Fluctara

Consciousness-grade audio entrainment

Grounded in SCPN physics. Verified by real-time EEG.

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Vision

Beyond audio. Beyond binaural beats.

A new class of entrainment engine built from first-principles physics, not frequency tables.

Physics-First

16-layer coupled oscillator model derived from first-principles dynamics. Not heuristic frequency tables.

Verified Per Session

EVS proves brain response every session. Not a claim — a measurement of spectral correlation with target bands.

Closed-Loop

Real-time EEG and HRV feedback drives protocol adaptation. The system responds to you, not a preset timer.

Applications

Built for real protocols

Concrete entrainment scenarios grounded in coupled oscillator physics and verified by EEG.

🌙

Sleep Optimization

Delta-band entrainment with closed-loop depth tracking. Circadian phase alignment via slow-wave induction protocols.

⚡

Focus Enhancement

Beta/gamma entrainment for sustained attention. EVS confirms cortical frequency locking in real time.

🧬

Clinical Protocols

40 Hz gamma for neurodegeneration research. HRV coherence training. Tinnitus masking with notched audio.

🧘

Meditation

Theta/alpha entrainment with progressive depth curves. Session-over-session adaptation based on outcome tracking.

🧠

Therapy & Mental Health

6 therapeutic frameworks (CBT, ACT, DBT, MI, MBCT, SF), structured conversation engine, and validated outcome measures.

🏢

Enterprise & Telehealth

Multi-tenant SaaS, EHR integration (Epic/Cerner via FHIR R4), HIPAA-aligned workflows, and role-based access control.

Protocols

6 core + 4 clinical entrainment protocols

Phase-transition state machines with tick, pause, resume, and stop. Each protocol targets specific brainwave bands with timed phase progressions.

Deep Sleep

4 phases 28 min

Progressive delta-band descent through theta into sustained deep-sleep oscillation. Slow-wave induction with gradual frequency reduction.

Delta 0.5–4 Hz

Deep Focus

4 phases 25 min

Beta ramp into sustained high-beta with SMR stabilisation. Designed for sustained concentration and cognitive clarity.

Beta 15–30 Hz

Zen Meditation

4 phases 20 min

Alpha-theta crossover for deep meditative states. Gradual descent from relaxed alpha to theta-dominant contemplation.

Theta 4–8 Hz

Instant Calm

3 phases 10 min

Rapid alpha induction for acute stress relief. Short protocol for immediate downregulation of sympathetic activity.

Alpha 8–13 Hz

Morning Energy

4 phases 14 min

Progressive beta ramp from resting state. Designed for post-wake cortical activation and alertness induction.

Beta 15–30 Hz

Creative Flow

4 phases 18 min

Alpha-theta oscillation promoting divergent thinking. Alternates between relaxed ideation and focused integration phases.

Alpha 8–13 Hz

40 Hz Gamma

3 phases 30 min

Sustained 40 Hz gamma entrainment for neuroplasticity research. Based on the MIT Picower Institute paradigm.

Gamma 40 Hz

Vagus Nerve

4 phases 20 min

SSP-inspired vagal tone protocol for autonomic regulation. Targets parasympathetic activation through auditory stimulation.

Theta 4–8 Hz

HRV Coherence

3 phases 15 min

0.1 Hz resonance frequency breathing at 6 breaths per minute. Heart rate variability coherence training with biofeedback.

Alpha 8–13 Hz

Tinnitus Relief

4 phases 25 min

Notched music therapy with residual inhibition. Frequency-specific sound shaping targeting individual tinnitus profiles.

Alpha 8–13 Hz

GENUS 40 Hz

MIT research 60 min

Gamma entrainment using sensory stimulation. 40 Hz audio-visual protocol with pre/post cognitive battery assessment.

Gamma 40 Hz

Lazarus Protocol

16-layer Kuramoto Variable

Consciousness-mediated healing via SCPN phase synchronisation. Global coherence parameter Phi drives theurgic mode at Φ > 0.95.

Multi-band

VIBRANA Geometry

Sacred geometry Visual sync

13-fold, Flower of Life, Metatron, Merkaba, Sri Yantra. Audio-to-visual phase mapping with 15 Hz photosensitivity safety ceiling.

Visual ≤15 Hz

Body Atlas

7 chakras • 12 meridians SCPN mapping

Chakra frequencies mapped to SCPN layers (L1–L16). Acupuncture meridian database with 14 key points and circadian peak hours.

