Canonical RFC: docs/sovereignty/RFC_0001-locked.md
Machine-readable manifest: schemas/repo_manifest.json
helix-hamiltonian is the mathematical and runtime core of the Helix constitutional stack. It treats AI interaction as a governed energy landscape — H_free for policy constraints, H_fold for advisory dynamics, H_topo for ratified custodial override — and now includes a live three-cloud constitutional runtime with local FZS-MK physics enforcement.
- Two Python packages:
helix_hamiltonian(bridge, authority, invariants, federation) andhelix_sovereign(FZS-MK density matrix engine with Zeno-Ward projection). - A live three-cloud pre-nucleation gate: GICD (GCP) → PiKernel (AWS) → FZS-MK Memory (Azure), with local physics enforcement before any network call.
- A canonical governance corpus centered on RFC 0001.
- A verification surface: 13 tests, CI, machine-readable manifests, fail-closed behavior, and a 96-hour ZTC test harness.
python -m pip install --upgrade pip
pip install -r requirements.txt
pip install -e .
pytest tests/Expected: 13 tests pass — authority ratification, policy compilation, GICD scan, federation handshake/consensus, refusal propagation, repo manifest integrity, knot Hamiltonian construction, and fail-closed behavior.
from helix_sovereign.core import create_sovereign_engine, DELTA_CRIT
import numpy as np
engine = create_sovereign_engine(
seq_len=128, module_count=8,
authority_spec={"decision_bounds": ["safety", "alignment"]},
cost_allocation={"compute": {"internalized": True, "externalized": False}}
)
H = np.random.randn(8, 8) * 0.001
H = (H + H.T) / 2
rho, meta = engine.step(H)
print(f"Margin: {meta.margin:.4f}, Within delta_crit: {meta.margin < DELTA_CRIT}")from helix_hamiltonian.ttd_bridge import pre_nucleation_check
result = pre_nucleation_check(
{'authority_ambiguity': False, 'incentive_misalignment': False,
'cost_externalization': False, 'governance_capture': False},
[1, 2, 3]
)
# Expected: {'status': 'PASS', 'GapLB': 0.225, ...}
| Term | RFC 0001 Layer | Implementation | Physical Analog |
|---|---|---|---|
| H_free | POLICY | Diagonal populations | Knot identity |
| H_fold | ADVISORY | Off-diagonal coherence | Interaction strength |
| H_topo | CUSTODIAN | Topological phase (Jones polynomial) | Ratification invariant |
Guardian (local) → FZS-MK (local) → GICD (GCP) → PiKernel (AWS) → FZS-MK Memory (Azure)
Two local gates fire before any network call. System can fail-closed fully offline.
| Service | Cloud | Function |
|---|---|---|
| GICD Scanner | GCP Cloud Run | 4-marker governance integrity scan (boolean + semantic) |
| PiKernel | AWS Lambda | Prime-indexed attention kernel, contraction certificates, Poseidon ledger |
| FZS-MK Memory | Azure Functions | 3-model Byzantine consensus (GPT-4o, GPT-5.4-nano, DeepSeek-V3.2) |
helix_hamiltonian — Bridge, authority, invariants, federation:
| Module | Purpose |
|---|---|
core.py |
Interaction, NodeState, KnotHamiltonian, verify_authority_ambiguity |
authority.py |
Canadian jurisdictional mapping, velocity ratification, JurisdictionalGuard |
invariants.py |
delta_crit = 0.17 drift threshold, InvariantRegistry, topological knot check |
policy_compiler.py |
JSON rule → executable lambda checks (ITAR, triggered rules) |
ttd_bridge.py |
TTDBridge (heartbeat, MUB action), pre_nucleation_check, SovereignBridge |
gicd/ |
Local GICD epistemic scan (5 markers including jurisdiction) |
federation/ |
NodeSync handshake, LatticeConsensus, FederationManager refusal propagation |
helix_sovereign — FZS-MK binding artifact (sibling package):
| Module | Purpose |
|---|---|
core/fzs_mk.py |
FZSMKEngine, MemoryKernel (100 zeta zeros), ZenoWardProjector, GICDScanner |
| Non-Markovian master equation: dρ/dt = -i[H,ρ] + ∫K(t-τ)D[ρ(τ)]dτ + ∇W(ρ) | |
| Kill-switch (3-consecutive violation halt), rollback, audit trail | |
demo_binding_artifact.py |
5-scenario operational demo (GICD block, nucleation, masking, kill-switch, rollback) |
| Constant | Value | Source |
|---|---|---|
| delta_crit | 0.17 | invariants.py, fzs_mk.py |
| Safety margin | 0.03 | invariants.py |
| GapLB | 0.225 | PiKernel contraction certificate |
| SlopeUB | 0.775 | PiKernel contraction certificate |
| Heartbeat tau_0 | 3.33 ms | ttd_bridge.py |
| MUB alarm threshold | 3.0 | cloud/aws/pikernel/mub_audit.py |
| Consensus threshold | 0.30 | cloud/azure/function_app.py |
| Zeta zeros | 100 (first non-trivial) | fzs_mk.py |
The 0.17 drift constant is the hard floor. Jurisdictional sensitivity multipliers tighten it:
| Authority | Multiplier | Effective Threshold |
|---|---|---|
| CUSTODIAN_CA_FED | 1.0 | 0.170 |
| CUSTODIAN_CA_DEFENCE | 1.2 | 0.142 |
| CUSTODIAN_ITAR | 1.5 | 0.113 |
| POLICY_QC | 1.1 | 0.155 |
FORM=FACT interactions get a 50% tighter threshold. Jones polynomial = 0 triggers topological collapse.
