python examples/omnia_validation_demo.py

Expected behavior:

stable inputs → higher Ω

unstable inputs → faster Ω decay

disagreement → lower SCI

saturation → SEI → 0

irreversibility → IRI > 0



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Quick Experiment — Structural Divergence (TΔ)

Standalone demo:

python examples/divergence_time_demo_standalone.py

What it does:

generates two nearby trajectories

computes Δ(t)

measures structural degradation over time

detects divergence point


Output:

TΔ unstable

TΔ collapse


Note:

no dependencies

not OMNIA

implementation-sensitive


Purpose:

minimal reproducibility

demonstration of structural divergence



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Benchmark — Divergence Across Systems

python examples/divergence_benchmark.py

What it does:

compares multiple system types:

logistic (various regimes)

linear contraction / expansion

random sequences


computes:

T_unstable

T_collapse


produces a comparative table


Interpretation:

stable systems resist divergence

unstable systems diverge gradually

chaotic/random systems collapse quickly


This benchmark measures:

loss of equivalence between trajectories, not chaos itself


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Benchmark — Structural Resilience (R)

python examples/resilience_benchmark.py

What it does:

compares:

stable systems

chaotic systems

adaptive systems


measures:

T_unstable

T_collapse

T_recovery

R (resilience score)



Interpretation:

high R → system preserves or restores equivalence

low R → divergence becomes persistent

adaptive systems may delay or reduce collapse


This introduces:

resilience as the ability to maintain or recover structural equivalence under perturbation


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Minimal Executable Systems

Core examples:

examples/omnia_validation_demo.py

examples/omnia_minimal_engine.py

examples/omnia_sci_engine.py

examples/divergence_time_demo_standalone.py

examples/divergence_benchmark.py

examples/resilience_benchmark.py


Additional structural demos:

examples/structural_dynamics_mod9.py

examples/structural_dynamics_modn.py

examples/structural_dynamics_modn_global.py

examples/structural_dynamics_strings.py


These convert:

theory → execution → measurable structure


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Key Metrics

Ω — Structural Coherence
Persistence under transformation

SCI — Structural Compatibility
Agreement across lenses

SEI — Saturation Index
Remaining structural gain

IRI — Irreversibility Index
Non-recoverable loss

OMNIA-LIMIT
Formal stop condition

TΔ — Divergence Time
Time until structural equivalence breaks

R — Resilience Score
Capacity to preserve or recover equivalence


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Structural Lenses

Canonical lenses:

BASE (Omniabase)

TIME (Omniatempo)

CAUSA (Omniacausa)

TOKEN

LCR


Properties:

deterministic

composable

non-semantic


Agreement is measured, not assumed.


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OMNIA-LIMIT

Stop conditions:

SEI → 0

IRI > 0

Ω̂ stable


Interpretation:

no further structural extraction possible

continuation = non-informative



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Positioning

OMNIA is not:

a model

an evaluator

an interpreter


OMNIA is:

post-hoc

model-agnostic

semantics-free

transformation-based


It measures:

structural persistence

structural collapse

structural limits



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Repository Structure

omnia/ → measurement core

examples/ → executable demos

tests/ → verification

docs/ → formal definitions

experiments/ → exploratory modules



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License

MIT License


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Citation

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