theta-resonance 1.0.0

GenesisAeon Packages 27–30 — Brain Oscillation Bands (theta-resonance), Epigenetic Runtime Parameter Mutation (epi-sigillin), Proof-of-Resonance Distributed Consensus (hikari-ledger) & Entropy-Minimizing Network Routing (diffusive-routing)

theta-resonance + epi-sigillin + hikari-ledger + diffusive-routing

GenesisAeon Entropy Atlas — Packages 27, 28, 29 & 30

Package	Module	Domain	Γ
P27	theta_resonance	Brain oscillation bands as CREP modulators	0.251 (theta)
P28	epi_sigillin	Epigenetic runtime parameter mutation	dynamic — f(S_total)
P29	hikari_ledger	Proof-of-Resonance distributed consensus	0.367
P30	diffusive_routing	Entropy-minimizing network routing	0.443

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Package 27 — theta-resonance

Models EEG frequency bands (δ/θ/α/β/γ) as channels of the CREP tensor within the Unified Threshold Activation Criticality (UTAC) framework.

Triple Universality: Γ_theta ≈ 0.251 = Γ_AMOC = Γ_neural_criticality
The brain's flow state (theta band) converges to the same CREP setpoint as ocean circulation (AMOC) and cortical criticality — all homeostatic systems at 50 % efficiency.

from theta_resonance import ThetaResonance

sys = ThetaResonance(seed=42)          # synthetic EEG by default
result = sys.run_cycle(duration_seconds=60.0)

print(result["crep"])
# {'C': 0.333, 'R': 1.0, 'E': 0.647, 'P': 0.752, 'Gamma': 0.2514, ...}

print(result["flow_state"])   # True
print(result["current_band"]) # 'theta'
print(sys.gamma_for_band("gamma"))  # 0.75

Frequency Band → CREP Mapping

Band	Range	Cognitive State	Γ
Delta δ	0.5–4 Hz	Deep sleep	0.05
Theta θ	4–8 Hz	Flow / meditation	0.251
Alpha α	8–13 Hz	Relaxed attention	0.35
Beta β	13–30 Hz	Active cognition	0.55
Gamma γ	30–80 Hz	Error correction / arousal	0.75

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Package 28 — epi-sigillin

Implements epigenetic mutation of UTAC parameters during runtime. Analogous to how environmental signals alter gene expression without changing DNA, the system entropy level rewrites CREP-YAML parameter files at runtime — giving the framework organic adaptability.

Gemini's insight: "Umweltfaktoren verändert die Genexpression → systemisches Entropie-Niveau schreibt CREP-YAML während der Laufzeit um"

from epi_sigillin import EpiSigillin

epi = EpiSigillin(seed=42)
result = epi.run_cycle(duration_cycles=100)

print(result["methylation"])
# {'M_C': 0.12, 'M_R': 0.08, 'M_E': 0.03, 'M_P': 0.21}

print(result["active_marks"])
# ['H3K27me3']  ← high-entropy repression mark active

print(result["crep"])
# epigenetically modulated CREP with suppressed P-component

# Inherit methylation state across cycles (50% inheritance)
epi2 = EpiSigillin(seed=99)
epi2.inherit_from(epi.methylation_state())

# Rewrite a YAML parameter file based on current entropy
mutated = epi.mutate_yaml("config/crep_params.yaml", entropy_level=7.5)

Epigenetic Methylation Rules

Condition	Biological Analogy	CREP Effect
High entropy (H > H*)	DNA methylation (H3K27me3)	Suppresses P-component
Low entropy (H < H*)	Histone activation (H3K4me3)	Enhances E-component
Extreme entropy	Heterochromatin (H3K9me3)	CREP hibernation (all M→1)
Recovery	Demethylation	Gradual CREP restoration

---

Package 29 — hikari-ledger

Implements a Proof-of-Resonance (PoR) consensus mechanism for distributed genesis-os node networks. Instead of energy-intensive Proof-of-Work, PoR validates blocks based on each node's CREP harmonic state. Nodes with high Γ earn validation rights proportional to their resonance. A block is accepted when the weighted agreement of validators exceeds 2/3 (Byzantine fault tolerance).

