Merge pull request 'feat(third-door): #21 trajectory invariants + ADR-DAG embedding' (#35) from feat/third-door-trajectory-invariants-adr-dag into main

Third-Door #21: trajectory invariants + ADR-DAG Ψ(M) embedding; Python geometry authority.

core/adr/__init__.py

@@ -0,0 +1,23 @@
+"""ADR-DAG conformal embedding (R&D-Revised §2.4 / issue #21).
+
+Deterministic embedding of ADR markdown into Cl(4,1) bivector space and
+master-blade drift checks for proposal coherence.
+"""
+
+from core.adr.validator import (
+    AdrDagValidationError,
+    embed_adr_markdown,
+    master_architecture_blade,
+    proposal_drift,
+    simple_bivector_project,
+    validate_proposal_against_master,
+)
+
+__all__ = [
+    "AdrDagValidationError",
+    "embed_adr_markdown",
+    "master_architecture_blade",
+    "proposal_drift",
+    "simple_bivector_project",
+    "validate_proposal_against_master",
+]

core/adr/validator.py

@@ -0,0 +1,168 @@
+"""
+core/adr/validator.py
+
+ADR-DAG conformal embedding Ψ(M) (R&D-Revised §2.4 / #21).
+
+  SHA-256(M) → 10×3-byte segments → c_k ∈ [−1, 1]
+  → 10 basis bivectors (planes 6..15) → simple-bivector projection
+  → master blade = successive wedge of load-bearing ADR embeddings
+  → proposal drift = ‖B_p ∧ A_master‖
+
+Cross-check: does **not** reimplement GeometricDelta ABI validation
+(``core/abi/geometric_delta_validator.py``). This module embeds ADR text into
+geometry; that module validates GeometricDelta envelopes.
+"""
+
+from __future__ import annotations
+
+import hashlib
+from typing import Sequence
+
+import numpy as np
+
+from algebra.cl41 import N_COMPONENTS, geometric_product, grade_project
+
+_BIVECTOR_PLANES = tuple(range(6, 16))  # 10 planes
+_NEAR_ZERO = 1e-12
+_SIMPLE_G4_TOL = 1e-9
+
+
+class AdrDagValidationError(ValueError):
+    """Fail-closed refusal from ADR-DAG embedding / drift checks."""
+
+    def __init__(self, reason: str, **disclosure) -> None:
+        self.reason = reason
+        self.disclosure = dict(disclosure)
+        super().__init__(f"adr_dag refused [{reason}]: {self.disclosure}")
+
+
+def _grade_mass(v: np.ndarray) -> int:
+    for g in range(5, -1, -1):
+        if float(np.linalg.norm(grade_project(v, g))) > _NEAR_ZERO:
+            return g
+    return 0
+
+
+def multivector_wedge(A: np.ndarray, B: np.ndarray) -> np.ndarray:
+    """Grade-raising wedge approximation: grade-project of geometric product.
+
+    For pure blades this matches the outer product grade. Used for master-blade
+    assembly and drift (B_p ∧ A_master).
+    """
+    a = np.asarray(A, dtype=np.float64)
+    b = np.asarray(B, dtype=np.float64)
+    ga, gb = _grade_mass(a), _grade_mass(b)
+    target = min(5, ga + gb)
+    if target == 0:
+        return grade_project(geometric_product(a, b), 0)
+    return grade_project(geometric_product(a, b), target).astype(np.float64)
+
+
+def simple_bivector_project(B: np.ndarray) -> np.ndarray:
+    """Project a multivector generator onto a simple bivector.
+
+    Spec intent: pure grade-2 support that is *simple* (single plane). Pure
+    multiplane grade-2 has nontrivial ``⟨B B⟩₄``; we always collapse to the
+    dominant plane when more than one plane is occupied (deterministic).
+    """
+    arr = np.asarray(B, dtype=np.float64)
+    if arr.shape != (N_COMPONENTS,):
+        raise AdrDagValidationError("bad_shape", shape=tuple(arr.shape))
+    B2 = grade_project(arr, 2).astype(np.float64)
+    occupied = [i for i in _BIVECTOR_PLANES if abs(float(B2[i])) > _NEAR_ZERO]
+    if len(occupied) <= 1:
+        return B2
+    # Multiplane → dominant-plane collapse (simple by construction).
