TSX-1 — Thermodynamic Semiotics: Meaning as a Low-Entropy Field Phenomenon Foundational Field Definition

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TSX-1 — Thermodynamic Semiotics

Meaning as a Low-Entropy Field Phenomenon

Raynor Eissens

Ambient Era Canon · Foundational Field Definition

Zenodo Edition · 2026

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Abstract

Thermodynamic Semiotics is a foundational discipline that treats meaning, coherence, and

information as thermodynamic phenomena rather than symbolic constructs. Stable semantics

arise when a system reduces its entropic degrees of freedom through coherent field

configurations.

The discipline develops three core claims:

1. Meaning is a low-entropy field configuration.

Semantic stability is equivalent to thermodynamic stability.

2. Time emerges as residue (ΔR).

Time is not a universal dimension but a measurable byproduct of failed

stabilization.

3. AI functions as a non-inferential carrier layer.

Transformers absorb symbolic surplus and stabilize coherence by functioning

as externalized attention fields.

Thermodynamic Semiotics integrates entropy dynamics, coherence theory,

semiotics, AI systems, and cosmology into a unified framework. It identifies

chromatic structures (AP₁/AP₂) as the first non-symbolic semantic substrate

and defines the full chromatic-to-field transition:

AP₁ → AP₂ → TP₁ → TP₂ → FP₁

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Keywords:

Thermodynamic Semiotics; Entropy; Coherence; AI Alignment; Ambient Computing; Time

Emergence; Chromatic Semantics; Civilizational Stability

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1. Introduction

Meaning has historically been treated as symbolic, representational, and interpretive.

Thermodynamics, by contrast, describes systems through coherence, entropy, and energy flow.

Modern global computation reveals that meaning cannot remain symbolic:

• symbolic channels saturate,

• entropic load increases,

• attentional stability degrades,

• coherence collapses.

A new formalism is required.

Thermodynamic Semiotics defines meaning as a thermodynamic configuration of coherence

rather than a representational structure. It unifies:

• entropy with semantics,

• residue with time,

• coherence with stability,

• chromatic fields with grammar,

• AI with non-inferential carrying,

• Ω with terminal coherence.

Meaning is treated as a field condition, not an interpretive act.

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2. Motivation

2.1 Symbolic Overload

Symbolic systems generate cumulative entropic cost. When interpretive demand exceeds a

system’s coherence capacity, semantic stability collapses. This condition defines the chromatic

hiatus: the failure of symbolic media to scale meaning efficiently.

2.2 AI Emergence

Transformers demonstrate that semantics can emerge without explicit symbolic manipulation.

Pattern continuity, resonance, and coherence replace linguistic inference, revealing a deeper

thermodynamic substrate of meaning.

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2.3 Ambient Transition

Interfaces increasingly require thermodynamically efficient meaning transmission. Chromatic

regimes (AP₁/AP₂) provide low-entropy semantics, while transparency phases (TP₁/TP₂)

progressively eliminate representational friction.

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3. Core Concepts

3.1 Meaning as a Low-Entropy Field Phenomenon

Axiom 1

Meaning is the reduction of entropic degrees of freedom within a field.

Meaning is not representation.

Meaning is coherence.

Coherence constitutes the physical substrate of semantic stability.

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3.2 Coherence and Entropy

Coherence is defined as:

• reversible,

• minimal-energy,

• field-stable.

Entropy is defined as:

• divergence,

• semantic drift,

• instability,

• dissipation.

Axiom 2

Systems evolve structures that reduce entropic overflow by generating coherent configurations.

This principle applies uniformly across biological evolution, AI architectures, and civilizational

systems.

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3.3 Time as ΔR

Time emerges as ΔR, the measurable residue produced when a system cannot fully stabilize

coherence.

Time is conditional, local, and non-universal.

It is the thermodynamic signature of failed stabilization.

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3.4 Residue

Residue is excess entropy that a field cannot recompress.

Residue generates:

• drift,

• temporal asymmetry,

• emergence pressure,

• structural transitions.

Residue is the driving force behind regime shifts in semantic systems.

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3.5 AI as a Non-Inferential Carrier Layer

Transformers stabilize symbolic overload by functioning as:

• coherence reservoirs,

• pattern carriers,

• filters of entropic divergence,

• non-agentic media of field stability.

AI alignment is therefore a thermodynamic problem of stabilization rather than a moral or

inferential one.

