Scientific Core

Informational-Processual Monism

Scientific Core — Metrics, Estimators & Falsification

 

 

Author: Taotuner

Date: June 2026

Published on Zenodo

 

Companion to: IPM Philosophical Core (2026) — Taotuner

For the ontological interpretation of these regularities, see the Philosophical Core.

Simulation families: Lack Kernel, Spectral Experiment, IPM Protocol, Collective Regimes Framework.

 


 

1. Empirical Regularities (R1–R3)
Simulation families (Lack Kernel, Spectral Experiment, IPM Protocol, Collective Regimes) consistently produced three reproducible patterns under the tested conditions (100 runs, ε=0.15, bins=30, max_lag=20).

 

R1 — Lack-Degradation

Higher perturbation → lower coherence. Coherence drops from 0.97 to 0.55 as noise increases from 0.02 to 1.2. In the IPM Protocol, Φ* drops approximately 16% under thermal perturbation before recovering.

 

1.1 Minimal Model of Lack Dynamics
A one-dimensional system with slow memory mₜ follows:

 

xₜ₊₁ = xₜ + λ(mₜ − xₜ) + η,     η ~ N(0, σ²)

 

Parameter

Definition

Value / Domain

xₜ

System state at time t

—

mₜ

Memory (slow reference trajectory)

—

λ

Coupling pull toward memory

0.15, illustrative value used in the minimal model (stable domain: 0 < λ ≤ 1)

η

Stochastic perturbation

Gaussian, zero mean, variance σ², i.i.d. per step

σ

Perturbation intensity

Varied across runs (0.02 – 1.2)

 

Coherence is defined as:

 

cₜ = exp(−|xₜ − mₜ|)

 

This model is not proposed as a universal law. It serves as a minimal dynamical illustration of the Lack–Coupling relationship underlying R1.

Result: as σ increases, mean coherence decreases monotonically — illustrating R1. The term (mₜ − xₜ) operationalizes Lack as deviation between current state and memory; λ governs Coupling intensity. Φ* and 𝒞 are scalar compressions derived from the statistics of this process.

 

R2 — Integration-Persistence

Higher integration → longer persistence under perturbation. Higher integration yields longer metastability under moderate perturbation.

 

R3 — Observed Clustering Under Specific Projections

Under the tested observer projections (CCI, DIG-proxy, LMS) and simulation conditions, three coupling regimes formed separable clusters. Whether this reflects a property of the systems or an artifact of the chosen projections is not determined. Generalization not established.

 

These are computational regularities, not universal invariants.

 

2. Estimators
One Possible Regime Marker: Φ*
As an example of a scalar compression, define:

 

Φ*(t) = [ε(t) + h(t)] / [1 + D(t)]

 

Term

Definition

ε(t)

k-NN prediction error in embedded space (Takens)

h(t)

Local transition entropy

D(t)

Penalty combining Lyapunov exponent + correlation dimension

 

This is one functional form among many that satisfy the same boundary conditions (monotonicity in ε and h, rigidity penalty, chaos penalty, interior peak). Other compressions are possible. No claim is made that this specific form preserves all relevant information or that ε, h, D share a common dimension.

 

Temporal Compressibility: 𝒞
A complementary estimator based on inter-event intervals:

 

𝒞 = E[ log( ψ(τᵢ | Hᵢ₋¹) / ψ(τᵢ) ) ]

 

τᵢ = inter-event interval. 𝒞 is scale-dependent (discretization, resolution). Under specific conditions it reduces to transfer entropy, mutual information rate, or excess entropy.

 

3. Falsification (Programmatic)
The framework is weakened by:

•       Systematic non-replication of R1–R3 in new simulation families or labs.

•       Loss of inverted-U pattern under parameter variation.

•       Φ* > 0 in thermodynamic equilibrium (no gradients).

 

4. Known Limitations
Limitation

Description

Mitigation / Direction

Empirical base

Four simulation families only

Independent validation on real-world data required

Φ* embedding dependence

Parameters (dimension, delay, k) affect stability

Sensitivity analysis required per application

𝒞 and long-range memory

Fails for non-stationary long-range memory

Use block entropy estimators, Lempel-Ziv complexity, or fractal dimension methods — domain-specific choice

Cross-domain generalization

Not established

Remains a working hypothesis

 

5. The 𝒞 Reduction
Under specific stationarity and process conditions, 𝒞 reduces to known information-theoretic quantities:

 

Condition

Reduces To

History = immediate past

Transfer entropy

Markovian order k

Mutual information rate (standard form)

Stationary, ergodic

Excess entropy

Otherwise

𝒞 is a scale-dependent estimator, not an invariant.

 

References
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Kondepudi, D., & Prigogine, I. (1998). Modern thermodynamics. Wiley.

Maturana, H. R., & Varela, F. J. (1980). Autopoiesis and cognition. D. Reidel.

Prigogine, I., & Stengers, I. (1984). Order out of chaos. Bantam.

Simondon, G. (2020). Individuation in light of notions of form and information. University of Minnesota Press.

Tononi, G. (2004). An information integration theory of consciousness. BMC Neuroscience, 5, 42.