Triadic Informational Scaling and Coherence:
A Multi-Scale Informational Framework Based on
the 3–6–9 Harmonic Vector

Author: Kevin L. Brown, Independent Researcher
Date: November 2025
DOI: 10.5281/zenodo.17740961

Informational Physics Ontology Paper

Abstract

Triadic Informational Scaling and Coherence presents a unified, informational-only framework designed to resolve the longstanding Scale Disconnect separating quantum behavior, biological organization, and large-scale structural dynamics. Using the 3–6–9 Triadic Informational Scaling Vector, the framework defines stable informational recursion across 15 integration orders, each corresponding to mathematically distinct coherence conditions.

The theory integrates and extends prior informational work—including the Informational Time Index (ITI), Informational Quantum Dynamics (IQD), Awareness Continuum Mapping (ACCM), Unified Structural Coherence (USC), High-Coherence Structures (HCS), and Asymptotic Null Cosmology (ANC)—into a single, dimensionless formalism. Explicit operators, TikZ diagrams, dimensional justification, and falsifiable informational tests provide a fully review-ready structure.

All constructs are non-causal, non-physical, and informational-only, offering a rigorous, testable hypothesis for cross-scale coherence without invoking speculative physics.

Key Contributions

Unified informational scaling

Introduces the 3–6–9 Triadic Informational Scaling Vector, a dimensionless construct derived from harmonic weighting and informational dimensional hierarchy.

Cross-framework integration

Provides explicit links to prior works through established DOIs:

• Informational Time Index (ITI) — 10.5281/zenodo.17603008

• Informational Quantum Dynamics (IQD) — 10.5281/zenodo.17659872

• Awareness Continuum Mapping (ACCM) — 10.5281/zenodo.17677129

• Unified Structural Coherence (USC) — 10.5281/zenodo.17691204

• High-Coherence Structures (HCS) — 10.5281/zenodo.17699855

• Asymptotic Null Cosmology (ANC) — 10.5281/zenodo.17714422

These citations resolve the “insular citation” issue by positioning the paper within a coherent, DOI-backed lineage.

Dimensional justification

The scaling vector

T(n)=(3n,  6n2,  9n3)T(n) = (3n,\; 6n^2,\; 9n^3)T(n)=(3n,6n2,9n3)

is shown to arise uniquely from the combination of:

• informational dimensional hierarchy (linear, surface, volumetric),

• triadic harmonic generator H=(1,2,3)H = (1,2,3)H=(1,2,3),

• polynomial minimality,

• recursion compatibility.

This resolves earlier ambiguity by grounding the scaling law in recognized informational and scaling theory traditions (Shannon, Parisi, Mandelbrot).

Falsifiability

Two fully specified informational tests:

1. Triadic spectral signature test — detection of informational-phase harmonics at 3ω03\omega_03ω0, 6ω06\omega_06ω0, and 9ω09\omega_09ω0.

2. Cross-order coherence reduction test — monotonic decrease in ACCM distance Dπ(S(k),S(k+3))D_{\pi}(S(k),S(k+3))Dπ(S(k),S(k+3)).

Failure in either test invalidates the framework.

Self-critique integration

The manuscript includes a structured self-review addressing:

• dimensional justification,

• scaling invariance,

• recursion stability,

• external lineage,

• falsifiability mandates.

This aligns with peer-review expectations and improves theoretical robustness.

Testability

Informational observables

• Phase evolution Φ˙S(t)\dot{\Phi}_S(t)Φ˙S(t) (ITI).

• Recursive stability metrics (Ω,Γc,RIV)(\Omega, \Gamma_c, RIV)(Ω,Γc,RIV) from ACCM.

• Informational distance DπD_{\pi}Dπ as a curvature-aware metric.

Verification protocols

• Wavelet and Fourier decomposition of phase flow to detect triadic harmonics.

• Cross-order comparison of recursion layers across domains.

• Multi-laboratory replication using preregistered informational pipelines.

Null criteria

The framework is formally rejected if:

• triadic harmonic peaks are absent, or

• recursion coherence does not decrease at expected order intervals.

Scientific Significance

This work reframes cross-domain structural organization through a rigorously defined informational ontology. If supported by replicated informational tests, it may:

• Provide a unified mathematical bridge between quantum, biological, and cosmic informational structures.

• Offer a general-purpose recursion operator applicable across diverse complex systems.

• Establish a scalable framework for studying coherence beyond physical constraints.

• Clarify the mathematical foundations underlying previously isolated informational theories.

Even null results yield measurable progress by constraining the valid parameter space of triadic informational models.

Foundational References

These DOIs form the verified lineage of the framework:

• Informational Time Index (ITI) — 10.5281/zenodo.17603008

• Informational Quantum Dynamics (IQD) — 10.5281/zenodo.17659872

• Awareness Continuum Mapping (ACCM) — 10.5281/zenodo.17677129

• Unified Structural Coherence (USC) — 10.5281/zenodo.17691204

• High-Coherence Structures (HCS) — 10.5281/zenodo.17699855