256–480 Hz

Interactive

Try it: phase coherence

Drag the slider to synchronize four coupled oscillators. Enable audio to hear the binaural beat narrow as coherence rises.

0.15
Order parameter: 0.15
Beat frequency: 12.2 Hz
Regime: Low

Headphones recommended

Interested in what you see?

Request Early Access

Science

16 coupled oscillator layers

The SCPN framework models consciousness as a hierarchy of coupled phase oscillators, from quantum coherence to high-level integration.

L01 Quantum Biological
L02 Neurochemical
L03 Genomic-Epigenetic
L04 Cellular Synchrony
L05 Intentional Frame
L06 Gaian Embodiment
L07 Geometrical-Symbolic
L08 Cosmic Information
L09 Memory Manifold
L10 Identity Manifold
L11 Noospheric-Cultural
L12 Ecological-Gaian
L13 Source-Field
L14 Transdimensional
L15 Consilium
L16 The Director

Coupled Oscillator Physics

Kuramoto-family phase coupling across all 16 layers with calibrated natural frequencies and inter-layer coupling strengths.

Entrainment Verification

Real-time composite score correlating delivered audio frequency with measured EEG spectral power in the target band.

Stochastic Geometry

Learned geometric structure that shapes how oscillators couple, with spectral observables feeding back into audio parameters.

Consciousness Boundary

Persistent homology extracts topological features from multichannel phase data, gating consciousness-level protocol modes.

Technology

Rust-first computation. Python orchestration.

Performance-critical paths in Rust with PyO3 bindings. Orchestration, ML, and API surface in Python.

Client
REST API WebSocket CLI
Python
FastAPI Orchestrator ML Pipeline PyO3 Bindings 60+ Modules
Rust
fluctara-types fluctara-audio fluctara-physics fluctara-consciousness fluctara-core fluctara-ssgf fluctara-signal fluctara-entrainment fluctara-closedloop fluctara-evs fluctara-protocols fluctara-analytics fluctara-python

13 Rust Crates

Types, audio synthesis (binaural/isochronic/cymatics/soundscape/vibrana), physics engine (UPDE/Lazarus Kuramoto), consciousness model (TCBO/PGBO), core solver, SSGF geometry, signal processing, entrainment control, closed-loop feedback, EVS scoring, protocols (PLL/IAF/PAC), analytics (temporal/astrology/wellness), and PyO3 bridge (30 classes + 47 functions).

345+ Python Modules

AI coaching, therapy engine, sleep analysis, device integrations, analytics pipelines, gamification, enterprise multi-tenancy, and research tools.

Real-Time Streaming

WebSocket streams for live phase evolution, SSGF geometry, EVS scoring, and closed-loop control at sub-second latency.

30+ Device Integrations

8 EEG headsets, 14 wearables, 5 biofeedback sensors, and 2 metabolic monitors. BrainFlow, BLE, OAuth, and HealthKit interfaces.

AI & Personalization

Biorhythm analysis, circadian scoring, adaptive protocol selection, and 5 coaching styles. Session-over-session learning from biometric outcomes.

Therapy Engine

6 therapeutic frameworks (CBT, ACT, DBT, MI, MBCT, Solution-Focused), crisis assessment protocols, and validated outcome measures.

Clinical Outcomes

PHQ-9, GAD-7, ISI outcome tracking. FHIR R4 resource generation for clinical interoperability. HIPAA-aligned data handling and session persistence.

Sleep & Circadian

5 sleep stage detection, circadian phase alignment, dream-state protocols, and polyphasic schedule support with delta-band entrainment.

Numerical Solvers

Euler-Maruyama stochastic integrators with noise-driven phase dynamics, property-based tests for all numerical paths, reproducible from fixed seeds.

4,800+
Tests Passing
11
Rust Crates
60+
Python Modules
30+
Devices
16
Oscillator Layers
<1ms
Solver Latency

Audio Engine

Synthesis from first principles

Every audio signal is generated mathematically. No sample libraries, no pre-recorded loops.

Binaural Beats

Stereo sine pair: L = sin(2π·f·t), R = sin(2π·(f+Δf)·t). Configurable carrier, beat frequency, amplitude, and phase offset.

Isochronic Pulses

Amplitude-modulated carrier with duty-cycle control. Raised-cosine edge smoothing eliminates transient clicks.

HRTF Spatial Audio

ITD via Woodworth formula, frequency-dependent ILD, inverse-distance attenuation. Based on Blauert (1997) psychoacoustic model.

