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b9161a8ea5
3 domain expert agents built the quintuplet consensus system:
AGENT 1 — DistributedSystemsExpert: quintuplet_consensus.py
- ByzantineConsensus: 5-way agreement, 2-fault tolerance
- Checkpoint: immutable receipt with SHA-256 hash linking
- DAG: directed acyclic graph with topological sort
- Fault classification: CRASH, BIT_FLIP, DETERMINISM_FAILURE,
STEALTH_FAULT, GÖDEL_BOUNDARY, FAMM_CORRUPTION
- Demo: all 6 fault types correctly detected, 4/5 clique found
AGENT 2 — ManifoldVerifier: manifold_verifier.py
- Fisher-Rao metric: g_ij = δ_ij/p_i + 1/p_8 on Δ₇
- Fisher distance: Bhattacharyya angle arccos(Σ√(pᵢqᵢ))
- Geodesic verification: coplanarity test on S⁷
- Stealth fault detection: DAG-agree + manifold-diverge
- Demo: 4 honest pass, 1 byzantine detected, stealth caught
AGENT 3 — LatticeImplementer: silversight_lattice.py
- SilverSightLattice: main engine integrating all components
- FAMMBank: delay-line memory with LWMA-1 guidance
- PhiCorkscrew: per-watchdog geodesic walk
- FisherGeometry: S⁷ ↔ Δ₇ conversions
- Demo: 10 iterations, 90% consensus, 9 checkpoints,
chain verified, FAMM stabilized
Architecture (ℒ Lattice emulation):
5 watchdogs = miners doing Φ-corkscrew PoW
DAG checkpoints = blocks in chain
FAMM guidance = per-iteration difficulty adjustment
Fisher-Chentsov = post-quantum lattice metric
4/5 consensus = 2-fault Byzantine tolerance
Perpetual emission = never stops computing
Refs: SILVERSIGHT_LATTICE.md (architecture),
EXPERIMENT_RADIAL_SELF_FIND.md (experiment),
PHI_CORKSCREW_PERFECT_RECOVERY.md (encoding)
846 lines
30 KiB
Python
846 lines
30 KiB
Python
"""
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MANIFOLD VERIFICATION — SilverSight Lattice Quintuplet Watchdog
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================================================================
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Verifies that 5 watchdog processes running Φ-corkscrew computation on
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the Fisher manifold S⁷ are actually on the SAME GEODESIC after reaching
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Byzantine consensus on a checkpoint.
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Mathematical Framework
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----------------------
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- State space: Δ₇ (7-simplex of 8 Hachimoji probabilities)
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p ∈ Δ₇ ⟺ p_i ≥ 0, Σᵢ pᵢ = 1 for i ∈ {0, ..., 7}
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- Fisher-Rao metric on Δ₇:
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gᵢⱼ(p) = δᵢⱼ/pᵢ + 1/p₇ for i,j ∈ {0, ..., 6}
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(using indices 0..6 with p₇ = 1 − Σᵢ₌₀⁶ pᵢ as the dependent coordinate)
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- √p-coordinate embedding (Chentsov):
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xᵢ = √pᵢ for i ∈ {0, ..., 7}
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This maps Δ₇ → S⁷₊ (positive octant of the 7-sphere)
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The Fisher metric becomes the ROUND metric on S⁷.
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- Geodesics: great circles on S⁷ (intersections of S⁷ with 2-planes
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through the origin).
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- Bhattacharyya / Fisher distance:
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d(p, q) = arccos( Σᵢ₌₀⁷ √(pᵢ qᵢ) )
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This is the great-circle arc length on S⁷ in √p coordinates.
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Core Insight for Verification
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-----------------------------
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Processes can agree on a checkpoint (similar DAGs) while being on
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different geodesics. This is the STEALTH FAULT — the most dangerous
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failure mode. To detect it, we verify that all agreeing processes lie
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on the same great circle of S⁷.
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A set of points {x⁽ᵏ⁾} on S⁷ lies on a single great circle iff all
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x⁽ᵏ⁾ are contained in a common 2-plane through the origin, i.e.
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rank[x⁽⁰⁾ | x⁽¹⁾ | ... ] ≤ 2.
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Equivalently: every x⁽ᵏ⁾ is orthogonal to the (ℓ-2)-dimensional normal
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space of the plane spanned by the first two independent vectors.
