pytest tests/ -v

Run the prime regime demo:

python examples/prime_gap_knn_demo.py

The demo prints:

current prime

true next gap

predicted gap (if admissible)

confidence

STOP / OK reason



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Stress Framework (Iriguchi Integration)

OMNIA includes a formal stress methodology.

Stress is not “more tests”.
Stress is controlled exposure of structural limits.

Failures are preserved as frozen boundary artifacts.

Official taxonomy:

docs/STRESS_TAXONOMY.md


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The OMNIA Measurement Chain

OMNIA
→ Ω
→ Ω under transformations
→ Ω̂ (Omega-set)
→ ΔΩ / ΔC
→ SEI (Saturation)
→ A → B → A′
→ IRI (Irreversibility)
→ Inference State (S1–S5)
→ OMNIA-LIMIT (STOP)
→ SCI (Structural Compatibility)
→ CG (Runtime STOP / CONTINUE)
→ OPI (Observer Perturbation Index)
→ PV (Perturbation Vector)
→ SI (Structural Indistinguishability)
→ OMNIA-GOV (Trajectory Certification)

Each step is measured, never inferred.


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1. Ω — Structural Coherence Score

Ω is the aggregated structural score produced by OMNIA lenses.

It reflects internal structural consistency, not correctness, usefulness, or semantic truth.

Ω is model-agnostic and semantics-free.


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2. Structural Lenses

OMNIA operates through independent, composable lenses:

BASE — Omniabase
Multi-base numeric structure analysis.

TIME — Omniatempo
Temporal drift and regime instability.

CAUSA — Omniacausa
Lagged relational and causal structure.

TOKEN
Structural instability in token sequences.

LCR — Logical Coherence Reduction
External coherence lens for audit and benchmarking.


All lenses are deterministic, composable, and non-semantic.


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3. APERSPECTIVE — Aperspective Invariance

Measures invariants that persist under transformations without a privileged observer.

Isolates structure that exists independently of human perception or encoding.


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4. Ω̂ — Omega-set (Residual Invariance)

Ω̂ is deduced by subtraction, not assumed.

It estimates the structural residue that survives representation change using robust statistics over transformed Ω values.


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5. SEI — Saturation / Exhaustion Index

Measures marginal structural yield:

SEI = ΔΩ / ΔC

SEI → 0 indicates structural saturation: further processing yields no new admissible structure.


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6. IRI — Irreversibility / Hysteresis Index

Measures irrecoverable structural loss in cycles:

A → B → A′

IRI detects collapse even when surface similarity appears intact.

IRI ≥ 0 by construction.


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7. Pre-Limit Inference States — INFERENCE

Inference is treated as a structural trajectory, not a decision.

States:

S1 — RIGID_INVARIANCE

S2 — ELASTIC_INVARIANCE

S3 — META_STABLE

S4 — COHERENT_DRIFT

S5 — PRE_LIMIT_FRAGMENTATION


Implementation:

omnia/inference/


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8. OMNIA-LIMIT — Epistemic Boundary

Declares a STOP condition when:

SEI → 0

IRI > 0

Ω̂ is stable


OMNIA-LIMIT does not retry, optimize, or escalate.

It marks the end of admissible structural extraction.


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9. Structural Time (τ)

τ is a non-human time coordinate.

It advances only when structure changes.

τ is not wall-clock time and not duration.


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10. Structural Compatibility — SCI

Measures whether measured structures can coexist without contradiction or loss.

SCI operates on OMNIA outputs, not on raw data.


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11. Compatibility Guard — CG

Converts SCI into a strict runtime STOP / CONTINUE signal.

CG introduces:

no policy

no semantics

no optimization


It enforces structural admissibility only.


---

12. Observer Perturbation Index — OPI

Measures the structural cost of introducing an observer or privileged basis:

OPI = Ω_ap − Ω_obs

OPI quantifies structural damage caused by enforced perspective, not intent or consciousness.


---

13. Perturbation Vector — PV

Formalizes how structure is destroyed, not why.

PV captures direction, composition, and intensity of structural loss.


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14. Structural Indistinguishability — SI

Principle:

> If all observable structural relations are invariant,
internal codifications are undecidable.



SI measures whether two systems may differ internally while remaining structurally indistinguishable under all admissible relations.

Implementation:

omnia/meta/structural_indistinguishability.py


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15. OMNIA-GOV — Trajectory Certification Layer (NEW)

Hallucinations are local failures.
The next failure class is global: irreversible trajectory collapse.

OMNIA-GOV is a deterministic governance layer that consumes OMNIA measurements and certifies whether an action or plan is structurally admissible.

OMNIA-GOV introduces no semantics and no learning.

It provides:

CVI — Constraint Violation Index

IRI_act — Irreversibility in action-space

HCI — Hypercoherence Collapse Index

SNRC-ACT — Boundary certificate for action-space


Output:

ALLOW

BOUNDARY_ONLY

REFUSE


Implementation:

omnia/gov/
  policy.py
  metrics.py
  invariants.py
  types.py

This extends OMNIA from representation measurement to trajectory certification, while preserving the non-decision constraint: measurement first, enforcement external.


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16. Experimental Module — Prime Regime Sensor

OMNIA can be applied to prime number sequences as a non-semantic structural regime sensor.

Deterministic state:

PrimeState = (Φ, S, T, τ)

Where:

Φ: modular residue vector (multi-base structure)

S: gap-distribution stability

T: structural drift

τ: structural time


This is not a prime oracle.

Implementation:

omnia/lenses/prime_regime.py
omnia/lenses/prime_gap_knn.py

Demo:

examples/prime_gap_knn_demo.py


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17. Repository Structure

omnia/
  inference/
  lenses/
  meta/
  runtime/
  gov/
  omega_set.py
  sei.py
  iri.py

examples/
tests/
docs/

All modules are:

deterministic

standalone

import-safe



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18. What OMNIA Is Not

OMNIA is not:

a model

an evaluator

a policy

a decision system

a truth oracle

a narrative framework


OMNIA is a measurement instrument.


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19. License

MIT License.


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20. Citation

Brighindi, M.
OMNIA — Unified Structural Measurement Engine (MB-X.01)
https://github.com/Tuttotorna/lon-mirror