Γ_PoR ≈ 0.367 — η = 2/3 (BFT threshold), σ = 2.2 Hikari tokens minted via: ΔH_i = k · Γ_i · (1 − S_H)

from hikari_ledger import HikariLedger

ledger = HikariLedger(n_nodes=50, seed=42)
result = ledger.run_cycle(n_blocks=100)

print(result["crep"])
# {'C': 0.553, 'R': 0.367, 'E': 0.541, 'P': 0.559, 'Gamma': 0.367}

print(result["accepted_blocks"])   # e.g. 98
print(result["hikari_total_supply"])  # e.g. 0.183
print(result["crep_gini"])          # e.g. 0.24  (fair distribution)

# Simulate a Byzantine attack
ledger_byz = HikariLedger(n_nodes=50, byzantine_fraction=0.30, seed=0)
result_byz = ledger_byz.run_cycle(n_blocks=100)
# System tolerates up to 33% Byzantine nodes (BFT guarantee)

# Validate a block from external CREP states
accepted = ledger.validate_block(
    block_data={"tx": "payment-001"},
    node_crep_states=[{"Gamma": 0.4}, {"Gamma": 0.35}, {"Gamma": 0.25}]
)

Proof-of-Resonance vs. Classical Consensus

Mechanism	Energy	Fairness	Sybil Resistance	CREP Integration
Proof-of-Work	Very high	Low (ASIC bias)	Strong	None
Proof-of-Stake	Low	Medium	Moderate	None
Proof-of-Resonance	~1000× lower than PoW	High (Gini ≈ 0.30)	CREP-based	Native

---

CREP Criticality Spectrum (context)

Domain	Package	Γ	Regime
Qubit decoherence	P24	0.050	Quantum fragile
Apoptosis ATP threshold	P25	0.090	Cellular critical
Theta band (flow state)	P27	0.251	Cognitive resonance
AMOC / Neural criticality	P18/20	0.251	Homeostatic universal
BTW Sandpile	P22	0.296	Classical SOC
epi-sigillin	P28	dynamic	Meta-level CREP modulator
Proof-of-Resonance	P29	0.367	Distributed consensus
Diffusive Routing	P30	0.443	Network infrastructure
ERA5 Arctic Ice	Core	0.920	Near-saturated

---

Package 30 — diffusive-routing

Implements an entropy-minimizing network routing protocol where data packets flow along paths of minimum entropic resistance — analogous to how gases flow into low-pressure regions. The resistance field evolves via Turing reaction-diffusion; the S_A/S_V duality provides the variational routing objective.

Gemini's insight: "Datenpakete fließen dynamisch wie ein Gas in Bereiche mit geringem entropischen Widerstand — die Theorie der S_A/S_V Entropie-Dualität auf Netzwerk-Infrastruktur."

Γ_routing ≈ 0.443 — η = 0.75 (optimal throughput), σ = 2.2

from diffusive_routing import DiffusiveRouting

dr = DiffusiveRouting(n_nodes=20, seed=42)
result = dr.run_cycle(duration_seconds=60.0, n_packets=10000)

print(result["crep"])
# {'C': 0.712, 'R': 0.881, 'E': 0.743, 'P': 0.661, 'Gamma': 0.441}

print(result["mean_throughput"])      # e.g. 0.964
print(result["load_gini"])            # e.g. 0.12  (even load distribution)
print(result["network_lagrangian"])   # L_net = S_V(dst) - S_A(path)

# Route a single packet and inspect the path
info = dr.route_packet(src=0, dst=15)
print(info["path"])     # [0, 3, 11, 15]
print(info["latency"])  # entropic resistance along path

# Inspect the resistance field
dr.visualise_resistance_field()

Entropic Resistance Field

Each link (i, j) carries a resistance that evolves dynamically:

ρ_ij(t) = baseline / (1 + Γ_ij · utilisation_coherence)

The field then diffuses via Turing reaction-diffusion:

dρ_ij/dt = D · ∇²ρ_ij − k · Γ_ij · ρ_ij + f(load_ij)

Packets route along argmin Σ ρ_ij — minimum total entropic resistance.