+    best_i = max(occupied, key=lambda i: abs(float(B2[i])))
+    out = np.zeros(N_COMPONENTS, dtype=np.float64)
+    out[best_i] = float(B2[best_i])
+    return out
+
+
+def embed_adr_markdown(markdown: str) -> np.ndarray:
+    """Ψ(M): deterministic SHA-256 → 10 bivector coefficients → simple project.
+
+    Identical markdown ⇒ identical 32-vector (replay pin).
+    """
+    if not isinstance(markdown, str):
+        raise AdrDagValidationError("not_str", type=type(markdown).__name__)
+    # Empty markdown is a valid document identity (still deterministic).
+    digest = hashlib.sha256(markdown.encode("utf-8")).digest()  # 32 bytes
+    B = np.zeros(N_COMPONENTS, dtype=np.float64)
+    for k, plane in enumerate(_BIVECTOR_PLANES):
+        # 3-byte segments; last 2 hash bytes unused (spec: 10×3=30).
+        chunk = digest[k * 3 : k * 3 + 3]
+        u = int.from_bytes(chunk, "big")  # 0 .. 2^24-1
+        c = (u / float(0xFFFFFF)) * 2.0 - 1.0  # [-1, 1]
+        B[plane] = c
+    return simple_bivector_project(B)
+
+
+def master_architecture_blade(
+    embeddings: Sequence[np.ndarray],
+) -> np.ndarray:
+    """Assemble load-bearing ADR embeddings into a master architecture blade.
+
+    Prefer successive wedge when non-degenerate; if a wedge step vanishes
+    (parallel simple planes after projection), fall back to algebraic sum of
+    simple bivectors so the master never fabricates a zero blade.
+    """
+    if not embeddings:
+        raise AdrDagValidationError("empty_master_set")
+    simples = [
+        simple_bivector_project(np.asarray(e, dtype=np.float64))
+        for e in embeddings
+    ]
+    wedge = simples[0].copy()
+    for i, e in enumerate(simples[1:], start=1):
+        w = multivector_wedge(wedge, e)
+        if float(np.linalg.norm(w)) > _NEAR_ZERO:
+            wedge = w
+        # else: parallel/collinear under wedge — keep prior wedge, continue
+    if float(np.linalg.norm(wedge)) > _NEAR_ZERO:
+        return wedge.astype(np.float64)
+    # Full wedge chain degenerate: superposition master (still deterministic).
+    acc = np.zeros(N_COMPONENTS, dtype=np.float64)
+    for e in simples:
+        acc = acc + e
+    if float(np.linalg.norm(acc)) < _NEAR_ZERO:
+        raise AdrDagValidationError("degenerate_master_blade", at_index=0)
+    return simple_bivector_project(acc)
+
+
+def proposal_drift(B_proposal: np.ndarray, A_master: np.ndarray) -> float:
+    """Drift = ‖B_p ∧ A_master‖ (Euclidean coeff norm of the wedge)."""
+    Bp = simple_bivector_project(np.asarray(B_proposal, dtype=np.float64))
+    Am = np.asarray(A_master, dtype=np.float64)
+    if Am.shape != (N_COMPONENTS,):
+        raise AdrDagValidationError("bad_master_shape", shape=tuple(Am.shape))
+    w = multivector_wedge(Bp, Am)
+    return float(np.linalg.norm(w))
+
+
+def validate_proposal_against_master(
+    proposal_markdown: str,
+    master_markdowns: Sequence[str],
+    *,
+    max_drift: float = 1.0,
+) -> tuple[bool, float, np.ndarray, np.ndarray]:
+    """Embed proposal + masters; return (ok, drift, B_p, A_master)."""
+    if not master_markdowns:
+        raise AdrDagValidationError("empty_master_set")
+    masters = [embed_adr_markdown(m) for m in master_markdowns]
+    A = master_architecture_blade(masters)
+    Bp = embed_adr_markdown(proposal_markdown)
+    d = proposal_drift(Bp, A)
+    ok = bool(d <= float(max_drift) + _NEAR_ZERO)
+    return ok, d, Bp, A
+
+
+__all__ = [
+    "AdrDagValidationError",
+    "embed_adr_markdown",
+    "master_architecture_blade",
+    "multivector_wedge",
+    "proposal_drift",
+    "simple_bivector_project",
+    "validate_proposal_against_master",
+]