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Author: Lattice Watchdog Geometric Verification Module
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License: Internal — SilverSight Consensus Stack
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"""
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from __future__ import annotations
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__all__ = [
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"fisher_rao_metric",
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"fisher_distance",
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"geodesic_point",
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"verify_same_geodesic",
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"verify_geodesic_consistency",
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"detect_stealth_fault",
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"is_valid_probability",
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"to_sqrt_sphere",
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"from_sqrt_sphere",
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"great_circle_plane",
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"angular_deviation_from_plane",
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]
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import math
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from typing import List, Tuple
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import numpy as np
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# ---------------------------------------------------------------------------
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# Constants
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# ---------------------------------------------------------------------------
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DIM_SIMPLEX: int = 7 # 7-simplex Δ₇
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N_PROBS: int = 8 # 8 probabilities p₀ … p₇
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PHI: float = (1.0 + math.sqrt(5.0)) / 2.0
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GOLDEN_ANGLE_RAD: float = 2.0 * math.pi / (PHI ** 2)
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EPS: float = 1e-12 # numerical zero
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# ===========================================================================
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# 1. Probability / Manifold utilities
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# ===========================================================================
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def is_valid_probability(p: np.ndarray) -> bool:
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"""Check whether *p* is a point on Δ₇ (non-negative, sums to 1)."""
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p = np.asarray(p, dtype=float)
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if p.shape != (N_PROBS,):
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return False
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if np.any(p < -EPS):
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return False
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if abs(p.sum() - 1.0) > 1e-9:
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return False
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return True
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def to_sqrt_sphere(p: np.ndarray) -> np.ndarray:
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"""Embed Δ₇ → S⁷ via the Chentsov map xᵢ = √pᵢ.
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Returns a unit vector in ℝ⁸ because Σᵢ (√pᵢ)² = Σᵢ pᵢ = 1.
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"""
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p = np.asarray(p, dtype=float)
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assert is_valid_probability(p), "Input must lie on Δ₇"
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x = np.sqrt(np.maximum(p, 0.0))
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# Renormalise to protect against drift
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norm = np.linalg.norm(x)
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if norm > EPS:
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x = x / norm
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return x
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def from_sqrt_sphere(x: np.ndarray) -> np.ndarray:
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"""Inverse Chentsov map: S⁷ ∩ ℝ₊⁸ → Δ₇ via pᵢ = xᵢ²."""
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x = np.asarray(x, dtype=float)
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assert x.shape == (N_PROBS,), f"Expected shape {(N_PROBS,)}, got {x.shape}"
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p = x * x
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s = p.sum()
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if s > EPS:
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p = p / s
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return p
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# ===========================================================================
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# 2. Fisher-Rao geometry
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# ===========================================================================
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def fisher_rao_metric(p: np.ndarray) -> np.ndarray:
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"""Compute the Fisher-Rao metric matrix at point *p* on Δ₇.
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Using the independent coordinates {p₀, …, p₆} with
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p₇ = 1 − Σᵢ₌₀⁶ pᵢ, the metric components are
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gᵢⱼ = δᵢⱼ / pᵢ + 1 / p₇ for i, j ∈ {0, …, 6}
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Parameters
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----------
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p : np.ndarray, shape (8,)
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A point on the 7-simplex (non-negative, sum = 1).
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Returns
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-------
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g : np.ndarray, shape (7, 7)
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The Fisher information matrix in the {p₀,…,p₆} coordinate basis.
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"""
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p = np.asarray(p, dtype=float)
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assert is_valid_probability(p), "fisher_rao_metric: p must be on Δ₇"
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p7 = p[-1] # dependent coordinate
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if p7 < EPS:
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raise ValueError("fisher_rao_metric: p₇ is too close to zero — metric singular")
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if np.any(p[:DIM_SIMPLEX] < EPS):
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raise ValueError("fisher_rao_metric: some pᵢ too close to zero — metric singular")
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# g_ij = δ_ij / p_i + 1 / p_7
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g = np.eye(DIM_SIMPLEX, dtype=float) / p[:DIM_SIMPLEX][:, None]
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g += 1.0 / p7
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return g
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def fisher_distance(p: np.ndarray, q: np.ndarray) -> float:
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"""Fisher-Rao distance between two points on Δ₇.
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In √p coordinates this is the great-circle arc length on S⁷:
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d(p, q) = arccos( Σᵢ₌₀⁷ √(pᵢ qᵢ) )
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The result lies in [0, π]. For nearby points this is ≈ the chord
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length; for antipodal points on the sphere it equals π.
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Parameters
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----------
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p, q : np.ndarray, shape (8,)
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Two points on Δ₇.
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Returns
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-------
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float
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The Fisher-Rao / Bhattacharyya angle between *p* and *q*.
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"""
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p = np.asarray(p, dtype=float)
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q = np.asarray(q, dtype=float)
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assert is_valid_probability(p), "fisher_distance: p must be on Δ₇"
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assert is_valid_probability(q), "fisher_distance: q must be on Δ₇"
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# Bhattacharyya coefficient: BC = Σ √(pᵢ qᵢ)
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# This is exactly the Euclidean inner product of √p and √q on S⁷.
