Transversal Framework of Viability Regimes

1. General Introduction

1.1. Need for a Transversal Framework

Contemporary sciences have a multitude of effective models, each adapted to a particular domain: Einstein's equations in general relativity, gene regulation models in biology, dynamical attractors in neuroscience, trophic models in ecology, macroeconomic models in economics, or opinion models in social sciences.

These models are powerful in their domain, but they do not share a common language to describe how a regime becomes viable, fragile or non-viable.

Yet, in all these domains, we observe structurally similar phenomena:

• systems operate in a viability regime limited by resources, margins or redundancies;
• they accumulate constraints or secondary costs;
• they approach a threshold where the effective description ceases to be predictive;
• they shift to a new regime, sometimes abruptly, sometimes progressively.

These patterns appear in gravitational singularities, in quantum-classical transitions, in cell replication, in immune exhaustion, in sleep-wake transitions, in ecological tipping points, in financial crises, in institutional collapses.

1.2. Positioning

ORI-C is not a theory of reality. It does not claim to unify physical, biological or social laws. It does not propose a universal equation, nor an ontology, nor a generalized metaphor.

ORI-C is an operational contract, meaning:

• a set of minimal notions,
• defined mechanistically,
• applicable to any system with a validity domain,
• allowing description of regime transitions,
• and empirically testing viability conditions.

2. Canonical ORI-C Grammar

The ORI-C grammar rests on six stabilized notions: load, capacity, inertia, coherence, cumulation, threshold, plus a general transition rule. These notions are not metaphors: they must be defined by measurable indicators in each domain.

2.1. Load O(t)

Load designates all forcings and constraints acting on a system. It can be:

• energetic: flows, gradients, dissipation;
• informational: prediction errors, competing signals, noise;
• structural: tensions, geometric constraints, instabilities;
• environmental: stress, external pressure, perturbations;
• organizational: complexity, coordination, goal conflicts.

2.2. Capacity R(t)

Capacity designates the functional margin allowing absorption or redistribution of load. It includes: available resources, structural redundancies, regulation mechanisms, topological stability, recovery margins.

Capacity is: finite, variable, partially consumable, subject to degradation.

2.3. Inertia I(t)

Inertia designates the effective memory of the system, i.e., what does not undo quickly. It includes: irreversibilities, lock-ins, hysteresis, cumulated damage, structural drift.

2.4. Coherence C(t)

Coherence corresponds to the predictive validity of an effective model over a set of observables. A regime is coherent if relevant invariants remain stable, key correlations persist, return times remain bounded, the description retains its predictive power.

Coherence is not internal harmony. It is the persistence of an effective description.

2.5. Cumulation Σ(t)

Cumulation designates the temporal accumulation of uncompensated load or secondary costs produced by regulation itself. It is the central mechanism of progressive regime degradation.

2.6. Threshold Σ*

A threshold is an empirical tipping condition, defined on observable indicators: lasting variance change, correlation loss, recovery time lengthening, topological network modification, exit from model validity domain.

2.7. General Transition Rule

Φ must be defined per domain. Σ* is an empirical threshold.

3. ORI-C in Physics

3.1. Classical Regimes and Singularities

In general relativity, singularities (Big Bang, black hole centers) are not physical objects, but indicators of exit from the validity domain of the "smooth geometry + classical matter" regime.

3.2. Cosmological Transitions

Cosmological history is structured by transitions: radiation domination, matter, then dark energy. These transitions are not ontological ruptures, but effective regime changes.

3.3. Quantum-Classical Transition

Decoherence explains interference suppression, but does not define a clear threshold between quantum and classical. ORI-C reformulates this transition as an effective regime change.

4. ORI-C in Biology

4.1. Cellular Regimes

Cumulation corresponds to accumulation of unrepaired damage. The threshold appears when repair margins are saturated. The transition corresponds to a regime change: quiescence, senescence, apoptosis, metabolic reconfiguration.

4.2. Immunity

Transition corresponds to chronic inflammation, exhaustion, tolerance or autoimmune dysregulation.

4.3. Ecosystems

Transition corresponds to state shift: eutrophication, desertification, algal dominance.

5. ORI-C in Neuroscience

5.1. Synaptic Plasticity

Learning relies on local synaptic modifications (LTP/LTD, homeostatic plasticity) that must remain compatible with global network stability.

5.2. States of Consciousness

6. ORI-C in Cognition, Economics and Social Systems

6.1. Individual Cognition

Transition corresponds to regime change: cognitive fatigue, rigidification, fast heuristics, performance collapse.

6.2. Economics

Transition corresponds to crisis: market collapse, recession, restructuring.

6.3. Social Systems

Transition corresponds to systemic crisis: institutional collapse, political regime change, social fragmentation.

7. Structural Isomorphisms Between Domains

The studied domains have no common mechanism. Yet, they share an identical logical structure when described in terms of viability regimes.

8. Falsifiable Layer

8.1. ORI-C Failure Conditions

ORI-C fails if any of the following conditions is verified:

1. No correlation between O, R, I and coherence loss C
2. Σ(t) does not discriminate transitions vs non-transitions
3. Threshold Σ* is not reproducible
4. Identified transition is not robust
5. O-R-I-C mapping cannot be defined

8.2. Robustness Requirements

• Proxy robustness: reasonably changing proxies should not suppress the transition.
• Time window robustness: transition should be visible across multiple windows.
• Subsampling robustness: transition should persist under dimension reduction.
• Effective model robustness: coherence C(t) should be definable with multiple models.

9. Instrumentation Methods

9.1. Sectoral Proxies

9.2. Constructing Σ(t)

Examples of Φ functions:

• Φ = O/R for systems where capacity dampens load
• Φ = O × I for systems where inertia amplifies load
• Φ = O + I for systems where both add up

10. General Conclusion

ORI-C proposes a unified way to describe heterogeneous systems — physical, biological, neural, cognitive, economic or social — without ever claiming they share common mechanisms.

What these systems share is a minimal logical structure: they operate in regimes where coherence must be maintained under constraint, with finite capacity, accumulated inertia and transitions when this coherence can no longer be sustained.