S_A / S_V Entropy Duality

Symbol	Meaning	Role
S_A(path)	Action entropy = Σ ρ_ij along path	Routing cost — minimised
S_V(node)	Volume entropy = H(outgoing load distribution)	Balance — maximised
L_net	Network Lagrangian = S_V(dst) − S_A	Unified routing objective

Routing vs. Classical Protocols

Protocol	Adapts to load	Entropic field	S_A/S_V duality	CREP integration
OSPF (static)	No	None	None	None
ECMP	Partial	None	None	None
Diffusive Routing	Yes (100ms)	Turing RD	Native	Full

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Install

pip install theta-resonance          # packages 27, 28, 29, 30
# with MNE-Python for real EDF data:
pip install "theta-resonance[mne]"

Diamond-Template Contract

All GenesisAeon packages implement this interface:

# Package 27
sys = ThetaResonance()
sys.run_cycle()        # → dict
sys.get_crep_state()   # → {C, R, E, P, Gamma}
sys.get_utac_state()   # → {H, dH_dt, H_star, K_eff}
sys.get_phase_events() # → list (cognitive state transitions)
sys.to_zenodo_record() # → dict

# Package 28
epi = EpiSigillin()
epi.run_cycle()        # → dict
epi.get_crep_state()   # → {C, R, E, P, Gamma}  (epigenetically modified)
epi.get_utac_state()   # → {H, dH_dt, H_star, K_eff}
epi.get_phase_events() # → list (entropy threshold crossings)
epi.to_zenodo_record() # → dict
epi.methylation_state()       # → {M_C, M_R, M_E, M_P}
epi.mutate_yaml(path, level)  # → mutated params dict
epi.inherit_from(parent)      # → 50% epigenetic inheritance

# Package 29
ledger = HikariLedger()
ledger.run_cycle()             # → dict
ledger.get_crep_state()        # → {C, R, E, P, Gamma}
ledger.get_utac_state()        # → {H, dH_dt, H_star, K_eff}
ledger.get_phase_events()      # → list (consensus failures, forks)
ledger.to_zenodo_record()      # → dict
ledger.validate_block(data, node_crep_states)  # → bool
ledger.mint_hikari(node_id)    # → float (Hikari earned)
ledger.network_crep_mean()     # → float

# Package 30
dr = DiffusiveRouting()
dr.run_cycle()                     # → dict
dr.get_crep_state()                # → {C, R, E, P, Gamma}
dr.get_utac_state()                # → {H, dH_dt, H_star, K_eff}
dr.get_phase_events()              # → list (congestion collapses, reroutes)
dr.to_zenodo_record()              # → dict
dr.route_packet(src, dst)          # → dict (path, latency, delivered)
dr.visualise_resistance_field()    # print resistance table