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bc = np.sum(np.sqrt(np.maximum(p * q, 0.0)))
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# Numerical guard: clamp to [-1, 1] before arccos
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bc = float(np.clip(bc, -1.0, 1.0))
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return math.acos(bc)
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# ===========================================================================
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# 3. Geodesic operations on S⁷
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# ===========================================================================
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def geodesic_point(p: np.ndarray, d: np.ndarray, t: float) -> np.ndarray:
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"""Point at Fisher distance *t* along the geodesic from *p* in direction *d*.
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On S⁷ in √p coordinates geodesics are great circles, so we use the
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standard spherical exponential map:
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γ(t) = cos(t) · x + sin(t) · v̂
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where x = √p (unit vector on S⁷)
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and v̂ = projₓ(d) / |projₓ(d)| (tangent direction, normalised).
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The result is projected back from √p coordinates to Δ₇ via pᵢ = xᵢ².
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Parameters
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----------
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p : np.ndarray, shape (8,)
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Starting point on Δ₇.
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d : np.ndarray, shape (8,)
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Direction vector in the tangent space at *p* (in √p coordinates).
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This need NOT be normalised or exactly tangent — it is projected.
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t : float
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Distance along the geodesic (same units as fisher_distance).
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Use small *t* for local steps.
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Returns
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-------
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q : np.ndarray, shape (8,)
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The point on Δ₇ reached after walking distance *t*.
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"""
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p = np.asarray(p, dtype=float)
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d = np.asarray(d, dtype=float)
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assert is_valid_probability(p), "geodesic_point: p must be on Δ₇"
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assert d.shape == (N_PROBS,), f"geodesic_point: d must have shape {(N_PROBS,)}"
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x = to_sqrt_sphere(p) # unit vector on S⁷
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# Project *d* onto the tangent space TₓS⁷: remove radial component
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d_dot_x = float(d @ x)
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v = d - d_dot_x * x # now orthogonal to x
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v_norm = np.linalg.norm(v)
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if v_norm < EPS:
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# Direction is radial — stay at the same point
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return p.copy()
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v_hat = v / v_norm # unit tangent vector
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# Great circle formula on S⁷
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gamma_sqrt = math.cos(t) * x + math.sin(t) * v_hat
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# Renormalise (protect against drift)
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gamma_sqrt_norm = np.linalg.norm(gamma_sqrt)
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if gamma_sqrt_norm > EPS:
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gamma_sqrt = gamma_sqrt / gamma_sqrt_norm
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# Map back to Δ₇
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q = from_sqrt_sphere(gamma_sqrt)
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return q
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def great_circle_plane(x0: np.ndarray, x1: np.ndarray) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
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"""Compute the 2-plane in ℝ⁸ that contains the great-circle geodesic
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through two points *x0*, *x1* on S⁷.
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Returns
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-------
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u, v : np.ndarray, shape (8,)
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Orthonormal basis vectors spanning the geodesic plane.
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normal : np.ndarray, shape (8, 6)
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Matrix whose columns form an orthonormal basis of the normal
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space to the geodesic plane (so that a point *y* lies in the
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plane iff y @ normal ≈ 0).
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Raises
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------
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ValueError
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If *x0* and *x1* are antipodal (lie on opposite poles) or
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collinear, in which case the geodesic is not unique.
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"""
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x0 = np.asarray(x0, dtype=float)
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x1 = np.asarray(x1, dtype=float)
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# Normalise
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x0 = x0 / (np.linalg.norm(x0) + EPS)
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x1 = x1 / (np.linalg.norm(x1) + EPS)
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# Check for antipodal / collinear
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inner = float(x0 @ x1)
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if abs(abs(inner) - 1.0) < 1e-6:
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raise ValueError(
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"great_circle_plane: points are (anti)collinear — "
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"geodesic plane is not unique"
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)
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# First basis vector: x0
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u = x0.copy()
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# Second basis vector: Gram-Schmidt orthonormalise (x1 - proj_u(x1))
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v_raw = x1 - inner * u
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v_norm = np.linalg.norm(v_raw)
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if v_norm < EPS:
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raise ValueError("great_circle_plane: degenerate points")
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v = v_raw / v_norm
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# Normal space: orthonormal complement of span{u, v} in ℝ⁸
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basis = np.eye(N_PROBS, dtype=float)
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# Use QR decomposition on [u, v, e₀, e₁, …] and extract Q[:, 2:]
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M = np.column_stack([u, v, basis])
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Q, _ = np.linalg.qr(M)
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normal = Q[:, 2:] # shape (8, 6)
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return u, v, normal
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def angular_deviation_from_plane(
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x: np.ndarray,
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normal: np.ndarray,
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) -> float:
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"""Compute the angular deviation (in radians) of a point *x* on S⁷
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from the 2-plane defined by *normal* (columns = orthonormal basis
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of the normal space).
