Informational-Processual Monism
Scientific Core — Metrics, Estimators,
Simulation Regularities & Falsification Protocol
Author: Taotuner
Date: June 2026
Published on Zenodo
https://doi.org/10.5281/zenodo.20582318
|
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.
Note on λ: the
value 0.15 is illustrative. The qualitative behavior described by R1 is robust
for any λ ∈ (0,1]. Varying λ within this domain shifts the rate of coherence
loss but does not alter the monotonic relationship between perturbation
intensity and coherence degradation.
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.
Auxiliary Metrics (used in R3 and monitoring)
The following
metrics appear in the simulation results (R3) and in the IPM Ethical Framework
monitoring protocol. Definitions are provided here for completeness.
|
Metric |
Definition |
Notes |
|
DIG
(Dynamical Independence Gap) |
maxτ
|corr(x(t), y(t+τ))| / [auto_corr(x) + ε] |
Ratio of
maximal cross-correlation to autocorrelation of the reference signal.
Provisional operationalization. |
|
CCI (Coupling
Coherence Index) |
I(A;B) /
min(H(A), H(B)) |
Mutual
information normalized by minimum marginal entropy. CCI = 0: independence;
CCI = 1: full informational equivalence. |
|
LMS (Latent
Manifold Stability) |
corr(z(t),
z(t+1)) |
Correlation
of the first principal component across consecutive timesteps. Linear proxy;
collapses for nonlinear manifolds. |
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).
Falsification per Concept
|
Concept |
Specific
Falsification Condition |
|
Lack |
Increasing
perturbation never reduces coherence (global counterexample to R1) |
|
Coupling |
Failure of R3
under any observer projection |
|
Integration |
Zero
correlation between Φ* and persistence across multiple system types |
|
Persistence |
Recovery time
uncorrelated with pre-perturbation integration |
|
Dynamic
Signature |
I or P
occurring without prior L or C in a dissipative system |
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. |
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