Volume 8 — Collapse Entropy and Information Geometry
Information Theory in Golden-Base Tensor Space
This volume develops information theory specifically for φ-constrained systems. Entropy, compression, and information flow take on new meanings when subject to the fundamental constraint that no two 1s can be adjacent.
Chapter Index
Chapter 128: TraceEntropy
Entropy Definition over Collapse Trace Paths
Fundamental entropy measure for trace structures.
Chapter 129: HSBound
Hurt–Sada Array as Compression Bound Mechanism
Optimal compression limits in φ-constrained space.
Chapter 130: InfoFlow
Trace-Based Collapse Information Current
Information as flow through trace networks.
Chapter 131: EntropyDensity
Local Structural Information Density in φ-Tensor Networks
Spatial distribution of information content.
Chapter 132: ObsInfoScope
Observer Trace Bandwidth and Info Cutoffs
Information limits from observer constraints.
Chapter 133: InfoMap
φ-Trace to Shannon Map on Collapse Structures
Connecting collapse entropy to Shannon theory.
Chapter 134: EntropyGradient
Collapse Divergence Field and Structural Gradient
Gradient flows in information space.
Chapter 135: EntropyLimit
φ-Saturation Threshold of Structural Compression
Maximum compression before violating constraints.
Chapter 136: CollapseThermo
Laws of Entropic Flow in Trace-Constrained Dynamics
Thermodynamic laws for collapse systems.
Chapter 137: MutualCollapseInfo
Inter-Trace Collapse Information Coupling
Mutual information between trace structures.
Chapter 138: EntropyDistance
Tensor-Based Collapse Divergence Metrics
Distance measures using entropy differences.
Chapter 139: PhiCompressCode
Optimized Collapse Encoding Grammar with Minimum Rank Loss
Compression algorithms preserving trace rank.
Chapter 140: SpectralEntropy
Flatness Constraints on Collapse Spectra
Entropy in frequency domain.
Chapter 141: InfoGeometry
Information-Theoretic Metrics on Collapse Field Manifolds
Geometric structure of information space.
Chapter 142: NoiseCollapse
Structural Uncertainty from Path Collapse Degradation
Noise as trace structure degradation.
Chapter 143: ZetaInfoManifold
ζ(s) Mapping onto Collapse Information Landscape
Spectral view of information geometry.
Key Concepts Introduced
- Trace Entropy: Information in φ-constrained space
- HS-Bounds: Compression limits from Hurt-Sada
- Information Flow: Current through trace networks
- Observer Bandwidth: Information capacity limits
- Entropy Gradients: Directional information flow
- Info-Geometry: Manifold structure of information
Dependencies
- Volume 0: Trace language and compression
- Volume 4: Geometric structures
- Volume 7: Observer information limits
Next Steps
- Volume 9: Measurement and information
- Volume 28: Memory and storage
- Volume 29: Information rewriting
"Information flows where golden traces allow."