Noise Colours

White xorshift64 RNG, flat spectrum
Pink Paul Kellet 3-tap IIR, −3 dB/oct
Brown Integrated white, −6 dB/oct
Blue First-difference, +3 dB/oct
Violet Second-difference, +6 dB/oct

Multi-Carrier Mixing

Golden-ratio (φ = 1.618) phase offsets with equal-amplitude 1/√N weighting. Raised-cosine ramps at session edges prevent spectral splatter.

Output Format

Stereo f32 internal processing. 16-bit PCM WAV export. Configurable sample rate: 8 kHz–96 kHz (default 44.1 kHz).

Biometrics

Real-time physiological signal processing

EEG band powers, HRV time/frequency metrics, artifact rejection, and coherence scoring — all computed in Rust.

Brainwave Bands

Delta
0.5–4 Hz
Theta
4–8 Hz
Alpha
8–13 Hz
SMR
12–15 Hz
Beta
15–30 Hz
Gamma
30–100 Hz

HRV Metrics

SDNN
Standard deviation of RR intervals (ms)
RMSSD
Root mean square of successive differences
pNN50
Proportion of RR diffs > 50 ms
LF/HF
Low-frequency / high-frequency power ratio
Stress
Composite stress index (0–100)
Recovery
Parasympathetic recovery index
Coherence
Cardiac coherence score
State
8-state autonomic classifier

EEG Processing

Radix-2 Cooley-Tukey FFT, Hanning window, per-band power extraction, peak frequency detection, and peak-to-peak artifact rejection.

Coherence Engine

Pearson temporal correlation, z-score normalisation, composite coherence index (70% temporal + 30% spectral), and IIT Φ approximation.

CLI

Command-line interface

Three commands. No GUI required. Python 3.11–3.13 on Linux, macOS, and Windows.

Install

$ pip install fluctara

Install from PyPI. Requires Python 3.11+. Rust crates compile automatically via maturin.

Usage

$ fluctara serve --port 8000

Start the API server with REST + WebSocket endpoints. Binds to 0.0.0.0 by default.

$ fluctara generate -o session.wav -d 300 --carrier 400 --beat 10 --noise pink

Generate entrainment audio to WAV. Supports all synthesis modes: binaural, isochronic, 5 noise colours, and combinations.

$ fluctara calibrate --duration 10 --sample-rate 256

Run EEG baseline calibration. Reads band powers for 10 seconds and prints average per-band results.

FHIR R4 Export

Session data exports to FHIR R4 Observation and CarePlan resources for clinical interoperability and EHR integration.

Session Persistence

SQLite-backed session store with full CRUD. Tracks EVS grade, duration, outcome, and protocol parameters per session.

90% Coverage Target

Configured in pyproject.toml. 4,800+ tests (518 Rust + 4,343 Python) across unit, integration, and end-to-end suites. CI-enforced on every push.

Positioning

How Fluctara differs

Approaches to audio entrainment vary widely. Here's where the field stands.

Approach Physics Model Per-Session Verification Closed-Loop Open Source
Heuristic Playlists ✕ Frequency tables ✕ None ✕ Static ✕
Fixed Neurofeedback ✕ Band-power thresholds ✕ Session-level only ✓ Threshold-based ✕
Black-Box Adaptive ✕ Proprietary ✕ Proprietary ✓ Proprietary ✕
Fluctara ✓ 16-layer Kuramoto ✓ EVS (0–100) ✓ EEG + HRV ✓ AGPL v3
Fluctara application interface

Research

Publications

Foundational papers describing the theoretical framework, verification methodology, and geometric extensions.

The SCPN framework from which Fluctara derives its physics model.

Published

The SCPN Master Publications — Scope & Table of Contents

Miroslav Šotek · October 2025 · DOI: 10.5281/zenodo.17419678

Public index for God of the Math — Mapping Consciousness to Spacetime. Foundational framework (Paper 0), sixteen domain monographs (Papers 1–16), and validation suite (Papers 17–20).

Published

SCPN Paper 1: Layer 1 (Quantum Biological) — Preview Edition

Miroslav Šotek · December 2025 · DOI: 10.5281/zenodo.18088340

Quantum-biological mechanisms of information coherence: microtubule Fröhlich dynamics, quantum error-correction shielding, gap-junction coordination, exosome transfer, and bioelectric field observables.

Published

SCPN Paper 2: Layer 2 — Transduction Interface

Miroslav Šotek · October 2025 · DOI: 10.5281/zenodo.17309834

Layer 2 as the transduction interface linking quantum-scale potentiality to classical biological realisation. VIBRANA–neurotransmitter coupling tensor, stochastic resonance as downward causation mechanism.

