Kuramoto synchronization  ·  Ricci curvature flow  ·  Free-energy thermodynamics  ·  Cryptobiosis

Physics-first quantitative infrastructure with 57 machine-checkable invariants. Every signal traces back to peer-reviewed science. Every clamp traces back to a law.

The Signal

GeoSync distils validated mechanisms from computational neuroscience, differential geometry, thermodynamics, and synchronization theory into a rigorous, production-oriented algorithmic infrastructure.

Order Parameter R(t) 1.0 ┤ ╭────── │ ╭──╯ 0.8 ┤ ╭──╯ │ ╭──╯ 0.6 ┤ ╭──╯ │ ╭──╯ 0.4 ┤ ╭──╯ │╭─╯ 0.2 ┤╯ │ 0.0 ┼────────────────────────── 0 200 400 600 800 t

The core question: when do markets synchronize? The Kuramoto order parameter R(t) quantifies instantaneous phase coherence across assets: R → 0 desynchronized, independent motion R → 1 full phase-lock, regime transition When R crosses critical coupling Kc, the market undergoes a phase transition — the geometric signal that conventional factor models systematically miss. dθᵢ/dt = ωᵢ + K · Σⱼ Aᵢⱼ sin(θⱼ − θᵢ)

Architecture

                    ┌─────────────────────────────────────────────────────┐
                    │                   G E O S Y N C                     │
                    │          Geometric Market Intelligence               │
                    └─────────────┬───────────────────┬───────────────────┘
                                  │                   │
              ┌───────────────────┼───────────────────┼───────────────────┐
              │                   │                   │                   │
     ┌────────▼────────┐ ┌───────▼────────┐ ┌────────▼────────┐ ┌───────▼────────┐
     │  DATA INGESTION │ │ FEATURE  STORE │ │ STRATEGY ENGINE │ │  RISK MANAGER  │
     │  CCXT · Alpaca  │ │ Redis · Feast  │ │ Policy  Router  │ │  TACL · Gates  │
     │  Polygon · WS   │ │ Parquet · PG   │ │ Walk-Forward    │ │  Kill Switch   │
     └────────┬────────┘ └───────┬────────┘ └────────┬────────┘ └───────┬────────┘
              │                  │                    │                  │
              └──────────────────┼────────────────────┼──────────────────┘
                                 │                    │
                    ┌────────────▼────────────────────▼────────────┐
                    │            EXECUTION  FABRIC                  │
                    │    OMS · Smart Routing · Capital Optimizer    │
                    │    Paper Trading · Compliance · Audit Trail   │
                    └──────────────────────┬───────────────────────┘
                                           │
                    ┌──────────────────────▼───────────────────────┐
                    │          OBSERVABILITY  STACK                 │
                    │  Prometheus · OpenTelemetry · 400-day Audit   │
                    │  Reliability Tests · Deterministic Replay     │
                    └──────────────────────────────────────────────┘

Module	Path	Lang	Purpose
CORE	core/indicators/	Python	50+ geometric and technical indicators — Kuramoto, Ricci, entropy, fractal, Hurst
KURAMOTO	core/kuramoto/	Python	RK4 · JAX/GPU · Sparse · Adaptive · Delayed · SecondOrder simulation engines
BACKTEST	backtest/	Python	Event-driven engine, walk-forward, Monte Carlo, property-based validation
EXECUTION	execution/	Python	OMS, smart routing, Kelly/MV sizing, compliance, paper trading
RUNTIME	runtime/	Python	Live orchestration, kill switch, CNS stabilizer, recovery agent
TACL	tacl/	Python	Thermodynamic autonomic control — free energy descent, protocol hot-swap
NEURO	core/neuro/	Python	Dopamine TD-learning, serotonin ODE stability, GABA inhibition gate, cryptobiosis survival
OBSERVE	observability/	Python	Prometheus, OpenTelemetry, structured audit logging, dashboards
ACCEL	rust/geosync-accel/	Rust	High-performance compute kernels for hot-path acceleration
UI	ui/dashboard/	TypeScript	React web interface — canonical interactive dashboard

Physics Kernel

GeoSync is a verified physical system, not a test-coverage theatre. The physics kernel (.claude/physics/) defines 57 machine-checkable invariants across 15 modules. Every test is a mathematical witness of a specific physical law, not a line-coverage artefact.