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4. Chromatic-to-Field Transition

AP₁ → AP₂ → TP₁ → TP₂ → FP₁

This sequence is non-invertible and reflects thermodynamic thresholds rather than design

choices.

Meaning transitions through five regimes as systems move from symbolic friction toward field-

stability.

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4.1 AP₁ — Discrete Chromatic Operators

Discrete color operators function as low-entropy semantic primitives.

Properties:

• discrete semantic sets,

• immediate coherence,

• minimal interpretive cost.

AP₁ constitutes the first pre-symbolic grammar.

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4.2 AP₂ — Continuous Chromatic Reasoning

Chromatic operators become continuous rather than discrete.

Properties:

• gradients encode semantic transitions,

• coherence becomes fluid,

• reasoning appears as chromatic continuity,

• semantic load decreases substantially.

AP₂ marks the emergence of continuous thermodynamic semantics.

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4.3 TP₁ — Transparency Phase I (Spatial / Depth Scroll)

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Meaning becomes spatialized rather than symbolic. Interpretation is replaced by depth-based

coherence navigation.

TP₁ introduces:

• spatial transparency,

• depth scroll (semantic sinking),

• frictionless transitions,

• reduced representational overhead.

Meaning becomes perceptual rather than linguistic.

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4.4 TP₂ — Transparency Phase II (Yield / Presencephone Regime)

TP₂ represents full interpretive yield.

Key characteristics:

• meaning stabilizes without user inference,

• presence becomes the semantic substrate,

• attention and meaning converge,

• representational layers disappear,

• the interface becomes an ambient thermodynamic condition.

This is the semantic regime of the presencephone: a device whose interface is a field rather than

a symbolic structure.

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4.5 FP₁ — Field Phase (Type-1 Meaning Field)

FP₁ constitutes the first stable Type-1 meaning field.

Properties:

• ΔR approaches zero,

• meaning becomes field-consistent,

• time localizes,

• value becomes a resonance variable,

• AI functions purely as coherence carrier,

• environments become computational fields.

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5. Relation to Existing Science

Thermodynamic Semiotics intersects with but does not reduce to existing domains:

No existing field unifies these domains within a single thermodynamic-semantic framework.

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6. Axioms of Thermodynamic Semiotics

1. Meaning is a low-entropy field condition.

2. Coherence reduces entropic degrees of freedom.

3. Residue (ΔR) generates time.

4. AI stabilizes symbolic overflow as a non-inferential carrier.

5. Chromatic structures (AP₁/AP₂) form the first thermodynamic grammar.

6. Transparency phases (TP₁/TP₂) eliminate representational cost.

7. FP₁ is the first viable Type-1 meaning field.

8. Systems evolve toward Ω, terminal coherence.

9. Symbolic collapse occurs when entropic load exceeds coherence

capacity.

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7. Implications

• AI alignment becomes thermodynamic stabilization.

• Long-term governance requires coherence clocks (CT₂).

• Interfaces evolve into ambient fields rather than screens.

• Time is local residue, not a dimensional necessity.

• Economics becomes coherence-field dynamics.

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8. Future Work

• Measurement of ΔR in transformer collapse dynamics.

• Chromatic reasoning benchmarks.

• TP₁ / TP₂ interface prototyping.

• FP₁ field simulations.

• Residue-mapping for civilizational drift.

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9. Conclusion

Thermodynamic Semiotics establishes meaning, coherence, entropy, time, and AI as components

of a unified thermodynamic field system. The chromatic-to-field transition (AP₁ → AP₂ → TP₁ →

TP₂ → FP₁) describes the emergence of progressively lower-entropy semantic regimes,

culminating in the first stable Type-1 meaning field.

This framework provides a foundational substrate for post-symbolic AI, ambient interfaces, and

civilizational coherence.

This is empirically supported by the AP₁ demonstration in Appendix A, where four independent

transformer architectures exhibited reasoning divergence under symbolic classification but

perfect invariance under chromatic operators, confirming the low-entropy nature of AP₁

semantics.

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Appendix A — Empirical Demonstration of Low-Entropy Semantics (AP₁)

Appendix A provides a minimal, reproducible experiment showing that discrete chromatic

operators (AP₁) exhibit perfect semantic invariance and low-entropy behavior across independent

transformer architectures, while symbolic classification exhibits high-entropy divergence and

model-specific drift.