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A point lies exactly in the plane iff the deviation is 0.
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"""
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x = np.asarray(x, dtype=float)
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x = x / (np.linalg.norm(x) + EPS)
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# Components in the normal directions
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normal_comps = x @ normal # shape (6,)
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sin_theta = np.linalg.norm(normal_comps)
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sin_theta = float(np.clip(sin_theta, 0.0, 1.0))
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return math.asin(sin_theta)
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# ===========================================================================
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# 4. Core verification routines
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# ===========================================================================
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def verify_same_geodesic(
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positions: List[np.ndarray],
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threshold: float = 1e-4,
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check_coincidence: bool = True,
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) -> Tuple[bool, dict]:
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"""Verify that all *positions* lie on the same geodesic of S⁷.
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Algorithm
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---------
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1. Convert every position to √p coordinates (points on S⁷).
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2. Find the pair of points with maximal angular separation and use
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them to build the geodesic plane (numerically stable).
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3. Measure the angular deviation of every point from that plane.
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4. (Optional) Compute pairwise Fisher distances — this checks that
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processes are not just on the same geodesic but at the same
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checkpoint position.
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5. PASS iff (a) all angular deviations < *threshold*, AND
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(b) if *check_coincidence*: all pairwise Fisher
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distances < *threshold*.
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Parameters
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----------
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positions : list of np.ndarray, each shape (8,)
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Points on Δ₇ from the consensus clique (typically 4–5 points).
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threshold : float
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Maximum allowed deviation (radians for angle; also used for
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Fisher distance when *check_coincidence* is True).
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Default 1e-4 is ~0.006°.
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check_coincidence : bool
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If True (default), also require that all points are close to
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each other in Fisher distance — this is the right mode when
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the consensus clique should be at the SAME checkpoint.
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Set to False when checking coplanarity of points that may be
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legitimately spread along the same geodesic.
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Returns
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-------
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ok : bool
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True if all processes are on the same geodesic (and optionally
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at the same position), False otherwise.
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report : dict
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Detailed measurements: angular deviations, pairwise distances,
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and human-readable diagnostics.
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"""
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if len(positions) < 2:
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return False, {
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"error": "Need at least 2 points to define a geodesic",
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"n_points": len(positions),
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}
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# Validate and convert to √p coordinates
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sqrt_pts = []
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for idx, p in enumerate(positions):
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if not is_valid_probability(np.asarray(p)):
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return False, {"error": f"positions[{idx}] is not on Δ₇", "point": p}
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sqrt_pts.append(to_sqrt_sphere(p))
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# ------------------------------------------------------------------
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# 4a. Angular-deviation test (great-circle coplanarity)
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# ------------------------------------------------------------------
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angular_devs = []
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plane_info = {}
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angular_ok: bool | None = None
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max_angular_dev = math.inf
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# Find the pair of points with maximal angular separation to define
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# the plane — this is numerically more stable than using adjacent
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# points that may be nearly collinear.
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n_pts = len(sqrt_pts)
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best_pair = (0, min(1, n_pts - 1))
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best_sep = -1.0
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for i in range(n_pts):
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for j in range(i + 1, n_pts):
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sep = float(abs(sqrt_pts[i] @ sqrt_pts[j]))
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# We want points that are well-separated (inner product small)
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# but not antipodal (inner product ≈ -1).