                     ┌──────────────────────────────────────┐
                     │   57 INVARIANTS  ·  15 MODULES       │
                     │   Every assert derives its tolerance  │
                     │   from the law's formula, not from    │
                     │   a magic literal.                    │
                     └──────────┬───────────────────────────┘
                                │
          ┌─────────────────────┼─────────────────────────┐
          │                     │                         │
  ┌───────▼────────┐   ┌───────▼────────┐   ┌────────────▼──────────┐
  │ GENERATORS     │   │ SUSTAINERS     │   │ PROTECTORS            │
  │ Kuramoto (K1-7)│   │ ECS (FE1-2)   │   │ GABA (GABA1-5)       │
  │ Dopamine (DA1-7)│  │ Serotonin tonic│   │ Serotonin veto (5HT7)│
  │ HPC (HPC1-2)  │   │ (5HT1-6)      │   │ Cryptobiosis (CB1-8) │
  │ Kelly (KELLY1-3)│  │ Thermo (TH1-2)│   │                       │
  └────────────────┘   └───────────────┘   └───────────────────────┘

Protectors have unconditional priority over Generators. A system without a gradient cannot use a gradient. See CLAUDE.md §0 for the full gradient ontology.

Metric	Value
Physics invariants	57 across 15 modules (P0: 37, P1: 17, P2: 3)
Grounded witnesses	67 tests with INV-* docstrings and 5-field error messages
C1/C2 code audit	0 undocumented physics clamps in core/
CI gate	physics-kernel-gate.yml — self-check + L1-L5 validation + C1/C2 audit
OOS walk-forward alpha	+78% vs equal-weight, drawdown -53% (5/5 folds protected)

Key invariants:

ID	Law	Module
INV-K2	K < K_c ⟹ R → 0 (subcritical decay, ε = 3/√N)	Kuramoto
INV-5HT7	stress ≥ 1 OR |drawdown| ≥ 0.5 → veto	Serotonin
INV-CB1	DORMANT ⟹ multiplier == 0.0 EXACTLY	Cryptobiosis
INV-FE1	Free energy non-increasing under active inference	ECS
INV-DA7	∂δ/∂r = 1 (RPE linear in reward)	Dopamine
INV-RC1	Ollivier-Ricci κ ≤ 1 (universal upper bound)	Ricci

Geometric Indicators

╭─╮ ╱ θ ╲ │phase│ ╲ ╱ ╰─╯ Kuramoto Phase synchrony

╭───╮ ╱ Ric ╲ │curva- │ │ ture │ ╲ ╱ ╰───╯ Ricci Flow Regime geometry

┌───┐ │ H │ │ = │ │ Σ │ │-pln│ └───┘ Entropy Shannon / Tsallis

╱╲╱╲ ╱╲╱╲╱╲ ╱╲╱╲╱╲╱╲ ╱╲╱╲╱╲╱╲╱╲ fractal Fractal Multi-scale self-similarity

┌─────┐ │ H(q)│ │ ↕ │ │0←→1 │ └─────┘ Hurst Long-range dependence

t₁─┐ t₂─┤►Σ t₃─┘ multi scale Multi-Scale Timeframe decomposition

TACL — Thermodynamic Autonomic Control

The governing brain of system stability. Every autonomous change must respect Monotonic Free Energy Descent.

  Free Energy F = U − T·S

  where   U = Σᵢ wᵢ · penalty(metricᵢ)       internal energy
          T = 0.60                              control temperature
          S = stability headroom                entropy term

  Envelope:  F ≤ 1.35   (12% safety margin)
  Rest:      F = 1.00   (stabilised baseline)
  Kill:      F > 1.35   (emergency halt)

Monitored Metrics Metric Threshold Weight latency_p95 85 ms 1.6 latency_p99 120 ms 1.9 coherency_drift 0.08 1.2 cpu_burn 0.75 0.9 mem_cost 6.5 GiB 0.8 queue_depth 32 msg 0.7 packet_loss 0.005 1.4

Safety State Machine ┌──────────────┐ │ NOMINAL │ F ≤ 1.00 └──────┬───────┘ │ F ↑ ┌──────▼───────┐ │ STRESSED │ 1.00 < F ≤ 1.35 └──────┬───────┘ │ F > 1.35 ┌──────▼───────┐ │ KILL SWITCH │ dual-approval │ ENGAGED │ or auto-rollback └──────────────┘

Protocol Hot-Swap — dynamic switching between RDMA, CRDT, gRPC, Shared Memory, Gossip with admissibility guards. Any swap that increases F beyond tolerance triggers automatic reversion within 30s.

