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
Introduction: The “Scale Disconnect” and Why Modern Science Still Has No Unified Cross-Scale Framework
Contemporary science is extraordinarily powerful — but structurally fragmented across scales.
We have:
- quantum field theory to describe microscopic excitation structures
- systems biology to describe recursive self-organizing organisms
- astrophysics to describe gravitational coherence and cosmic structure
- information theory for communication and entropy
- nonlinear dynamics for recursion and attractors
- complexity science for emergent behavior
Yet none of these explain why structures at completely different scales often exhibit:
- similar coherence transitions,
- similar harmonic organization,
- similar recursion depths,
- similar boundary-integration behaviors,
- and similar stability plateaus.
We still lack a single, unified mechanism that explains why:
- quantum decoherence thresholds,
- biological self-reflective cognition thresholds,
- stellar boundary stabilization,
- and galactic-core anchoring
all appear to cluster around specific integration orders. In other words:
Modern science has no general explanation for the coherence patterns shared across quantum, biological, and cosmic systems.
This paper provides the first mathematically explicit attempt to bridge that divide.
The Core Leap: Triadic Informational Scaling Provides a Single Cross-Domain Structure
The breakthrough principle of this work is simple but profound:
All stable multi-scale structures follow a triadic recursion pattern defined by a dimensionless informational operator.
This operator is the 3–6–9 Triadic Informational Scaling Vector:
[T(n) = (3n, ; 6n^2, ; 9n^3)]
derived from:
- the triadic harmonic generator (H = (1,2,3)),
- the informational hierarchy (linear → surface → volume), and
- recursion-invariant dimensional analysis.
This creates a single mapping capable of expressing multi-scale coherence across:
- microscopic informational fields (ITI, IQD),
- biological reflectivity and awareness structures (ACCM, AWAKEN),
- boundary-dominated stellar and cosmic structures (USC, HCS, ANC).
The result is a unified informational geometry — one capable of tracing coherence across 15 discrete integration orders.
The 15-Order Informational Ladder: A Single Coherence Geometry Across Scales
Triadic scaling produces five stability nodes:
3, 6, 9, 12, 15
Each corresponds to a different informational integration role:
- 3 — Local structural stability
- 6 — Reflective self-modeling
- 9 — Boundary stabilization
- 12 — Systemic anchoring
- 15 — Full recursion convergence
Across your full body of work, these map naturally onto:
- quantum stability (IQD → 3)
- biological/reflective systems (ACCM → 6)
- heliospheric or stellar boundary systems (USC/HCS → 9)
- galactic integration (USC → 12)
- cosmic-scale informational convergence (ANC → 15)
This produces the first scale-independent coherence description.
What the Triadic Framework Actually Allows Us to Understand
This is not a new physical theory.
It is a structural, informational interpretation of how systems maintain coherence across scale transitions.
It supports four major interpretive capabilities:
1. A Unified Explanation of Multi-Scale Coherence
The framework provides:
- a common mathematical operator,
- a dimensional justification,
- harmonically consistent recursion,
- and falsifiable informational tests.
This replaces scale-fragmentation with a single structure.
2. A Structural Interpretation of Why Observer-Level Systems Arise at Order 6
Order 6 becomes the first recursion depth capable of:
- sustained self-reflection,
- stable model-building,
- coherent identity formation (ACCM),
- long-phase informational integration (ITI),
- boundary manipulation and learning.
It is the logical threshold for “observerhood” within an informational ontology.
3. A General Framework for Comparing Vastly Different Systems
Because the 15-order map is dimensionless and informational, we can compare:
- quantum systems,
- human cognitive reflectivity,
- stellar structure,
- galactic anchoring,
- cosmic convergence
on a single axis of:
[C_k = \frac{1}{3}(\Omega + \Gamma_c + RIV)]
derived from ACCM.
Cross-domain coherence becomes:
- quantitative,
- comparable,
- falsifiable.
4. A Coherence Geometry for Earth’s Informational Trajectory
Using the ACCM vector:
[W(t) = [I, S, A, C, R]]
the framework clarifies:
- how human systems increase informational reflectivity,
- where coherence thresholds lie,
- and how long-scale informational integration compares with universal patterns.
This avoids prediction; it provides structural literacy.
Why This Is Not “Just Another Scaling Framework”
This approach is distinct for three reasons.
1. It Provides a Single Generative Mechanism
Everything — coherence, recursion, stability — arises from:
- the same operator (T(n)),
- the same harmonic generator (H),
- the same dimensional justification,
- the same informational ontology.
One mechanism, many domains.
2. It Is Fully Falsifiable
The framework explicitly fails if:
- triadic harmonic peaks at 3f/6f/9f are absent,
- ACCM coherence distance rises rather than falls across recursion orders,
- the informational phase flow shows no triadic modulation.
Null results are scientifically valuable.
3. It Integrates Six Foundational Informational Theories into One Narrative
For the first time, this unifies:
- ITI (temporal information flow)
- IQD (tri-field informational dynamics)
- ACCM (reflective coherence metrics)
- USC (structural coherence at boundary scales)
- HCS (multi-domain coherence behavior)
- ANC (cosmic informational convergence)
into one coherent cross-scale interpretation.
The Bigger Picture
This framework does not claim a new physics.
It claims a new geometry of informational structure, one that:
- spans quantum to cosmic scales,
- maintains dimensional invariance,
- obeys simple triadic recursion,
- and yields explicit falsifiability conditions.
In doing so, it transforms our understanding of structure itself:
**The universe is not just a set of physical systems.
It is a hierarchy of informational structures connected by triadic coherence.**
And for the first time, we have a unified mathematical map that makes those connections visible.