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score = 1.0 - abs(sep) # 0 = collinear, 1 = orthogonal
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if score > best_sep and score > 1e-3:
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best_sep = score
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best_pair = (i, j)
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try:
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u, v, normal = great_circle_plane(sqrt_pts[best_pair[0]], sqrt_pts[best_pair[1]])
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plane_info = {
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"basis_u": u.tolist(),
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"basis_v": v.tolist(),
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"plane_from_pair": best_pair,
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}
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for idx, x in enumerate(sqrt_pts):
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dev = angular_deviation_from_plane(x, normal)
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angular_devs.append({
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"index": idx,
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"deviation_rad": float(dev),
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"deviation_deg": float(math.degrees(dev)),
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})
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max_angular_dev = max(d["deviation_rad"] for d in angular_devs)
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angular_ok = max_angular_dev < threshold
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except ValueError as exc:
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# Points are collinear / antipodal — fall back to distance-only
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angular_ok = None
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max_angular_dev = math.inf
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plane_info = {"error": str(exc)}
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# ------------------------------------------------------------------
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# 4b. Pairwise Fisher-distance test (redundant safety net)
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# ------------------------------------------------------------------
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n = len(positions)
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pairwise = []
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max_fisher_dist = 0.0
|
||
max_pair = (0, 0)
|
||
|
||
for i in range(n):
|
||
for j in range(i + 1, n):
|
||
d = fisher_distance(positions[i], positions[j])
|
||
pairwise.append({
|
||
"i": i,
|
||
"j": j,
|
||
"fisher_distance": float(d),
|
||
})
|
||
if d > max_fisher_dist:
|
||
max_fisher_dist = d
|
||
max_pair = (i, j)
|
||
|
||
distance_ok = max_fisher_dist < threshold
|
||
|
||
# ------------------------------------------------------------------
|
||
# 4c. Decide
|
||
# ------------------------------------------------------------------
|
||
if angular_ok is not None:
|
||
ok = angular_ok
|
||
if check_coincidence:
|
||
ok = ok and distance_ok
|
||
else:
|
||
# Degraded mode: angular test failed, fall back to distance
|
||
ok = distance_ok if check_coincidence else False
|
||
|
||
report = {
|
||
"verdict": "PASS" if ok else "FAIL",
|
||
"n_points": n,
|
||
"threshold": threshold,
|
||
"angular_test": {
|
||
"performed": angular_ok is not None,
|
||
"max_deviation_rad": float(max_angular_dev),
|
||
"max_deviation_deg": float(math.degrees(max_angular_dev)),
|
||
"details": angular_devs,
|
||
},
|
||
"distance_test": {
|
||
"max_fisher_distance": float(max_fisher_dist),
|
||
"max_pair": max_pair,
|
||
"pairwise": pairwise,
|
||
},
|
||
"plane": plane_info,
|
||
"same_geodesic": ok,
|
||
}
|
||
return ok, report
|
||
|
||
|
||
def verify_geodesic_consistency(
|
||
chain_0: List[np.ndarray],
|
||
chain_i: List[np.ndarray],
|
||
tolerance: float = 0.05,
|
||
) -> Tuple[bool, float]:
|
||
"""Verify that process *i* followed the same geodesic as process 0.
|
||
|
||
We compare the **step sizes** (Fisher distances between consecutive
|
||
checkpoints). If both processes traverse the same geodesic with the
|
||
same speed profile, the step-size sequences must match up to a
|
||
common scaling factor (clock drift).
|
||
|
||
Algorithm
|
||
---------
|
||
1. Compute step-size arrays:
|
||
s_0[k] = d(chain_0[k], chain_0[k+1])
|
||
s_i[k] = d(chain_i[k], chain_i[k+1])
|
||
2. Find the optimal ratio α that minimises |s_i − α·s_0|₂.
|
||
(This accounts for a constant clock-speed difference.)
|
||
3. Compute the maximum relative deviation after scaling.
|
||
4. PASS if max deviation < *tolerance* (default 5 %).
|
||
|
||
Parameters
|
||
----------
|
||
chain_0 : list of np.ndarray
|
||
Reference checkpoints from the leader process.
|
||
chain_i : list of np.ndarray
|
||
Checkpoints from process *i*.
|
||
tolerance : float
|
||
Maximum allowed relative deviation (default 5 % to account for
|
||
clock jitter and floating-point noise).
|
||
|
||
Returns
|
||
-------
|
||
ok : bool
|
||
True if the step-size profiles are consistent.
|
||
max_deviation : float
|
||
Maximum relative deviation between scaled step sequences.
|
||
"""
|
||
if len(chain_0) < 2 or len(chain_i) < 2:
|
||
return False, math.inf
|
||
|
||
# Compute step sizes
|
||
s_0 = np.array([fisher_distance(chain_0[k], chain_0[k + 1])
|
||
for k in range(len(chain_0) - 1)])
|
||
s_i = np.array([fisher_distance(chain_i[k], chain_i[k + 1])
|
||
for k in range(len(chain_i) - 1)])
|
||
|
||
min_len = min(len(s_0), len(s_i))
|
||
s_0 = s_0[:min_len]
|
||
s_i = s_i[:min_len]
|
||
|
||
# Filter out zero steps (shouldn't happen in normal operation)
|
||
mask = (s_0 > EPS) & (s_i > EPS)
|
||
if not np.any(mask):
|
||
return False, math.inf
|
||
|
||
s_0_f = s_0[mask]
|
||
s_i_f = s_i[mask]
|
||
|
||
# Optimal scale factor: minimise |s_i − α·s_0|² → α = (s_i·s_0)/(s_0·s_0)
|
||
alpha = float(s_i_f @ s_0_f) / float(s_0_f @ s_0_f)
|
||
if alpha < EPS or not np.isfinite(alpha):
|
||
return False, math.inf
|
||
|
||
# Relative deviation after scaling
|
||
rel_dev = np.abs(s_i_f - alpha * s_0_f) / (alpha * s_0_f + EPS)
|
||
max_deviation = float(np.max(rel_dev))
|
||
|
||
ok = max_deviation < tolerance
|
||
return ok, max_deviation
|
||
|
||
|
||
# ===========================================================================
|
||
# 5. Stealth-fault detection
|
||
# ===========================================================================
|
||
|
||
def detect_stealth_fault(
|
||
proposals: List[dict],
|
||
clique: List[int],
|
||
) -> Tuple[bool, dict]:
|
||
"""Detect the stealth fault: DAGs agree but manifold positions diverge.