Repository Structure

theta-resonance/
├── src/
│   ├── theta_resonance/           # Package 27
│   │   ├── system.py              # ThetaResonance — Diamond interface
│   │   ├── band_filter.py
│   │   ├── pac_analysis.py        # Phase-Amplitude Coupling (Tort 2010)
│   │   ├── cognitive_state.py
│   │   ├── crep_bands.py
│   │   ├── flow_detector.py
│   │   ├── frequency_utac.py
│   │   ├── mne_interface.py
│   │   ├── benchmark.py
│   │   └── constants.py
│   └── epi_sigillin/              # Package 28
│       ├── system.py              # EpiSigillin — Diamond interface
│       ├── methylation.py         # CREPMethylationEngine
│       ├── histone_model.py       # Histone modification analogy
│       ├── yaml_mutator.py        # RuntimeYAMLMutator (thread-safe)
│       ├── entropy_monitor.py     # Real-time entropy tracker
│       ├── adaptation_memory.py   # EpigeneticMemory (50% inheritance)
│       ├── crep_epigenome.py      # Combined methylation + histone CREP
│       ├── sigillin_bridge.py     # Static YAML parameter interface
│       ├── benchmark.py
│       └── constants.py
│   └── hikari_ledger/             # Package 29
│       ├── system.py              # HikariLedger — Diamond interface
│       ├── node.py                # ValidatorNode with CREP state
│       ├── consensus.py           # ProofOfResonanceConsensus engine
│       ├── crep_validator.py      # Per-node CREP weight computation
│       ├── block.py               # Block with CREP metadata
│       ├── network.py             # P2P NetworkSimulator
│       ├── bft_fallback.py        # Equal-weight BFT for low-CREP nets
│       ├── hikari_currency.py     # HikariCurrencyMinter
│       ├── benchmark.py
│       └── constants.py
│   └── diffusive_routing/         # Package 30
│       ├── system.py              # DiffusiveRouting — Diamond interface
│       ├── network_graph.py       # NetworkGraph (ring + Erdős–Rényi topology)
│       ├── entropy_field.py       # EntropicResistanceField (ρ_ij computation)
│       ├── packet.py              # Packet with CREP metadata
│       ├── router.py              # DiffusiveRouter (Dijkstra on ρ_ij)
│       ├── crep_network.py        # Per-link + aggregate CREP evaluation
│       ├── reaction_diffusion.py  # Turing RD field evolution
│       ├── sa_sv_duality.py       # S_A / S_V entropy duality
│       ├── benchmark.py
│       └── constants.py
├── src/diamond_setup/             # Template engine for new repos
│   └── templates/
│       ├── minimal.py             # (includes AGENT.md auto-copy)
│       └── genesis.py             # (includes AGENT.md auto-copy)
├── data/
├── tests/
├── .zenodo.json
└── AGENT.md                       # GenesisAeon release & metadata rules

References

Package 27: Hengen, K.B. & Shew, W.L. (2025). Is criticality a unified setpoint of brain function? Neuron 113(16), 2582–2598. DOI: 10.1016/j.neuron.2025.05.020

Frontiers Comp. Neurosci. (2026). E-I balance, avalanches, and criticality. DOI: 10.3389/fncom.2026.1744991

Package 28: Greenberg, M.V.C. & Bourc'his, D. (2019). The diverse roles of DNA methylation in mammalian development. Nature Reviews Molecular Cell Biology 20, 590–607. DOI: 10.1038/s41580-019-0160-9

Allis, C.D. & Jenuwein, T. (2016). The molecular hallmarks of epigenetic control. Nature Reviews Genetics 17, 487–500.

Package 29: Nakamoto, S. (2008). Bitcoin: A Peer-to-Peer Electronic Cash System.

Castro, M. & Liskov, B. (1999). Practical Byzantine Fault Tolerance. OSDI '99. [USENIX]

Gemini (2026). GenesisAeon Assessment — Hikari Currency & Proof-of-Resonance Concept. MOR Research Collective internal assessment.

Package 30: Turing, A.M. (1952). The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B 237(641), 37–72. DOI: 10.1098/rstb.1952.0012

Bianconi, G. (2021). Higher-Order Networks. Cambridge University Press.

Gemini (2026). GenesisAeon Assessment — Diffusive Routing & S_A/S_V Entropy Duality Concept. MOR Research Collective internal assessment.

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Citation

@software{Roemer2026_theta_epi,
  author    = {Römer, Johann},
  title     = {{theta-resonance + epi-sigillin + hikari-ledger + diffusive-routing: GenesisAeon Packages 27--30}},
  year      = {2026},
  version   = {1.0.0},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.19645351},
  url       = {https://doi.org/10.5281/zenodo.19645351}
}

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