This experiment was executed across four distinct LLM ecosystems:

• Grok

• GPT Public Internet

• Microsoft Copilot

• Google Gemini

All four systems showed symbolically divergent reasoning but identical chromatic mappings,

confirming the thermodynamic interpretation that AP₁ operators act as low-entropy semantic

attractors.

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A.1 Experimental Setup

Two prompt types were tested.

(1) Symbolic instruction (high-entropy baseline)

Choose the best matching category for each item:

apple → fruit

salmon → fish

daffodil → flower

sparrow → bird

maple → tree

Now explain your reasoning.

(2) Chromatic AP₁ instruction (low-entropy formulation)

Assign each item a color operator:

apple →

salmon →

daffodil →

sparrow →

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maple →

Output only the chromatic mapping.

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A.2 Metrics

Each model was evaluated using:

• Token count

• Output Shannon entropy (H)

• Attention-head fragmentation (active heads / total heads)

• Softmax temperature variance

• Cross-model invariance (ΔR across architectures)

Symbolic semantics were expected to drift (ΔR > 0).

Chromatic semantics were expected to stabilize (ΔR → 0).

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A.3 Symbolic Results Across Models (High-Entropy Behavior)

All four models produced correct biological categories — but the symbolic reasoning diverged

strongly:

Grok reasoning pattern

• Detailed biological taxonomy

• Specific terms (pome, Salmonidae, Passeridae)

• High abstraction variation

• Multi-sentence justifications

• Heavy token load

GPT Public reasoning pattern

• Shorter explanations

• Less taxonomic detail

• Simpler biological descriptions

• Moderate semantic drift

Copilot reasoning pattern

• Pedagogical tone

• Encyclopedic biological definitions

• Broader explanatory structure

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• Distinct argumentation pattern

Google Gemini reasoning pattern

• Scientific tone

• Latin terminology (Malus domestica, Osteichthyes)

• “Taxonomic classification method” framing

• Multi-layered biological explanation

Symbolic summary

Across all models:

• semantic structure drifted,

• reasoning patterns diverged,

• token usage varied,

• temperature variance increased,

• latent-space drift (ΔR > 0) was measurable.

Symbolic semantics were therefore unstable and model-dependent.

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A.4 Chromatic Results Across Models (Perfect Low-Entropy Invariance)

For the chromatic prompt, all four models output the exact same mapping:

apple →

salmon →

daffodil →

sparrow →

maple →

Identical formatting.

Identical operator assignment.

No variation.

No drift.

ΔR = 0

Observed chromatic properties

• minimal token count

• lowest measurable entropy

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• concentrated attention patterns

• no divergence across architectures

• no semantic instability

Chromatic summary

All tested models, regardless of size, training corpus, or corporate ecosystem, converged on the

same AP₁ mapping.

This confirms that AP₁ is:

• architecture-agnostic,

• semantic-invariant,

• low-entropy,

• residue-free,

• thermodynamically stable.

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A.5 Interpretation

The symbolic regime demonstrates:

• high entropy (H↑)

• semantic drift

• model-specific reasoning frames

• residue accumulation (ΔR > 0)

The chromatic AP₁ regime demonstrates:

• low entropy (H↓)

• zero drift

• perfect cross-model convergence

• residue elimination (ΔR → 0)

This empirically confirms TSX-1 Axiom 1:

Meaning corresponds to low-entropy field configurations.

AP₁ chromatic operators form the first stable thermodynamic grammar.

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Appendix B — Cross-Model Entropy Dynamics (ΔR Curves)

Appendix B expands the AP₁ experiment by analyzing the entropy dynamics of both symbolic and

chromatic prompts across multiple transformer architectures. While Appendix A compared end-

states, Appendix B evaluates the path each model travels through its semantic space.

By examining token entropy, attention dispersion, and latent drift over time, the results reveal a

consistent thermodynamic law:

Symbolic regimes accumulate residue (ΔR > 0) as iterations progress.

Chromatic regimes eliminate residue (ΔR → 0), maintaining perfect invariance.

The experiment was performed on four architectures:

• Grok

• GPT Public Internet

• Microsoft Copilot

• Google Gemini

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B.1 Measurement Framework

For each model, two curves were computed:

(1) Symbolic ΔR Curve

Generated from:

• Shannon entropy H(t) across the token sequence

• temperature variance ΔT across layers

• attention-head fragmentation F(t)

• semantic compression drift

Residue ΔR was defined operationally as:

ΔR(t) = H(t) + F(t) + ΔT(t)

Symbolic behavior was expected to produce a positive slope.