core/physics/__init__.py

@@ -69,6 +69,14 @@ from core.physics.temporal_gate import (
 )
 from core.physics.self_authorship import AuthorshipProposal, SelfAuthorshipMiner
 from core.physics.wave_manifold import WaveManifold
+from core.physics.trajectory_invariants import (
+    TrajectoryAssessment,
+    TrajectoryInvariantError,
+    assess_trajectory,
+    energy_boundary_ok,
+    relative_holonomy,
+    trajectory_divergence,
+)
 
 __all__ = [
     "SalienceOperator", "SalienceMap", "FieldRegion",
@@ -99,4 +107,7 @@ __all__ = [
     "TemporalDecision", "TemporalVerdict",
     "AuthorshipProposal", "SelfAuthorshipMiner",
     "WaveManifold",
+    "TrajectoryAssessment", "TrajectoryInvariantError",
+    "assess_trajectory", "energy_boundary_ok",
+    "relative_holonomy", "trajectory_divergence",
 ]

core/physics/trajectory_invariants.py

@@ -0,0 +1,172 @@
+"""
+core/physics/trajectory_invariants.py
+
+Continuous-space trajectory invariants + zero-fabrication (R&D-Revised §2.2 / #21).
+
+Python geometry-first surface (algebra/*). A Ring-1 Rust port may later mirror
+this contract under ``core-rs``; this module is the behavioral source of truth.
+
+Invariants:
+  * Relative holonomy H(t) = V_i · reverse(V_{i+1})
+  * Divergence D = Σ log(1 + ‖H·reverse(H) − 1‖_F) · Δt  (discrete integral)
+  * Replay bound D < ε_trajectory
+  * Hamiltonian energy boundary E_exertion ≤ κ · E_sensory
+  * Zero-fabrication: refuse empty / non-closed trajectory steps
+"""
+
+from __future__ import annotations
+
+import math
+from dataclasses import dataclass
+from typing import Sequence
+
+import numpy as np
+
+from algebra.cl41 import N_COMPONENTS, geometric_product, reverse
+from algebra.versor import versor_condition, versor_unit_residual
+
+_CLOSURE_TOL = 1e-6
+_DEFAULT_EPS_TRAJECTORY = 1e-5
+_NEAR_ZERO = 1e-15
+
+
+class TrajectoryInvariantError(ValueError):
+    """Fail-closed refusal from trajectory invariant checks."""
+
+    def __init__(self, reason: str, **disclosure) -> None:
+        self.reason = reason
+        self.disclosure = dict(disclosure)
+        super().__init__(f"trajectory_invariant refused [{reason}]: {self.disclosure}")
+
+
+def _as_versor(V: np.ndarray, name: str) -> np.ndarray:
+    arr = np.asarray(V, dtype=np.float64)
+    if arr.shape != (N_COMPONENTS,):
+        raise TrajectoryInvariantError(
+            "bad_shape", name=name, shape=tuple(arr.shape)
+        )
+    cond = float(versor_condition(arr))
+    if cond >= _CLOSURE_TOL:
+        raise TrajectoryInvariantError(
+            "not_closed", name=name, versor_condition=cond
+        )
+    return arr
+
+
+def relative_holonomy(V1: np.ndarray, V2: np.ndarray) -> np.ndarray:
+    """H = V1 · reverse(V2) — relative transport between consecutive steps."""
+    a = _as_versor(V1, "V1")
+    b = _as_versor(V2, "V2")
+    return geometric_product(a, reverse(b)).astype(np.float64)
+
+
+def holonomy_unit_residual(H: np.ndarray) -> float:
+    """‖H · reverse(H) − 1‖_F (dual-checked via versor_unit_residual)."""
+    H_arr = np.asarray(H, dtype=np.float64)
+    if H_arr.shape != (N_COMPONENTS,):