|
||
|
||
After Byzantine consensus, the processes in *clique* have all
|
||
committed to the same checkpoint DAG. This routine extracts their
|
||
actual manifold positions from the *proposals* and verifies that
|
||
they are on the same geodesic.
|
||
|
||
Parameters
|
||
----------
|
||
proposals : list of dict
|
||
One dict per process. Each dict must contain a key
|
||
``'manifold_position'`` whose value is an np.ndarray of shape
|
||
(8,) on Δ₇, and optionally a key ``'dag_hash'`` for
|
||
cross-checking.
|
||
clique : list of int
|
||
Process indices that formed the consensus clique.
|
||
|
||
Returns
|
||
-------
|
||
stealth_detected : bool
|
||
True if the DAGs agree BUT the positions are NOT all on the
|
||
same geodesic (this is the attack / fault).
|
||
details : dict
|
||
Full diagnostic report.
|
||
"""
|
||
if len(clique) < 2:
|
||
return False, {"error": "Clique too small for geodesic check", "clique": clique}
|
||
|
||
# Extract positions of clique members
|
||
positions = []
|
||
missing = []
|
||
for pid in clique:
|
||
if pid < 0 or pid >= len(proposals):
|
||
missing.append(pid)
|
||
continue
|
||
prop = proposals[pid]
|
||
if "manifold_position" not in prop:
|
||
missing.append(pid)
|
||
continue
|
||
positions.append(np.asarray(prop["manifold_position"], dtype=float))
|
||
|
||
if missing:
|
||
return True, {
|
||
"stealth_detected": True,
|
||
"reason": "missing_positions",
|
||
"missing_processes": missing,
|
||
"clique": clique,
|
||
}
|
||
|
||
# Check DAG agreement (basic sanity)
|
||
dag_hashes = []
|
||
for pid in clique:
|
||
h = proposals[pid].get("dag_hash")
|
||
if h is not None:
|
||
dag_hashes.append(h)
|
||
|
||
dags_agree = len(set(dag_hashes)) <= 1 if dag_hashes else True
|
||
|
||
# Now the crucial test: are they on the same geodesic AND at the
|
||
# same checkpoint position? Use a slightly relaxed threshold for
|
||
# stealth detection because real processes have small clock jitter.
|
||
geodesic_ok, geo_report = verify_same_geodesic(
|
||
positions, threshold=1e-3, check_coincidence=True
|
||
)
|
||
|
||
stealth_detected = dags_agree and (not geodesic_ok)
|
||
|
||
details = {
|
||
"stealth_detected": stealth_detected,
|
||
"dags_agree": dags_agree,
|
||
"n_clique": len(clique),
|
||
"n_positions": len(positions),
|
||
"geodesic_report": geo_report,
|
||
}
|
||
|
||
if stealth_detected:
|
||
details["severity"] = "CRITICAL"
|
||
details["description"] = (
|
||
"STEALTH FAULT: Byzantine clique agreed on DAG but processes "
|
||
"are on DIFFERENT GEODESICS of S⁷. This is a manifold-level "
|
||
"equivocation attack — the processes appear consistent from "
|
||
"the consensus layer but diverge in the physical state space."
|
||
)
|
||
|
||
return stealth_detected, details
|
||
|
||
|
||
# ===========================================================================
|
||
# 6. Helpers for unit tests / demos
|
||
# ===========================================================================
|
||
|
||
def random_point_on_simplex(rng: np.random.Generator | None = None) -> np.ndarray:
|
||
"""Generate a uniformly random point on Δ₇ (Dirichlet(1,…,1))."""
|
||
rng = rng or np.random.default_rng()
|
||
p = rng.random(N_PROBS)
|
||
p = p / p.sum()
|
||
return p
|
||
|
||
|
||
def random_tangent_direction(x: np.ndarray, rng: np.random.Generator | None = None) -> np.ndarray:
|
||
"""Generate a random unit vector in the tangent space TₓS⁷."""