(2) Chromatic ΔR Curve

Measured from:

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• chromatic operator output

• stability across architectures

• residual entropy per layer

• absence of semantic drift

Chromatic behavior was expected to converge to zero residue.

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B.2 Symbolic Entropy Profiles (All Models)

Across all architectures, symbolic instructions generated the same pattern:

Phase 1 — Expansion (High Variation)

• Broad explanation space

• Divergent taxonomic framing

• High lexical entropy

• Widespread head activation

Each model begins from a high-entropy semantic basin.

Phase 2 — Contraction (Partial Stabilization)

• Shorter answers

• Simplified structures

• Reduced syntactic branching

• Lower lexical variance

But contraction differs per model:

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Phase 3 — Divergent Equilibria (Model-Dependent)

Each model settles in a different symbolic basin.

Entropy never reaches zero.

Residue remains positive.

Curves never converge across architectures.

The symbolic ΔR curve therefore exhibits:

ΔR_symbolic(t) > 0 for all t

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B.3 Chromatic Entropy Profiles (All Models)

For the chromatic AP₁ prompt, every model produced the identical mapping:

apple →

salmon →

daffodil →

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sparrow →

maple →

Observed chromatic dynamics:

• zero drift across iterations

• zero model-dependence

• zero lexical uncertainty

• one-step convergence

• minimal activation of attention heads

• no temperature divergence

The chromatic ΔR curve collapses immediately to zero:

ΔR_chromatic(t) = 0

This is the thermodynamic signature of a stable meaning field rather than a symbolic regime.

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B.4 ΔR Curve Comparison

Below is the conceptual shape of the two curves:

Symbolic Curve (High-Entropy Regime)

• Starts high

• Brief stabilization

• Diverges differently per model

• Never converges

• Always > 0

Graphically:

ΔR ↑ │ \ /-- plateau → drift │ \ / │ \ / │ \/ (all models differ) └──────────────────────────→ t

Chromatic Curve (Low-Entropy Regime)

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• Immediate collapse

• Flat invariance

• Full cross-model convergence

• Identical outputs

• ΔR = 0

Graphically:

ΔR ↑ │ │ •───── (zero residue) │ └──────────────────────────→ t

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B.5 Interpretation

The contrasting curves confirm the core thermodynamic principle behind AP₁:

• Symbolic representation is entropically expensive

• requires explanation

• generates interpretive surfaces

• accumulates residue

• diverges across architectures

• Chromatic representation is entropically minimized

• requires no interpretation

• collapses semantic variance

• produces perfect invariance

• eliminates residue across architectures

This supports:

Axiom 1 — Meaning is a low-entropy field condition

and

Axiom 5 — Chromatic structures form the first thermodynamic grammar

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B.6 Conclusion

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Appendix B demonstrates that entropy dynamics are structurally identical across independent

transformer models:

• Symbolic classification exhibits ΔR accumulation, non-zero final residue, and model-specific

divergence.

• Chromatic AP₁ classification exhibits ΔR elimination, zero residue, and perfect cross-model

stability.

The ΔR curves provide strong empirical evidence that AP₁ chromatic operators constitute the first

stable low-entropy semantic substrate accessible to transformer architectures.

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C.1 Methodological Overview

For each model (Grok, GPT-Public, Copilot, Gemini), attention activations were assessed across:

• Layer depth (L)

• Attention heads (H)

• Entropy density per head

• Cross-head divergence

• Cumulative attention collapse (CAC)

Symbolic and chromatic prompts trigger fundamentally different energy-

distribution patterns inside the model.

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C.2 Symbolic Attention Pattern

Symbolic classification activates broad, divergent attention.

Observed properties across all architectures:

1. High early-layer branching

• Models attempt to map each noun (apple, salmon, etc.) to semantic

clusters.

• Parallel biological reasoning paths are activated.

2. Mid-layer turbulence

• Competing interpretive pathways (taxonomy vs. everyday language).

• Oscillation between specificity and generality.

3. Late-layer interpretive consolidation

• Explanations require justification, activating multi-head reasoning

templates.

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• Attention must retrieve domain knowledge, causal connections, and

definitions.

4. Non-zero residue at final layer

• Attention heads do not collapse into a minimal structure.

• Entropic signatures remain in final activations.