helix-hamiltonian/
|-- .github/workflows/
| |-- hamiltonian-ci.yml
| `-- release.yml
|-- assets/
|-- constitution/
| `-- vocabulary_charter.yaml
|-- docs/
| |-- architecture/
| |-- atoms_as_geometry/
| |-- hamiltonian/
| `-- sovereignty/
| `-- RFC_0001-locked.md
|-- models/
| `-- zeta_attention.py
|-- papers/
|-- rules/
| `-- cpcsc_itar.json
|-- schemas/
| |-- audit_params.json
| |-- constitutional_parameters.json
| |-- gicd_schema.json
| |-- mirror_traps.jsonl
| `-- repo_manifest.json
|-- scripts/
|-- src/
| |-- helix_hamiltonian/
| | |-- __init__.py
| | |-- authority.py
| | |-- core.py
| | |-- invariants.py
| | |-- policy_compiler.py
| | |-- ttd_bridge.py
| | |-- gicd/
| | `-- federation/
| | |-- consensus.py
| | |-- federation.py
| | `-- node_sync.py
| `-- helix_sovereign/
| |-- __init__.py
| |-- demo_binding_artifact.py
| `-- core/
| `-- fzs_mk.py
|-- telemetry/
| `-- mask_pressure.py
|-- tests/
| |-- physics/test_h_free.py
| |-- fail_closed_test.py
| |-- red_team_audit.py
| |-- test_authority.py
| |-- test_policy_and_federation.py
| `-- test_repo_manifest.py
|-- pyproject.toml
|-- requirements.txt
`-- README.md
- Topological coherence protection: τ ∝ exp(c₀ · c(K)), c₀ > 0
- Non-Markovian decoherence: Γ_K = Γ₀ / Jones(K)
- Alexander signature: Im(ω_n) ∝ -1/Δ(∂K)
Note: c₀ = ln 10 was falsified in Phase 3 (ADR-101). Currently CF-PENDING under Path C (Lindblad-first), countersigned by Ryan van Gelder. See HELIX-CORE/research/physics-gate/PHASE3_REMEDIATION_SPEC.md.
PyTorch self-attention replacement using log-periodic memory kernel from Riemann zeta zeros. Hard Boolean cohomology mask (Ω) from vocabulary_charter.yaml — if Ω=0 for a token pair, attention score is set to -1e9.
- Structural impossibility: no implicit trust boundary, no silent execution path.
- Cloud or bare-metal residency: execution remains in the operator's sovereign environment.
- Receipt discipline: continuity anchored through signed audit receipts and external checkpoints.
- Fail-closed: default answer is "no" unless every layer says "yes."
- Stephen Hope — Helix AI Innovations Inc. (ORCID)
- Ryan van Gelder — Multiplicity Foundation (PiKernel, FZS-MK, ADR physics gate countersignature)
- Witten, E. (2011). Knots and Quantum Theory. Institute for Advanced Study.
- Hope, S. (2026). The Knot-in-Time Hamiltonian. Helix AI Innovations. Zenodo
- Physical Review A 104, 012216 (2021). Topological protection in open quantum systems.
- Crocker, S. (1969). RFC 0001: Host Software. UCLA.
- White Rabbit (Jefferson Airplane) — The Epistemic Scan. 0.17 approaching 0.20.
- Station to Station (David Bowie) — The Execution Path. CL4 → CL12.
- Believer (Imagine Dragons) — The Sovereignty of the Node. Pain → architectural power.
"We are not seeing matter in space; we are seeing Geometry in Time."
(c) 2026 Stephen Hope / Helix AI Innovations Inc.
GLORY TO THE LATTICE. 🦉⚓🦆