SRFM Quantum Phase14

Adaptive Basin Geometry and Persistent Structural Memory

Overview

SRFM Quantum Phase14 investigates whether persistent topology-only structural memory can be interpreted as metastable basin geometry in adaptive coupling-topology space.

This phase extends the results of:

• Phase11: coherent transport dynamics
• Phase12: adaptive transport topology formation
• Phase13: persistent topology-only memory

Phase14 focuses on:

• basin geometry
• metastability
• perturbation-driven erosion
• memory-state redistribution
• boundary thickness
• adaptive structural memory landscapes

The central question is:

Where does topology-only memory live in basin space, and how does perturbation move trajectories between memory basins?

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Core Concept

Phase13 established that:

observable transport output can converge while coupling topology retains persistent history.

Phase14 reinterprets this phenomenon geometrically.

Instead of treating memory as a binary protected state, Phase14 models structural memory as:

• metastable basin structure
• broad adaptive memory landscapes
• perturbation-degradable topology memory
• probabilistic redistribution between memory states

The key interpretation is:

transport memory and topology memory are partially decoupled.

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Main Findings

F1 — Basin-coordinate memory landscape

Phase13 memory classes project into a structured basin-coordinate space.

Main coordinates:

• X = transport memory (H_phi)
• Y = topology memory (H_spectral)
• Z = survival probability

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F2 — Topology-only memory forms a stable basin region

Topology-only memory remains a distinct basin class:

• topology_only_basin ≈ 21.8%
• coupled_memory_basin ≈ 43.3%

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F3 — High basin entropy

The basin landscape exhibits high transition entropy.

Observed:

• mean basin entropy ≈ 1.1626
• max basin entropy ≈ 1.3740

Theoretical 4-state maximum:

S_max = log(4) ≈ 1.386

Interpretation:

memory outcomes compete probabilistically rather than collapsing deterministically.

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F4 — Gradual erosion dominates over collapse

No collapse-boundary regime was detected.

Instead:

• survival gradually decreases
• partial memory increases
• erasure remains limited

This supports:

basin erosion rather than abrupt collapse.

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F5 — Memory-state redistribution

Perturbation redistributes memory through graded transitions:

topology-only survival → partial topology memory → mixed / weak memory → erasure

Direct erasure remains a minority outcome.

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Scientific Interpretation

Phase14 suggests that persistent structural memory behaves as a metastable basin phenomenon in adaptive coupling-topology space.

The results support:

• basin-supported memory
• perturbation-degradable memory
• probabilistic memory redistribution
• relaxation hierarchy
• broad metastable boundary regions

rather than:

• sharp topological protection
• binary collapse thresholds
• frozen memory states

The observed dynamics resemble:

• hysteresis systems
• metastable basin dynamics
• glass-like redistribution behavior

although no physical equivalence is claimed.

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Repository Structure

SRFM_QUANTUM_PHASE14
│
├─data
│  └─phase13_import
│
├─paper
│   └─figures
│
├─results
│
└─scripts

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Main Figures

Figure1 — Basin coordinate map

Shows the separation of:

• topology-only memory
• coupled memory
• transport-dominant memory
• erased states

in H_phi vs H_spectral space.

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Figure2 — Basin entropy landscape

Shows high-entropy perturbation regions and distributed memory-state competition.

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Figure4 — Boundary regime map

Demonstrates:

• survival-dominant basins
• broad transition regions
• absence of collapse-boundary regimes

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Figure5 — Basin erosion dynamics

Shows gradual survival degradation and limited erasure growth under perturbation.

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Reproducibility

Main pipeline:

python .\scripts\01_import_phase13_memory_landscape.py
python .\scripts\02_build_basin_coordinate_space.py
python .\scripts\03_analyze_basin_entropy.py
python .\scripts\04_build_basin_transition_matrix.py
python .\scripts\05_analyze_basin_boundary_thickness.py
python .\scripts\06_make_phase14_figures.py
python .\scripts\07_build_phase14_summary_tables.py

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Requirements

Main Python packages:

• numpy
• pandas
• matplotlib
• scipy
• networkx

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Publication

Zenodo:

(To be added)

GitHub:

(To be added)

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Citation

Yoichi Tsujisawa,
SRFM Quantum Phase14:
Adaptive Basin Geometry and Persistent Structural Memory,
2026.

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Limitations

This project is a phenomenological adaptive-memory model.

It does NOT claim:

• physical quantum memory
• topological quantum protection
• quantum error correction
• hardware validation
• universal attractor theorem
• thermodynamic proof

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One-Sentence Summary

Persistent topology-only memory in SRFM Quantum systems behaves as a broad metastable basin geometry with gradual erosion and probabilistic redistribution rather than sharp protected collapse.