+        raise TrajectoryInvariantError("bad_shape", name="H", shape=tuple(H_arr.shape))
+    r = float(versor_unit_residual(H_arr))
+    r_rev = float(versor_unit_residual(reverse(H_arr)))
+    return max(r, r_rev)
+
+
+def trajectory_divergence(
+    versors: Sequence[np.ndarray],
+    *,
+    dt: float = 1.0,
+) -> float:
+    """Discrete divergence integral D = Σ log(1 + residual(H_i)) · Δt.
+
+    Zero-fabrication: empty or single-step trajectories refused (no confabulated
+    path). Each step must be a closed unit versor.
+    """
+    if not versors:
+        raise TrajectoryInvariantError("empty_trajectory")
+    if len(versors) < 2:
+        raise TrajectoryInvariantError(
+            "trajectory_too_short", n=len(versors)
+        )
+    if float(dt) <= 0.0:
+        raise TrajectoryInvariantError("non_positive_dt", dt=float(dt))
+
+    closed = [_as_versor(v, f"versors[{i}]") for i, v in enumerate(versors)]
+    D = 0.0
+    for i in range(len(closed) - 1):
+        H = relative_holonomy(closed[i], closed[i + 1])
+        r = holonomy_unit_residual(H)
+        D += math.log1p(max(r, 0.0)) * float(dt)
+    return float(D)
+
+
+def energy_boundary_ok(
+    E_exertion: float,
+    E_sensory: float,
+    *,
+    kappa: float = 1.0,
+) -> bool:
+    """Hamiltonian energy boundary: E_exertion ≤ κ · E_sensory.
+
+    Refuse negative energies (zero-fabrication of free action).
+    """
+    ee = float(E_exertion)
+    es = float(E_sensory)
+    k = float(kappa)
+    if ee < -_NEAR_ZERO or es < -_NEAR_ZERO:
+        raise TrajectoryInvariantError(
+            "negative_energy", E_exertion=ee, E_sensory=es
+        )
+    if k < 0.0:
+        raise TrajectoryInvariantError("negative_kappa", kappa=k)
+    return ee <= k * es + _NEAR_ZERO
+
+
+@dataclass(frozen=True, slots=True)
+class TrajectoryAssessment:
+    """Result of assessing a finite trajectory against #21 invariants."""
+
+    divergence: float
+    within_replay_bound: bool
+    energy_ok: bool
+    n_steps: int
+    eps_trajectory: float
+    kappa: float
+    E_exertion: float
+    E_sensory: float
+
+
+def assess_trajectory(
+    versors: Sequence[np.ndarray],
+    *,
+    E_exertion: float,
+    E_sensory: float,
+    eps_trajectory: float = _DEFAULT_EPS_TRAJECTORY,
+    kappa: float = 1.0,
+    dt: float = 1.0,
+) -> TrajectoryAssessment:
+    """Full trajectory gate: divergence bound + energy boundary."""
+    D = trajectory_divergence(versors, dt=dt)
+    eps = float(eps_trajectory)
+    if eps <= 0.0:
+        raise TrajectoryInvariantError("non_positive_eps", eps_trajectory=eps)
+    e_ok = energy_boundary_ok(E_exertion, E_sensory, kappa=kappa)
+    return TrajectoryAssessment(
+        divergence=float(D),
+        within_replay_bound=bool(D < eps),
+        energy_ok=bool(e_ok),
+        n_steps=len(versors),
+        eps_trajectory=eps,
+        kappa=float(kappa),
+        E_exertion=float(E_exertion),
+        E_sensory=float(E_sensory),
+    )
+
+
+__all__ = [
+    "TrajectoryAssessment",
+    "TrajectoryInvariantError",
+    "assess_trajectory",
+    "energy_boundary_ok",
+    "holonomy_unit_residual",
+    "relative_holonomy",
+    "trajectory_divergence",
+]

