SRFM Quantum Phase13

Adaptive Transport Phase Memory and Persistent Topology-Only Structural Memory

Yoichi Tsujisawa

Overview

SRFM Quantum Phase13 investigates adaptive transport hysteresis, structural memory persistence, and topology-only memory phases in adaptive coupled network systems.

This phase extends previous SRFM Quantum studies by introducing path-dependent adaptive transport dynamics and separating:

observable transport memory
hidden topology memory

within adaptive coupling evolution systems.

The core result of Phase13 is the discovery that:

transport observables can converge while hidden coupling topology retains persistent history dependence.

This introduces a new SRFM concept:

Persistent Topology-Only Structural Memory

where the observable transport field loses memory of the past, but the internal adaptive coupling structure continues to preserve historical information.

Core Findings

F1 — Adaptive Transport Hysteresis

Forward and backward adaptive transport sweeps produce different final transport states.

This demonstrates:

path dependence
adaptive hysteresis
memory retention in transport dynamics

F2 — Transport/Topology Memory Separation

Observable transport quantities may converge toward identical values while coupling topology remains different.

This indicates that:

transport memory
topology memory

are distinct physical layers.

F3 — Persistent Topology-Only Memory

A large subset of simulations exhibits:

near-zero transport hysteresis
strong topology hysteresis

indicating persistent hidden structural memory.

F4 — Basin-Supported Memory Stability

Memory persistence is not purely transient.

Perturbation studies reveal:

metastable memory basins
graded memory survival
partial memory erosion
memory collapse regions

under external perturbations.

F5 — Long-Lifetime Structural Retention

Selected topology-only states preserve structural memory over long relaxation trajectories even after transport observables fully converge.

Scientific Interpretation

Phase13 suggests that adaptive network systems may contain:

hidden structural memory layers
metastable topology basins
path-dependent adaptive phases

that are not directly observable from transport outputs alone.

The results imply that:

structural memory may persist even when macroscopic observables appear fully relaxed.

This resembles generalized hysteresis phenomena found in:

nonequilibrium systems
adaptive complex systems
neural adaptation
glassy relaxation systems
topology-constrained dynamics

while remaining entirely within the SRFM adaptive framework.

Repository Structure

SRFM_QUANTUM_PHASE13/
│
├─ README.md
├─ LICENSE
├─ CITATION.cff
├─ requirements.txt
├─ run_all.ps1
├─ CHANGELOG.md
├─ ZENODO_DESCRIPTION.txt
│
├─ paper/
│   ├─ phase13_interim_summary.md
│   └─ phase13_interim_summary.pdf
│
├─ figures/
│   └─ paper/
│
├─ scripts/
│
├─ results/
│
└─ data/

Main Figures

Figure 1

Adaptive transport hysteresis loop.

Figure 2

Transport-topology hysteresis memory map.

Figure 6

Topology-only memory phase space.

Figure 10

Topology memory lifetime persistence.

Figure 14

Memory survival probability under perturbation.

Figure 18

Topology-only memory survival landscape.

Reproducibility

Environment

Recommended:

Python 3.10+
Windows PowerShell

Install dependencies

pip install -r requirements.txt

Run full pipeline

.\run_all.ps1

Key Scripts

Hysteresis Analysis

scripts/04c_analyze_hysteresis_and_memory_tanhbounded.py

Basin Perturbation Trials

scripts/06_run_basin_perturbation_trials.py

Topology-Only Memory Extraction

scripts/06b_extract_topology_only_memory_from_hysteresis.py

Memory Lifetime Analysis

scripts/07_run_memory_lifetime_analysis.py

Memory Basin Stability

scripts/08_run_memory_basin_stability.py

Interim Summary Builder

scripts/09_build_phase13_interim_summary_tables.py

Main Quantities

Transport Memory

H_phi = |phi_forward - phi_backward|

Measures path dependence in observable transport fields.

Topology Memory

H_spectral = |rho(C_forward) - rho(C_backward)|

Measures hysteresis in coupling topology structure using spectral radius differences.

Adaptive Coupling Dynamics

dC_ij/dt = alpha * tanh(phi_i * phi_j) - gamma * C_ij

Tanh-bounded adaptive coupling evolution used throughout Phase13.

Limitations

Phase13 remains a phenomenological adaptive systems study.

Current limitations include:

no rigorous theorem for memory persistence
no hardware quantum validation
no many-body quantum derivation
no formal attractor proof

The present work establishes reproducible empirical adaptive-memory phenomena within the SRFM framework.

Future Directions

Planned future work includes:

attractor geometry analysis
metastable basin theory
topology locking mechanisms
relaxation hierarchy studies
adaptive phase transition analysis
quantum hardware validation
generalized SRFM memory functional development

Citation

If you use this work, please cite:

Yoichi Tsujisawa,
"SRFM Quantum Phase13: Adaptive Transport Phase Memory and Persistent Topology-Only Structural Memory"

License

MIT License

Author