ORI-C: Cumulative Coherence Under Constraint as a Transversal Operator of Living Systems

Living systems are not defined by equilibrium but by their capacity to stabilize internal coherence under constraint. Across scalesmolecular, biological, psychological, social, ecological, and hybrid human-machine systems-adaptive dynamics operate far from equilibrium while maintaining viability. Yet contemporary sciences lack a transversal operator capable of distinguishing local adaptation from stabilized cumulativitiy.

ORI-C (Observation - Regulation - Integration - Coherence) proposes a measurable architecture of cumulative stabilization dynamics. The framework formalizes six time-dependent variables - O(t), R(t), I(t), Σ(t), S(t), C(t) - and introduces C(t) as an order parameter detecting transitions toward cumulative regimes. Combined with the Principle of Living Coherence and the typology of Mutation Under Constraint (MSC), ORI-C constitutes a falsifiable, multi-scale framework applicable from molecular systems to socio-technical and artificial life systems.

1. Introduction - The Problem of Cumulativity

Biological and complexity sciences describe adaptation, resilience, emergence, and critical transitions. However, these phenomena are typically analyzed within fragmented disciplinary boundaries.

A system may continue adapting while progressively undermining its own coherence. Adaptation is not equivalent to viability.

What remains insufficiently formalized is an operator capable of distinguishing:

• local adaptation,

• stabilized cumulative dynamics,

• adaptive saturation,

• destructive rigidification.

We propose the following invariant:

A living system remains viable as long as its adaptation does not destroy its internal coherence.

ORI-C seeks to render this invariant measurable.

2. Principle of Coherence

Coherence is neither harmony nor static equilibrium. It is a local stabilization of relations under constraint within a given regime, with defined margins of viability.

A living system is characterized by:

• openness,

• far-from-equilibrium operation,

• regulatory capacity,

• internal integration,

• ability to transmit stabilizing traces.

Under increasing constraint, adaptive responses emerge. Some expand coherence; others rigidify the system or displace costs into the future.

Distinguishing these trajectories requires a transversal operator.

3. ORI-C Architecture

ORI-C formalizes six interdependent dynamic variables:

O(t) - Observation

Structured sensitivity to internal and external signals.

R(t) - Regulation

Compensatory mechanisms maintaining viability.

I(t) - Integration

Coordination among subsystems.

Σ(t) - Mismatch

Divergence between environmental constraints and integrated systemic capacity.

S(t) - Symbolic Stabilization

A transmissible trace stabilizing correlations across time.

C(t) - Cumulative Coherence

An order parameter detecting transition toward a stabilized cumulative regime.

The term “symbolic” does not refer exclusively to language. It denotes any transmissible structural trace: genes, epigenetic patterns, neural memory, norms, institutions, codebases, algorithmic architectures.

C(t) emerges when S(t) durably restructures adaptive dynamics.

4. Minimal Formalization

Consider an open system subjected to dynamic constraint E(t).

Define:

Cap(t) = f(O(t), R(t), I(t)) Σ(t) = max(0, E(t) − Cap(t))

A trace S(t) is stabilizing if:

1. It reduces Σ(t) over a time horizon Δt,

2. It remains transmissible,

3. It does not reduce future integrative capacity.

One may define:

C(t) = ∫₀ᵗ g(S(τ), −dΣ/dτ, I(τ)) dτ

where g is positive when stabilization reduces mismatch durably without rigidifying integration.

A regime transition is detected when:

• C(t) crosses an endogenous threshold,

• internal dynamics become dominated by S(t) rather than Σ(t).

C(t) does not measure quantitative growth but transmissible structural stabilization.

5. Typology of Adaptive Trajectories (MSC)

5.1 Viable Adaptation

• C(t) increases durably.

• Σ(t) decreases or stabilizes.

• Internal coherence expands.

5.2 Destructive Adaptation

• C(t) increases locally.

• Σ(t) diverges globally.

• Costs are displaced into the future.

5.3 Adaptive Saturation

• O-R-I remain active.

• C(t) stagnates.

• Σ(t) increases.

• The attractor rigidifies.

5.4 Latent Adaptation

• S(t) prepares a transmissible structure.

• C(t) remains low.

• A future regime becomes possible.

This typology provides dynamic classification without normative judgment.

6. Multi-Scale Applicability

ORI-C applies to any open, integrative, transmissible system.

6.1 Molecular Level

• S(t): genetic memory

• Σ(t): environmental stress

• C(t): evolutionary cumulability

6.2 Organisms

• S(t): intergenerational transmission

• Σ(t): environmental mismatch

• C(t): durable adaptive stabilization

6.3 Individual Cognition

• S(t): symbolic schemas

• Σ(t): internal incoherence

• C(t): cumulative restructuring of attractors

6.4 Ecosystems

• S(t): trophic structure

• Σ(t): ecological pressure

• C(t): regime shift or resilience stabilization

6.5 Human Societies

• S(t): institutions and norms

• Σ(t): socio-economic divergence

• C(t): institutional consolidation or collapse

6.6 Hybrid Human-Machine Systems

• S(t): code, datasets, protocols

• Σ(t): operational drift

• C(t): cumulative architectural stabilization

The substrate differs; the dynamical grammar remains.

7. Falsifiability

ORI-C is refutable if:

• C(t) increases without transmissible stabilization,

• Σ(t) diverges without affecting coherence,

• no structural reorganization accompanies threshold crossing,

• O-R-I fail to correlate with observed transitions.

The framework predicts that any durable regime transition corresponds to measurable cumulative stabilization.

8. Epistemological Implication

Truth is not static absoluteness. It corresponds to local coherence between a system, its constraints, and the information it can integrate within a given regime.

This perspective dynamizes rather than relativizes truth.

9. Discussion

ORI-C does not replace existing disciplines. It proposes a transversal operator linking:

• biological evolution,

• cognitive dynamics,

• ecological resilience,

• institutional trajectories,

• hybrid architectures.

It distinguishes adaptation from cumulativitiy. It detects saturation and rigidification. It offers a basis for computational modeling.

10. Conclusion

ORI-C proposes a unified architecture of cumulative coherence under constraint in living systems.

Adaptation is universal. Stabilized cumulative coherence is not.

C(t) makes the distinction measurable.

Site : https://dalozedidier-dot.github.io/CumulativeSymbolicThreshold/ori-c-presentation-en.html

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