Published

SCPN Paper 3: Layer 3 — Genomic–Epigenomic–Morphogenetic

Miroslav Šotek · November 2025 · DOI: 10.5281/zenodo.17508894

Layer 3 specifications: definitions, axioms, cross-layer interface contracts and empirical programme for genomics, epigenomics, and morphogenesis.

Forthcoming

In Preparation

Entrainment Verification Score: Per-Session Proof of Neural Entrainment

Miroslav Šotek · Anulum Institute

In Preparation

Stochastic Synthesis of Geometric Fields for Oscillator Networks

Miroslav Šotek · Anulum Institute

MS

Miroslav Sotek

Principal Researcher · Anulum Institute

ORCID: 0009-0009-3560-0851

API

API Preview

60+ REST endpoints, 7 WebSocket streams. Selected routes shown below.

Core Engine

Audio Generation

/api/v1/audio
POST

Biometric Processing

/api/v1/biometrics
POST GET

Entrainment Verification

/api/v1/evs
POST GET

SCPN Physics Bridge

/api/v1/scpn
POST GET

SSGF Geometry

/api/v1/ssgf
POST GET

Closed-Loop Control

/api/v1/closedloop
POST GET

Platform

Device Management

/api/v1/devices
POST GET

Session Management

/api/v1/sessions
POST GET PATCH DELETE

Clinical Outcomes

/api/v1/clinical
POST GET

Protocol Intelligence

/api/v1/intelligence
GET

Authentication

/api/v1/auth
POST

Real-Time Streams

/ws/*
WS

AI & Clinical

Therapy

/api/v1/therapy
POST GET

Sleep

/api/v1/sleep
POST GET

AI Coach

/api/v1/advancedai
POST GET

Analytics

/api/v1/analytics
GET

Predictive Health

/api/v1/predictive
POST GET

Growth & Enterprise

Gamification

/api/v1/gamification
POST GET

Enterprise

/api/v1/enterprise
POST GET PATCH

Research

/api/v1/research
POST GET
GET /health

{
  "status": "ok",
  "version": "0.x.y"
}

Hardware

Supported devices

30+ consumer and research-grade devices across four categories.

Device Type Details Interface
EEG & Neuroimaging
Muse 2 / Muse S EEG 4 ch, 256 Hz BLE via BrainFlow
OpenBCI Cyton EEG 8/16 ch, 250 Hz Serial / Wi-Fi
Neurosity Crown EEG 8 ch, 256 Hz BLE via BrainFlow
Emotiv EPOC X / Insight EEG 14/5 ch USB / BLE
FocusCalm EEG 4 ch, 256 Hz BLE
Mendi fNIRS 1 region BLE
Heart Rate & Wearables
Polar H10 / Verity Sense HR RR + ECG BLE
Oura Ring Wearable HRV, SpO2, Temp API
Whoop 4.0 Wearable HRV, Strain API
Fitbit / Garmin / Samsung / Huawei Wearable HR, HRV, Sleep OAuth API
Apple Watch / Withings Wearable HR, HRV, ECG HealthKit / API
Eight Sleep Wearable Sleep, HR, Temp API
Terra (Unified API) Wearable Multi-device REST API
Generic BLE HR HR RR intervals BLE Heart Rate Profile
Biofeedback
EmotiBit Biofeedback PPG, EDA, Temp Wi-Fi
HeartMath / Lief / Spire Biofeedback HRV, Respiration BLE
Apollo Neuro Biofeedback Haptic output BLE
Metabolic
Dexcom G7 / Freestyle Libre Metabolic CGM Glucose BLE / NFC

EEG enables closed-loop adaptation and EVS verification. Wearables add HRV coherence and sleep tracking. Audio entrainment works standalone without hardware.

Examples

Quick start

Core API patterns for generating audio, verifying entrainment, and streaming real-time data.

