Holographic Harmonic Model — Components

Observable signatures and scores derived from Ψ(x,t), grounded in HHM operators

🧩 Core Components of Ψ(x,t)

Components are the measurable expressions of structure inside the Ψ(x,t) field. While operators tell us how to interact with the field, components tell us what we find when we do. Each component defines a specific observable, transformation, or signature that reveals something about the modal state of the system.

In HHM v2.2 we currently curate ~36 components, labeled C001…C041 (with some reserved/deprecated). These include field projections, identity scores, entropy measures, symbol traces, rhythm gradients, and more.

The list is not closed—you can define your own component if it has a clear definition, a computational basis, and a measurable effect in the field.

Grab the files:
Download HHM Bundle Download Component Spec

Component Index (selected)

IDs and names should match the downloadable JSON. Some components are reserved for future revisions; others may be deprecated as we refine definitions.

C001 — ModalField

The ModalField is the foundational projection of the Ψ(x,t) state into a measurable waveform or modal vector. It represents the raw “shape” of the field—before interpretation, classification, or comparison.

What it is

C001 takes the full, high-dimensional Ψ(x,t) field and projects it into a lower-dimensional structure: a waveform, frequency distribution, or symbolic pattern. This is the field’s first collapse—the moment it takes on analyzable form.

How it’s calculated

Linked operators

Why it matters

Without C001 there is no observable structure. ModalField gives the first “window” into the invisible—the emergence of pattern from potential.

Related domains

Used in

C003 — UnifiedEntropy

UnifiedEntropy measures overall complexity and information density within a collapsed modal field, across time, frequency, or symbol space.

What it is

C003 generalizes entropy for time-series, symbolic, quantum, and biological data. It returns a unified value (often ~0 to 2.5) reflecting how “structured” a field state is.

Lower values (e.g., < 0.8) indicate coherence; higher values (> 1.8) indicate rich dispersion or interference.

How it’s calculated

Computed from the normalized distribution of ModalField (C001) or CollapsePattern (OP001):

Entropy(Ψ) = - ∑ pᵢ · log₂(pᵢ)

Linked operators

Why it matters

Entropy in HHM is meaning range: how much variation a collapse is holding. It supports identity tests and cross-system comparisons.

Used in validation

Linked Theorems/Axioms

C005 — ID (Modal Identity Vector)

A multi-dimensional vector encoding the persistent structural signature of a Ψ(x,t) state.

What it is

How it’s used

Linked operators

Validated in

Used in

C006 — FieldSimilarityScore

Quantifies structural similarity between two Ψ(x,t) states (0.0–1.0), enabling cross-domain matching.

What it detects

How it’s computed

The score is a weighted average of deep structural overlap, not surface resemblance.

Linked operators

Validation examples

Why it matters

C006 is a bridge across systems: it asks whether two very different signals share the same modal “DNA.”

Used in

C009 — EchoScore

Measures how strongly a Ψ(x,t) field resonates with itself over time/space/systems (repetition strength).

How it’s calculated

Echo(Ψ) = max{ R(τ) } for τ ≠ 0
where R(τ) = ∫ Ψ(t) · Ψ(t+τ) dt

In symbolic/non-temporal systems, use recurrence plots / RQA.

Used in

Linked operators

Why it matters

Echo underlies rhythm, recognition, and memory—“this has happened before.”

Used in

C010 — IdentityMatchScore

A robust metric estimating whether two Ψ(x,t) states represent the same underlying identity.

How it’s computed

Scores ≥ 0.85 usually indicate “same identity” under the current thresholds (see your bundle).

Why it matters

Used in

Operators involved

C011 — RhythmGradient

Captures the rate/direction of structural change in Ψ(x,t) over time—transition intensity.

Definition

RhythmGradient = avg_t (1 – Rec(Ψₜ, Ψₜ₊₁))

Optionally weight by Echo or CollapseEnergy for non-linear shifts.

Applications

Used in

Linked operators

C030 — RhythmStabilityScore

Measures how stable rhythmic structure remains over time—consistency of recurrence, tempo, and alignment.

How it’s calculated

High ≈ 1.0 (metronomic), low < 0.5 (erratic).

Validation examples

Used in

Linked operators

C041 — TraceIdentityScore

Indicates whether a field state matches or belongs to a previously observed identity trace—long-range memory and inheritance.

How it’s calculated

If Rec ≥ 0.85, Entropy Δ ≤ 0.15, and trace match ≥ 0.80, the score is high (≥ 0.90).

Applications

Used in

Linked operators

📦 Extending the Component Library

The HHM component model is modular. Working with a new dataset—or a new symbolic/biological/physical domain—where you see recurring structure? You can define a new component.

A solid new component should have:

You don’t need to update the official file unless you want to publish. Keep your additions in your project and they’ll remain HHM-compatible. When you’re ready to share, include: the definition, the dataset, and a minimal reproduction script or prompt.

Safety & claims: HHM measures patterns; it does not diagnose disease, guarantee forecasts, or replace professional judgment. Treat outputs as research signals until independently validated.