|
||
rng = rng or np.random.default_rng()
|
||
v = rng.standard_normal(N_PROBS)
|
||
v = v - (v @ x) * x # project onto tangent space
|
||
v_norm = np.linalg.norm(v)
|
||
if v_norm < EPS:
|
||
return random_tangent_direction(x, rng)
|
||
return v / v_norm
|
||
|
||
|
||
# ===========================================================================
|
||
# 7. Demonstration
|
||
# ===========================================================================
|
||
|
||
if __name__ == "__main__":
|
||
print("=" * 70)
|
||
print("MANIFOLD VERIFICATION — SilverSight Lattice Quintuplet Watchdog")
|
||
print("Fisher manifold S⁷ | Φ-corkscrew consensus verification")
|
||
print("=" * 70)
|
||
|
||
rng = np.random.default_rng(42)
|
||
|
||
# ------------------------------------------------------------------
|
||
# 7.1 Create a common geodesic (shared by 4 honest processes)
|
||
# ------------------------------------------------------------------
|
||
print("\n--- 1. Creating 4 honest processes on the SAME GEODESIC ---")
|
||
|
||
# Random starting point on Δ₇
|
||
p0 = random_point_on_simplex(rng)
|
||
x0 = to_sqrt_sphere(p0)
|
||
|
||
# Random tangent direction → defines a unique great circle
|
||
d_hat = random_tangent_direction(x0, rng)
|
||
|
||
# Walk 5 checkpoints along the great circle
|
||
N_CHECKPOINTS = 5
|
||
STEP_SIZE = 0.1 # Fisher distance per step
|
||
JITTER = 1e-5 # tiny clock jitter (small enough for clean tests)
|
||
|
||
honest_chains: List[List[np.ndarray]] = [[] for _ in range(4)]
|
||
|
||
for proc in range(4):
|
||
for k in range(N_CHECKPOINTS):
|
||
t = k * STEP_SIZE + rng.normal(0, JITTER)
|
||
# Great circle: γ(t) = cos(t)·x0 + sin(t)·d̂
|
||
x_t = math.cos(t) * x0 + math.sin(t) * d_hat
|
||
x_t = x_t / (np.linalg.norm(x_t) + EPS)
|
||
p_t = from_sqrt_sphere(x_t)
|
||
honest_chains[proc].append(p_t)
|
||
|
||
# Print first and last checkpoint for this process
|
||
p_first = honest_chains[proc][0]
|
||
p_last = honest_chains[proc][-1]
|
||
print(f" Process {proc}: d(p₀, p₄) = {fisher_distance(p_first, p_last):.6f}")
|
||
|
||
# ------------------------------------------------------------------
|
||
# 7.2 Verify all 4 honest processes are on the same geodesic
|
||
# ------------------------------------------------------------------
|
||
print("\n--- 2. Verifying SAME GEODESIC for honest processes ---")
|
||
|
||
latest_positions = [chain[-1] for chain in honest_chains]
|
||
ok, report = verify_same_geodesic(
|
||
latest_positions, threshold=1e-3, check_coincidence=True
|
||
)
|
||
|
||
print(f" Result: {'PASS ✓' if ok else 'FAIL ✗'}")
|
||
print(f" Max angular deviation: {report['angular_test']['max_deviation_deg']:.6f}°")
|
||
print(f" Max Fisher distance: {report['distance_test']['max_fisher_distance']:.8f}")
|
||
|
||
# ------------------------------------------------------------------
|
||
# 7.3 Verify geodesic consistency (step-size profiles match)
|
||
# ------------------------------------------------------------------
|
||
print("\n--- 3. Verifying GEODESIC CONSISTENCY (step-size profiles) ---")
|
||
|
||
for proc in range(1, 4):
|
||
ok_dev, max_dev = verify_geodesic_consistency(honest_chains[0], honest_chains[proc])
|
||
status = "PASS ✓" if ok_dev else "FAIL ✗"
|
||
print(f" Process {proc} vs 0: max_dev = {max_dev:.6f} ({status})")
|
||
|
||
# ------------------------------------------------------------------
|
||
# 7.4 Introduce a BYZANTINE process on a DIFFERENT GEODESIC
|
||
# ------------------------------------------------------------------
|
||
print("\n--- 4. Creating 1 BYZANTINE process on a DIFFERENT GEODESIC ---")
|
||
|
||
# Same starting point, but DIFFERENT tangent direction
|
||
d_byz = random_tangent_direction(x0, rng)
|
||
# Ensure it's actually different (not close to d_hat)
|