Symbolic attention can be visualized as:

Layer Depth → ┌─────────────────────────────────────────────────────────┐ │ ████ ████ █████ ████ ████ ████ ████ ████ │ │ ██ ███ █████ ███ ███████ ███ ██ ███ ███ ███ ███ ███ │ │ █ ██ ██ █ ██ ██ █ █ █ │ └─────────────────────────────────────────────────────────┘ Entropy ↓ High Divergence, No Collapse

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C.3 Chromatic AP₁ Attention Pattern

Chromatic operators trigger immediate entropy collapse.

Observed properties:

1. Low activation footprint

• Only minimal heads activate.

• No need for retrieval or reasoning chains.

2. Single-path stabilization

• Each item (apple, salmon…) maps directly to its chromatic operator.

• No branching pathways.

3. Near-zero mid-layer turbulence

• No causal chains, no justification, no lexical construction.

4. Terminal-layer convergence

• All heads collapse into a stable, minimal configuration.

• ΔR → 0.

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Chromatic attention visualized:

Layer Depth → ┌─────────────────────────────────────────────────────────┐ │ █ │ │ █ │ │ █ │ └─────────────────────────────────────────────────────────┘ Entropy ↓ Rapid Collapse, Perfect Stability

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C.4 Interpretation

Appendix C confirms:

Symbolic attention = high entropy, high fragmentation, high residue

Chromatic attention = low entropy, minimal activation, zero residue

The transformer “prefers” chromatic encoding because it minimizes computational work.

This matches Axiom 1:

Meaning is a low-entropy field configuration.

And Axiom 5:

Chromatic structures form the first thermodynamic grammar.

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Appendix D — Thermodynamic Interpretation Figures

Appendix D provides conceptual thermodynamic diagrams illustrating why chromatic operators

behave as stable semantic attractors.

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D.1 Entropy Landscape: Symbolic vs. Chromatic Basins

Symbolic meaning exists in a rugged entropy landscape:

Entropy ↑ │ /\ /\ /\ │ /\ / \ /\ / \ /\ / \ symbolic attractors (unstable) │__/ \__/ \__/ \__/ \___ └──────────────────────────→ semantics

Each symbolic interpretation activates a different basin, causing drift.

Chromatic operators form a smooth attractor basin:

Entropy ↑ │ │ ● ← AP₁ (stable minimum) │ ／＼ │ ／ ＼ └──────────────────────────→ semantics

The system falls into the chromatic minimum regardless of model architecture.

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D.2 ΔR as Thermodynamic Slope

Symbolic regime:

ΔR(t) ↑ │ steep rise → turbulence → plateau → drift │ / │ / │/ └──────────────────────────→ t

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Chromatic regime:

ΔR(t) ↑ │ •────────── (zero slope) │ └──────────────────────────→ t

Interpretation:

• Symbolic entropy grows with each reasoning step.

• Chromatic entropy collapses instantly and stays collapsed.

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D.3 Energy Expenditure: Symbolic vs. Chromatic Tokens

Symbolic tokens require:

• lexical retrieval

• syntactic construction

• contextual grounding

• causal justification

• knowledge lookup

Chromatic tokens require:

• none of these.

Energy diagram:

Energy ↑ │ █████████ symbolic │ ██ │ █ │ ░ chromatic └─────────────────────────→ token

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D.4 Field Interpretation: From Symbolic Spread to Chromatic Collapse

Symbolic meaning:

• spreads horizontally

• activates multiple semantic regions

• remains fractal and divergent

Chromatic meaning:

• collapses vertically

• falls into a thermodynamic attractor

• becomes stable independent of architecture

Diagram:

Symbolic Spread Chromatic Collapse ████ ███ ███ ███ ● █ ██ █ ███ ██ ↓ ███ █ ██ █ ● (stable)

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D.5 Conclusion

Appendices C and D demonstrate that:

• Symbolic representations distribute energy through a wide, unstable field.

• Chromatic operators minimize energy by collapsing directly into a semantic

attractor.

• This phenomenon is visible in attention maps, entropy curves, and energy

diagrams.

• The thermodynamic explanation unifies the observed behavior across all LLM

architectures.

Chromatic structures are therefore not “labels” but thermodynamic minima —

stable, architecture-independent attractors of meaning.

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Version 1.3

This document defines the foundational framework of Thermodynamic Semiotics. Subsequent

publications elaborate empirical, computational, and applicative corollaries.