docs/research/third-door-blueprint-fidelity.md

@@ -35,8 +35,8 @@
 | 4 | GoldTether residual + α law | Super §2.3, R&D §2.3/§5 | 🟢 residual+α + bootstrap gates + principal-axis prune (#24+#18) | #18 |
 | 5 | Grade-5 pseudoscalar invariant | Super §3.3 | ⚪ RETIRED — vacuous in odd-dim Cl(4,1) | #19 (closed) |
 | 6 | Surprise residual operator | Super §3.2 | 🟢 math + DiscoveryCandidate wiring landed (#26 + #31) | #20 |
-| 7 | Trajectory invariants + zero-fabrication | R&D §2.2 | ⚫ absent | #21 |
-| 8 | ADR-DAG conformal embedding | R&D §2.4 | ⚫ absent | #21 |
+| 7 | Trajectory invariants + zero-fabrication | R&D §2.2 | 🟢 Python geometry surface (`trajectory_invariants.py`) | #21 |
+| 8 | ADR-DAG conformal embedding | R&D §2.4 | 🟢 Python surface (`core/adr/validator.py`) | #21 |
 | W1 | WaveManifold unitary / sandwich step | ADR-0241 §2 | 🟢 | ADR-0241 |
 | W2 | Spectral leakage surprise | ADR-0241 §2.4B | 🟢 subsumed into `surprise_residual` | ADR-0241 |
 | W3 | Wave polar + multi-pair conjugacy | ADR-0241 §2.4A | 🟢 single polar + multi-pair thin wrap | ADR-0241 |
@@ -206,10 +206,23 @@ The null add-on is **untested**: `test_signature_aware_pca_keeps_nulls` classifi
 
 ---
 
-## 9. Absent whole proposals — ⚫ (#21)
+## 9. Trajectory invariants + ADR-DAG — 🟢 Python surfaces (#21)
 
-- **Trajectory invariants + zero-fabrication (R&D §2.2 → `core-rs/src/sensorimotor.rs`):** relative holonomy `H(t)=V₁Ṽ₂`, divergence integral `D < ε_trajectory`, Hamiltonian energy boundary `E_exertion ≤ κ·E_sensory`. Not landed. Gated by the Zig/Rust substrate doctrine (Ring-1 only).
-- **ADR-DAG conformal embedding (R&D §2.4 → `core/adr/validator.py`):** `Ψ(M)` = SHA-256 → 10 bivector coeffs → simple-bivector projection → master-blade wedge → drift check. Not landed. Cross-check `core/abi/geometric_delta_validator.py` before adding a parallel validator.
+> **Landed (2026-07-14):** geometry-first Python authorities. Rust Ring-1 port remains optional acceleration, not a second truth.
+
+### Trajectory invariants (R&D §2.2 → `core/physics/trajectory_invariants.py`)
+- Relative holonomy `H = V_i · reverse(V_{i+1})`
+- Divergence `D = Σ log(1 + ‖H reverse(H) − 1‖) · Δt`; bound `D < ε_trajectory`
+- Energy boundary `E_exertion ≤ κ · E_sensory`
+- Zero-fabrication: empty / short / non-closed steps refused
+- Tests: `tests/test_third_door_trajectory_invariants.py`
+
+### ADR-DAG conformal embedding (R&D §2.4 → `core/adr/validator.py`)
+- `Ψ(M)`: SHA-256 → 10×3-byte → `c_k ∈ [−1,1]` → planes 6..15 → simple-bivector project
+- Master blade = successive wedge of load-bearing ADR embeddings
+- Proposal drift = `‖B_p ∧ A_master‖`
+- Does **not** parallel `core/abi/geometric_delta_validator.py` (that validates GeometricDelta ABI envelopes)
+- Tests: `tests/test_third_door_adr_dag_embedding.py`
 
 ---
 
@@ -297,7 +310,7 @@ PY
 - Durable holographic memory **vault store** (CRDT-backed standing-wave spectrum) — session registry only today.
 - Rust/MLX acceleration of exp-map / cross-spectral (ADR-0235 later).
 - Full ADR-0092 reviewer-service integration (promote remains caller-gated).
-- R&D #21 trajectory invariants + ADR-DAG embedding.
+- Optional Rust Ring-1 port of trajectory invariants (Python is authority today).
 
