real-time streaming artifacts.
8. Large dependency graphs.
9. Automated certificate generation.
10. Formal treatment of kernel non-uniqueness and repair optimality.

---

# 20. Final v1.0 Status

```yaml
release: VK-IRA-v1.0
type: research_specification
domain_general_status: strong_candidate
universal_status: not_claimed
benchmark_campaign: Run01-33
negative_controls_present: true
misses_preserved: true
invalid_oracles_preserved: true
cross_representation_test: complete
external_empirical_full_replay_positive: open
independent_reproduction: open
statistical_performance_certification: open
```