spectral-narrative-analysis 0.2.1

Narrative graph stability analysis using eigenmode decomposition and spectral perturbation theory.

spectral-narrative-analysis

A Python package for analyzing narrative graph stability using eigenmode decomposition and spectral perturbation theory.

Narrative graphs are converted into operator matrices whose eigenmodes represent dominant narrative patterns. Evidence shocks are modeled as perturbations, and eigenmode shifts measure how structurally stable — or fragile — a narrative is.

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Why this exists

Existing tools can tell you what events happened or how confident you are in them. This package asks a different question:

If new evidence appears, does the entire narrative structure change — or just one edge?

spectral-narrative-analysis answers this by treating the narrative as an operator system:

• Dominant eigenmodes = stable narrative patterns
• Eigenvalue magnitude = how strongly that pattern dominates
• Spectral perturbation = what happens when evidence shocks the system
• Eigenvector shift = whether the core narrative axis changed

This is inspired by the Seoul Interpretation of Quantum Mechanics (SIQM), which treats state description (상태서술) not as a fixed entity but as a structured organization of events and evidence.

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Installation

pip install spectral-narrative-analysis

With optional scipy for optimal mode matching:

pip install spectral-narrative-analysis "scipy"

Requires Python 3.10 or later. Core dependency: numpy.

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Quick start

from sna import (
    NarrativeNode,
    NarrativeEdge,
    PerturbationEntry,
    SpectralConfig,
    NarrativeStabilityAnalyzer,
)

# 1. Define nodes (confidence can come from evidence-confidence-propagation)
nodes = [
    NarrativeNode(id="kain",    label="Kain Incident",  confidence=0.9),
    NarrativeNode(id="rift",    label="Rift Opening",   confidence=0.8),
    NarrativeNode(id="archive", label="Archive Fall",   confidence=0.7),
]

# 2. Define edges (p_forward can come from temporal-belief-graph)
edges = [
    NarrativeEdge(source_id="kain",  target_id="rift",    p_forward=0.9, confidence=0.8),
    NarrativeEdge(source_id="rift",  target_id="archive", p_forward=0.8, confidence=0.7),
]

# 3. Define a perturbation (new evidence shock)
perturbations = [
    PerturbationEntry(
        source_id="kain", target_id="rift",
        delta=0.5,
        note="New official source confirms Kain caused the Rift.",
    )
]

# 4. Analyze
analyzer = NarrativeStabilityAnalyzer()
result = analyzer.analyze(nodes, edges, perturbations)

print(result.stability_score)       # float in [0, 1]
print(result.stability_label)       # stable / moderate / fragile / unstable
print(result.regime_changed)        # True if dominant narrative node shifted
print(result.report())              # full Markdown report
print(result.summary())             # compact dict

A full working example is in examples/basic_usage.py.

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Core concepts

Narrative Operator

The narrative graph is converted into a matrix A where:

A[i, j] = node_factor(i, j) × p_forward × confidence × causal_strength

Default node factor: sqrt(source.confidence × target.confidence)

Three symmetry modes:

Mode	Construction	Use case
symmetric	(A + A.T) / 2	Real eigenvalues, clean analysis
directed	raw A	Preserves causal direction
undirected_laplacian	D - (A + A.T)/2	Structural clustering
directed_laplacian	D - A	Direction-sensitive stability

Eigenmodes

Eigenmodes of A represent dominant narrative patterns. The most dominant eigenmode (largest eigenvalue magnitude) tells you which nodes are central to the current narrative structure.

Spectral Perturbation

When new evidence appears, a perturbation matrix V is constructed:

A' = A + epsilon × V

Three perturbation modes:

Mode	Formula	Use case
raw	A + εV	Default; unconstrained experiments
bounded	clip(A + εV, min, max)	Confidence-bounded systems
relative	A × (1 + εV)	Proportional strengthening/weakening

Mode Matching

After perturbation, eigenmodes may reorder. SNA matches original and perturbed modes using:

cost = (1 - eigenvector_overlap) + 0.05 × relative_eigenvalue_gap

Method	Complexity	When used
hungarian	polynomial	scipy available (best)
permutation	O(k!)	small k, no scipy
greedy	O(k² log k)	fallback
auto	adaptive	default

Stability Score

stability = exp(-alpha × instability)

Score	Label
≥ 0.85	stable
≥ 0.60	moderate
≥ 0.35	fragile
< 0.35	unstable

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Package structure

sna/
├── schema.py       NarrativeNode, NarrativeEdge, PerturbationEntry, SpectralConfig
├── operator.py     NarrativeOperator, OperatorResult
├── spectral.py     EigenmodeAnalyzer, SpectralResult, EigenMode
├── perturbation.py SpectralPerturbationAnalyzer, PerturbationResult, ModeShift
└── stability.py    NarrativeStabilityAnalyzer, NarrativeStabilityResult

docs/
└── model.md        Full mathematical model documentation

examples/
└── basic_usage.py  End-to-end example

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Relationship to other packages

This package is the third layer in a narrative intelligence stack:

Layer	Package	Question
Ordering	temporal-belief-graph	Does A happen before B?
Trustworthiness	evidence-confidence-propagation	How much should I trust this item?
Structure	spectral-narrative-analysis	Is the narrative structurally stable?

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Development

pip install -e ".[dev]"
pytest
tox
python -m build

This package is currently in alpha. APIs may change before version 1.0.0.

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Contributing

Contributions, issues, and feature requests are welcome. Please open an issue before submitting a pull request.

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Contributors

Handle	GitHub	Role
lajjadred	@lajjadred	Project lead
이채문	@CHML-real	Mathematical algorithm development
CUBE	@90cube	Idea proposal and data collection

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License

MIT License. See LICENSE for details.