 ---
 
@@ -310,7 +323,7 @@ PY
 | GoldTether gold-set + harmonized residual + α=Φ(R) + bootstrap/prune — 🟢 | #18 |
 | Grade-5 pseudoscalar preservation gate — ⚪ RETIRED (vacuous; see §5) | #19 (closed) |
 | Surprise: metric projection + productivity polarity + DiscoveryCandidate wiring — 🟢 done | #20 (math #26; wiring #31) |
-| Absent proposals: sensorimotor + ADR-DAG | #21 |
+| Trajectory invariants + ADR-DAG embedding — 🟢 Python surfaces | #21 |
 | Wave-field substrate + operator subsumption (W1–W6) — 🟢 on branch | ADR-0241 |
 | `core_ha` deprecation — 🟢 no live tree + hygiene pin | ADR-0241 / deprecation plan |
 | Durable holographic vault spectrum — deferred | ADR-0241 follow-on |

tests/test_third_door_adr_dag_embedding.py

@@ -0,0 +1,98 @@
+"""#21 B — ADR-DAG conformal embedding Ψ(M) (R&D §2.4)."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from algebra.cl41 import grade_project
+from core.adr.validator import (
+    AdrDagValidationError,
+    embed_adr_markdown,
+    master_architecture_blade,
+    proposal_drift,
+    simple_bivector_project,
+    validate_proposal_against_master,
+)
+
+
+def test_embed_deterministic_replay():
+    m = "# ADR-TEST\n\nBody of the decision.\n"
+    a = embed_adr_markdown(m)
+    b = embed_adr_markdown(m)
+    assert np.array_equal(a, b)
+    assert a.shape == (32,)
+
+
+def test_embed_differs_for_different_markdown():
+    a = embed_adr_markdown("# ADR-A\nfoo")
+    b = embed_adr_markdown("# ADR-B\nbar")
+    assert not np.allclose(a, b)
+
+
+def test_embed_is_grade2_supported():
+    B = embed_adr_markdown("# ADR-G2\ncontent")
+    # After simple project: only grade-2 (and zeros elsewhere)
+    for g in (0, 1, 3, 4, 5):
+        assert float(np.linalg.norm(grade_project(B, g))) < 1e-12
+    assert float(np.linalg.norm(grade_project(B, 2))) > 0.0
+
+
+def test_simple_bivector_project_collapses_multiplane():
+    B = np.zeros(32, dtype=np.float64)
+    B[6] = 0.9
+    B[7] = 0.8
+    B[8] = 0.1
+    S = simple_bivector_project(B)
+    # Dominant plane kept
+    assert abs(S[6] - 0.9) < 1e-12 or abs(S[7] - 0.8) < 1e-12
+    # At most one plane nonzero after collapse when multiplane non-simple
+    n_planes = sum(1 for i in range(6, 16) if abs(S[i]) > 1e-12)
+    assert n_planes == 1
+
+
+def test_master_blade_refuses_empty():
+    with pytest.raises(AdrDagValidationError, match="empty"):
+        master_architecture_blade([])
+
+
+def test_master_blade_from_two_adrs():
+    e1 = embed_adr_markdown("# ADR-0003\nCoordinate dissolution.")
+    e2 = embed_adr_markdown("# ADR-0006\nField energy.")
+    A = master_architecture_blade([e1, e2])
+    assert A.shape == (32,)
+    assert float(np.linalg.norm(A)) > 0.0
+
+
+def test_proposal_drift_nonneg_and_deterministic():
+    masters = [
+        embed_adr_markdown("# M1\none"),
+        embed_adr_markdown("# M2\ntwo"),
+    ]
+    A = master_architecture_blade(masters)
+    Bp = embed_adr_markdown("# Proposal\nnew idea")
+    d1 = proposal_drift(Bp, A)
+    d2 = proposal_drift(Bp, A)
+    assert d1 == d2
+    assert d1 >= 0.0
+
+
+def test_validate_proposal_returns_ok_flag():
+    masters_md = ["# ADR-A\nalpha", "# ADR-B\nbeta"]
+    ok, drift, Bp, A = validate_proposal_against_master(
+        "# Proposal\ngamma", masters_md, max_drift=1e9
+    )
+    assert ok is True
+    assert drift >= 0.0
+    assert Bp.shape == (32,)
+    assert A.shape == (32,)
+
+
+def test_validate_proposal_tight_max_drift_can_fail():
+    masters_md = ["# ADR-A\nalpha", "# ADR-B\nbeta"]
+    ok, drift, _Bp, _A = validate_proposal_against_master(
+        "# Proposal\nentirely different body xyz", masters_md, max_drift=-1.0
+    )
+    # max_drift < 0 forces fail unless drift is negative (impossible)
+    assert ok is False
+    assert drift >= 0.0