Quick Start

git clone https://github.com/neuron7xLab/GeoSync.git
cd GeoSync
python -m venv .venv && source .venv/bin/activate
make install

First Analysis

from core.indicators.kuramoto_ricci_composite import GeoSyncCompositeEngine
import numpy as np, pandas as pd

index  = pd.date_range("2024-01-01", periods=720, freq="5min")
prices = 100 + np.cumsum(np.random.normal(0, 0.6, 720))
volume = np.random.lognormal(9.5, 0.35, 720)
bars   = pd.DataFrame({"close": prices, "volume": volume}, index=index)

engine   = GeoSyncCompositeEngine()
snapshot = engine.analyze_market(bars)

print(f"Phase:      {snapshot.phase.value}")
print(f"Confidence: {snapshot.confidence:.3f}")
print(f"Entry:      {snapshot.entry_signal:.3f}")

=== GeoSync Market Analysis ===
Phase:      transition
Confidence: 0.893
Entry:      0.000

Kuramoto Simulation

from core.kuramoto import KuramotoConfig, run_simulation

cfg = KuramotoConfig(N=50, K=3.0, dt=0.01, steps=1000, seed=42)
result = run_simulation(cfg)

print(f"Trajectory: {result.phases.shape}")       # (1001, 50)
print(f"Final R:    {result.order_parameter[-1]:.4f}")

Backtest

from backtest.event_driven import EventDrivenBacktestEngine
from core.indicators import KuramotoIndicator

indicator = KuramotoIndicator(window=80, coupling=0.9)
prices = 100 + np.cumsum(np.random.default_rng(42).normal(0, 1, 500))

def signal(series):
    order = indicator.compute(series)
    s = np.where(order > 0.75, 1.0, np.where(order < 0.25, -1.0, 0.0))
    s[:min(indicator.window, s.size)] = 0.0
    return s

result = EventDrivenBacktestEngine().run(prices, signal, initial_capital=100_000)

CLI

tp-kuramoto simulate --N 50 --K 3.0 --steps 2000 --seed 42
geosync-server --allow-plaintext --host 127.0.0.1 --port 8000

Kuramoto ODE Engine

Six specialized integrators for every scale:

Engine	Method	Use Case
Standard	RK4	General-purpose, N < 10K
JAX	XLA-compiled	GPU/TPU acceleration
Sparse	O(E) coupling	Large networks, sparse topology
Adaptive	Dormand-Prince / LSODA	Error-controlled step size
Delayed	DDE	Time-delayed coupling
SecondOrder	Inertia + damping	Swing equations, power grids

Standard ODE:    dθᵢ/dt = ωᵢ + (K/N) · Σⱼ≠ᵢ sin(θⱼ − θᵢ)
Adjacency ODE:   dθᵢ/dt = ωᵢ + K · Σⱼ Aᵢⱼ sin(θⱼ − θᵢ)
Order Parameter: R(t) = |1/N · Σⱼ exp(iθⱼ)| ∈ [0, 1]

Parameter	Default	Description
N	10	Coupled oscillators (int >= 2)
K	1.0	Global coupling strength
omega	N(0,1)	Natural frequencies (rad/time)
dt	0.01	RK4 integration step
steps	1000	Integration steps
adjacency	None	Weighted coupling matrix
theta0	U(0, 2pi)	Initial phases
seed	None	RNG seed for reproducibility

Testing & Quality

 10,051 collected  ·  681 passing  ·  71% line coverage  ·  57 physics invariants  ·  67 witnesses  ·  0 mypy errors

Unit tests/unit/

Integration tests/integration/

Property tests/property/

Fuzz tests/fuzz/

Contract tests/contracts/

Mutation mutmut

pytest tests/                          # full suite
pytest tests/ -m "not slow"            # fast feedback
pytest tests/property/                 # hypothesis-driven
mutmut run --use-coverage              # mutation testing
cd ui/dashboard && npm test            # UI smoke

CI Merge Gates: ruff, mypy (strict), bandit, pip-audit, CodeQL, Semgrep, TruffleHog, CycloneDX SBOM generation.

Performance

Design targets — NOT measured results. See METRICS_CONTRACT.md.