Python Generate entrainment audio 
import httpx

resp = httpx.post("http://localhost:8000/api/v1/audio", json={
    "target_hz": 10.0,
    "duration_s": 300,
    "protocol": "alpha_entrainment",
})
audio = resp.json()
print(audio["session_id"], audio["sample_rate"])
Python Start EVS session with EEG 
resp = httpx.post("http://localhost:8000/api/v1/evs/session/start", json={
    "target_hz": 10.0,
    "device": "muse_2",
})
# Poll or stream for verification score
snapshot = httpx.get("http://localhost:8000/api/v1/evs/snapshot").json()
print(f"EVS: {snapshot['evs_score']:.0f}/100  Verified: {snapshot['is_verified']}")
Python WebSocket — real-time UPDE phase stream 
import asyncio, websockets, json

async def stream_phases():
    async with websockets.connect("ws://localhost:8000/ws/scpn/stream") as ws:
        await ws.send(json.dumps({"action": "start", "dt": 0.01}))
        async for msg in ws:
            data = json.loads(msg)
            print(f"R={data['r_global']:.3f}  t={data['time']:.2f}")

asyncio.run(stream_phases())

Performance

Benchmarks

Criterion benchmarks on a single core. No GPU required. 165× real-time headroom at 50 Hz.

121
μs
Pipeline Tick
Full entraining tick: Lazarus + Vibrana + telemetry
0.4
μs
EVS Sample
Entrainment verification scoring (Rust)
11.7
ns
PLL Update
Phase-locked loop (native Rust criterion)
1.49
ms
Binaural 1s
44.1 kHz stereo WAV (native Rust criterion)
4,800+
tests
Test Suite
518 Rust + 4,343 Python
700+
routes
API Endpoints
73 REST routers + 14 WebSocket handlers

Reference

Glossary

Key terms used throughout Fluctara documentation and API.

SCPN
Self-Consistent Phenomenological Network
16-layer coupled oscillator framework modeling consciousness-related dynamics from quantum coherence to high-level integration.
UPDE
Unified Phase Dynamics Equation
Master ODE governing all 16 SCPN layers. Kuramoto-family coupling with calibrated natural frequencies and inter-layer coupling matrix Knm.
EVS
Entrainment Verification Score
Real-time composite score (0–100) measuring spectral correlation between delivered audio frequency and measured EEG response in the target band.
SSGF
Stochastic Synthesis of Geometric Fields
Two-timescale engine converting stochastic Kuramoto microcycles into stable geometry carriers W(t) that shape oscillator coupling topology.
TCBO
Topological Consciousness Boundary Observable
Persistent homology pipeline extracting H1 cycles from delay-embedded phase data. Yields scalar pH1 gating consciousness-level protocol modes.
PGBO
Phase→Geometry Bridge Operator
Converts coherent phase dynamics into a symmetric rank-2 tensor field hμν that modulates propagation and coupling in the SSGF geometry channel.
R
Kuramoto Order Parameter
Global phase coherence measure in [0, 1]. R = |N−1 Σ eiθn|. R > 0.95 triggers theurgic mode.
Knm
Coupling Matrix
16×16 matrix of inter-layer coupling strengths. Base coupling K=0.45 with exponential decay α=0.3 and calibrated cross-hierarchy boosts.

Citing

How to cite

If you use Fluctara or the SCPN framework in your research, please cite:

BibTeX (Framework)

@misc{sotek2025scpn,
  author    = {Sotek, Miroslav},
  title     = {The SCPN Master Publications -- Scope and Table of Contents},
  year      = {2025},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.17419678},
  url       = {https://doi.org/10.5281/zenodo.17419678}
}

BibTeX (Software)

@software{fluctara2026,
  author    = {Sotek, Miroslav},
  title     = {Fluctara: Consciousness-Grade Audio Entrainment Engine},
  year      = {2026},
  publisher = {GitHub},
  url       = {https://github.com/anulum/fluctara},
  license   = {AGPL-3.0}
}

Licensing

Open core, dual license

The engine is open source. Commercial and research options are available.

OPEN SOURCE

AGPL v3

Full engine, solvers, and API. Free for open-source projects, academic research, and personal use. Modifications must be shared under the same license.

COMMERCIAL

Commercial License

Proprietary deployment without AGPL obligations. Includes priority support, SLA, and custom integration assistance. Contact for pricing.

RESEARCH

Research Collaboration

Extended data access, co-authorship opportunities, and dedicated engineering support for IRB-approved studies and academic partnerships.

Roadmap

Where we're headed

Alpha

Core engine, 4,800+ tests, 700+ API endpoints, CLI

Closed Beta

30 device integrations, AI coaching, therapy engine, researcher access

Clinical Pilot

IRB-approved sleep study, outcome tracking, EVS validation

Public API

Developer access, SDK, documentation, commercial licensing

FAQ

Common questions

Early Access

Fluctara is in active development. Researchers and clinicians interested in early access or collaboration can reach out directly.

Request Access

Team

People

MS

Miroslav Sotek

Founder & Principal Researcher

Anulum Institute

ORCID: 0009-0009-3560-0851