||
dot = abs(float(d_byz @ d_hat))
|
||
while dot > 0.3:
|
||
d_byz = random_tangent_direction(x0, rng)
|
||
dot = abs(float(d_byz @ d_hat))
|
||
|
||
byz_chain: List[np.ndarray] = []
|
||
for k in range(N_CHECKPOINTS):
|
||
t = k * STEP_SIZE + rng.normal(0, JITTER)
|
||
x_t = math.cos(t) * x0 + math.sin(t) * d_byz
|
||
x_t = x_t / (np.linalg.norm(x_t) + EPS)
|
||
byz_chain.append(from_sqrt_sphere(x_t))
|
||
|
||
p_byz_first = byz_chain[0]
|
||
p_byz_last = byz_chain[-1]
|
||
print(f" Byzantine: d(p₀, p₄) = {fisher_distance(p_byz_first, p_byz_last):.6f}")
|
||
print(f" Direction dot-product |honest · byz|: {dot:.4f} (low = different geodesic)")
|
||
|
||
# ------------------------------------------------------------------
|
||
# 7.5 Verify the mixed group (4 honest + 1 byzantine) FAILS
|
||
# ------------------------------------------------------------------
|
||
print("\n--- 5. Verifying mixed group (4 honest + 1 byzantine) ---")
|
||
|
||
mixed_positions = latest_positions + [byz_chain[-1]]
|
||
ok_mix, report_mix = verify_same_geodesic(
|
||
mixed_positions, threshold=1e-3, check_coincidence=True
|
||
)
|
||
|
||
print(f" Result: {'PASS ✓' if ok_mix else 'FAIL ✗'}")
|
||
print(f" Max angular deviation: {report_mix['angular_test']['max_deviation_deg']:.6f}°")
|
||
print(f" Max Fisher distance: {report_mix['distance_test']['max_fisher_distance']:.8f}")
|
||
|
||
if not ok_mix:
|
||
print(" → Byzantine process detected via manifold divergence!")
|
||
|
||
# ------------------------------------------------------------------
|
||
# 7.6 Detect STEALTH FAULT: DAGs agree but positions diverge
|
||
# ------------------------------------------------------------------
|
||
print("\n--- 6. STEALTH FAULT detection ---")
|
||
|
||
# Build mock proposals: all processes claim the same DAG hash
|
||
dag_hash = "checkpoint_42_deadbeef"
|
||
proposals = []
|
||
for proc in range(4):
|
||
proposals.append({
|
||
"dag_hash": dag_hash,
|
||
"manifold_position": honest_chains[proc][-1],
|
||
})
|
||
# Byzantine process claims the SAME DAG but is on a different geodesic
|
||
proposals.append({
|
||
"dag_hash": dag_hash,
|
||
"manifold_position": byz_chain[-1],
|
||
})
|
||
|
||
clique_all = [0, 1, 2, 3, 4] # all 5 appeared to agree
|
||
stealth_detected, details = detect_stealth_fault(proposals, clique_all)
|
||
|
||
print(f" DAGs agree: {details['dags_agree']}")
|
||
print(f" Same geodesic: {details['geodesic_report']['same_geodesic']}")
|
||
print(f" STEALTH DETECTED: {stealth_detected}")
|
||
if stealth_detected:
|
||
print(f" SEVERITY: {details['severity']}")
|
||
print(f" Description: {details['description']}")
|
||
|
||
# Now test the honest-only clique (should NOT detect stealth)
|
||
print("\n --- Honest-only clique (control) ---")
|
||
clique_honest = [0, 1, 2, 3]
|
||
stealth_h, details_h = detect_stealth_fault(proposals, clique_honest)
|
||
print(f" STEALTH DETECTED: {stealth_h} (expected False)")
|
||
if not stealth_h:
|
||
print(" → Control passed: honest clique correctly cleared.")
|
||
|
||
# ------------------------------------------------------------------
|
||
# 7.7 Summary
|
||
# ------------------------------------------------------------------
|
||
print("\n" + "=" * 70)
|
||
print("SUMMARY")
|
||
print("=" * 70)
|
||
honest_geo, _ = verify_same_geodesic(
|
||
latest_positions, threshold=1e-3, check_coincidence=True
|
||
)
|
||
print(f" Honest clique same-geodesic test: {'PASS ✓' if honest_geo else 'FAIL ✗'}")
|
||
print(f" Mixed clique same-geodesic test: {'FAIL ✓ (Byzantine caught)' if not ok_mix else 'PASS ✗'}")
|
||
print(f" Stealth fault on 5-process clique: DETECTED = {stealth_detected}")
|
||
print(f" Stealth fault on honest clique: DETECTED = {stealth_h} (should be False)")
|
||
print("=" * 70)
|