  Backtesting throughput     1M+ bars/second
  Order latency              < 5 ms (exchange-dependent)
  Signal generation          < 1 ms (cached indicators)
  Memory steady-state        ~ 200 MB live trading
  Hot-path budget            > 30% → Rust accelerator fallback

Security

  Framework       NIST SP 800-53  ·  ISO 27001  (design aligned)
  Encryption      AES-256 at rest  ·  TLS 1.3 in transit
  Secrets         HashiCorp Vault  ·  AWS Secrets Manager
  Auth            JWT + MFA for admin operations
  Compliance      GDPR · CCPA · SEC · FINRA patterns
  Audit           400-day immutable append-only log
  Supply chain    pinned SHA actions · dependency hash verification
  CVE target      < 7-day remediation
  Type safety     mypy strict · Pydantic 2.0 · 0 type errors

Deployment

# Docker Compose (dev/staging)
cp .env.example .env && docker compose up -d

# Kubernetes (production)
terraform -chdir=infra/terraform/eks apply -var-file=environments/production.tfvars
kubectl apply -k deploy/kustomize/overlays/production

Configuration via Hydra — conf/, config/, configs/, envs/, .env. Override anything from CLI:

geosync run strategy.capital=200000 data.timeframe=4h

Technology Stack

  NUMERICAL       NumPy 2.3  ·  SciPy 1.16  ·  Pandas 2.3  ·  Numba 0.60
  ML              PyTorch 2.1  ·  scikit-learn  ·  Optuna
  GRAPH           NetworkX 3.5
  API             FastAPI 0.120  ·  Strawberry GraphQL
  DATABASE        PostgreSQL + SQLAlchemy 2.0  ·  Alembic
  CACHE           Redis 7.0
  MESSAGING       Apache Kafka (aiokafka)
  OBSERVABILITY   Prometheus  ·  OpenTelemetry
  CONFIGURATION   Hydra-core 1.3  ·  OmegaConf 2.3
  VALIDATION      Pydantic 2.12  ·  Pandera 0.20
  INFRASTRUCTURE  Docker  ·  Kubernetes  ·  Helm  ·  Terraform
  ACCELERATION    Rust (geosync-accel)  ·  CuPy (GPU optional)
  QUALITY         ruff · black · mypy · pytest · Hypothesis · mutmut

Project Status

  VERSION         v0.1.0   Pre-Production Beta
  CORE ENGINE     stable   production-ready
  INDICATORS      stable   50+ geometric + technical
  BACKTESTING     stable   event-driven, walk-forward
  LIVE TRADING    beta     active development
  DASHBOARD       alpha    early preview
  DOCUMENTATION   85%      170+ files

Roadmap

  Q1 2026         v1.0 production release
  Q2 2026         options & derivatives support
  Q3-Q4 2026      multi-asset portfolio optimization

Path to v1.0: 98% coverage gate activation, dashboard auth hardening, external security audit, P99 benchmark suite, SBOM publication.

Documentation

Getting Started Environment Setup Quickstart Guide CLI Reference User Interaction Guide Architecture System Architecture Architecture Map ADR Records (19) Independent Models

Operations Deployment Guide Live Trading Runbook Kill Switch Failover Disaster Recovery Research Bibliography Indicator Library TACL Documentation Metrics Contract

Institutional Overview | Roadmap | Security Framework | Contributing | Full Documentation

Contributing

git clone https://github.com/neuron7xLab/GeoSync.git && cd GeoSync
python -m venv .venv && source .venv/bin/activate
make dev-install

make test          # core test suite
make lint          # ruff + mypy + bandit
make format        # black + isort
make audit         # security audit
make golden-path   # full workflow demo
make help          # all commands

Contributing Guide | Code of Conduct | Good First Issues

Citation

If you use GeoSync in academic research, industry reports, or derivative work, please cite it. A machine-readable manifest lives in CITATION.cff; GitHub renders a ready-to-copy citation in the sidebar of the repository page.

@software{geosync_2026,
  title   = {GeoSync: Geometric Market Intelligence Platform},
  author  = {Vasylenko, Yaroslav},
  year    = {2026},
  version = {1.0.0},
  url     = {https://github.com/neuron7xLab/GeoSync},
  license = {MIT}
}

Risk Disclosure

Trading financial instruments involves substantial risk of loss. GeoSync provides quantitative research infrastructure and execution tooling — it does not constitute investment advice, and no component guarantees profitable performance. Live trading modules are in pre-production beta. Backtested results do not guarantee future performance. Users bear full regulatory responsibility.

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GeoSync — Geometric Market Intelligence

neuron7xLab · Poltava, Ukraine 🇺🇦

_{Built on peer-reviewed science. Physics-first, 57 invariants, every clamp documented.}