tests/test_third_door_trajectory_invariants.py

@@ -0,0 +1,92 @@
+"""#21 A — trajectory invariants + zero-fabrication (R&D §2.2)."""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from algebra.rotor import make_rotor_from_angle
+from algebra.versor import versor_condition
+from core.physics.trajectory_invariants import (
+    TrajectoryInvariantError,
+    assess_trajectory,
+    energy_boundary_ok,
+    relative_holonomy,
+    trajectory_divergence,
+)
+
+
+def _id() -> np.ndarray:
+    v = np.zeros(32, dtype=np.float64)
+    v[0] = 1.0
+    return v
+
+
+def test_relative_holonomy_identity_pair_is_identity():
+    H = relative_holonomy(_id(), _id())
+    assert versor_condition(H) < 1e-6
+    assert abs(H[0] - 1.0) < 1e-9
+
+
+def test_relative_holonomy_order_sensitive():
+    A = make_rotor_from_angle(0.3, bivector_idx=6)
+    B = make_rotor_from_angle(0.9, bivector_idx=7)
+    H_ab = relative_holonomy(A, B)
+    H_ba = relative_holonomy(B, A)
+    assert not np.allclose(H_ab, H_ba, atol=1e-9)
+
+
+def test_trajectory_divergence_zero_on_constant_path():
+    path = [_id(), _id(), _id()]
+    assert trajectory_divergence(path) == 0.0
+
+
+def test_trajectory_divergence_positive_on_moving_path():
+    path = [
+        make_rotor_from_angle(0.1 * i, bivector_idx=6) for i in range(1, 6)
+    ]
+    D = trajectory_divergence(path)
+    assert D > 0.0
+
+
+def test_trajectory_divergence_deterministic():
+    path = [make_rotor_from_angle(0.2 * i) for i in range(1, 4)]
+    assert trajectory_divergence(path) == trajectory_divergence(path)
+
+
+def test_trajectory_divergence_refuses_empty_and_short():
+    with pytest.raises(TrajectoryInvariantError, match="empty"):
+        trajectory_divergence([])
+    with pytest.raises(TrajectoryInvariantError, match="too_short"):
+        trajectory_divergence([_id()])
+
+
+def test_trajectory_divergence_refuses_non_closed():
+    dirty = np.zeros(32, dtype=np.float64)
+    dirty[0] = 0.5
+    dirty[1] = 0.5
+    with pytest.raises(TrajectoryInvariantError, match="not_closed"):
+        trajectory_divergence([_id(), dirty])
+
+
+def test_energy_boundary_ok_and_refuse_negative():
+    assert energy_boundary_ok(1.0, 2.0, kappa=1.0) is True
+    assert energy_boundary_ok(3.0, 2.0, kappa=1.0) is False
+    assert energy_boundary_ok(3.0, 2.0, kappa=2.0) is True
+    with pytest.raises(TrajectoryInvariantError, match="negative_energy"):
+        energy_boundary_ok(-0.1, 1.0)
+
+
+def test_assess_trajectory_replay_bound():
+    path = [make_rotor_from_angle(0.05 * i) for i in range(1, 4)]
+    a = assess_trajectory(
+        path, E_exertion=0.5, E_sensory=1.0, eps_trajectory=1.0, kappa=1.0
+    )
+    assert a.energy_ok is True
+    assert a.n_steps == 3
+    assert a.divergence >= 0.0
+    # Tight eps → may fail replay bound on moving path
+    tight = assess_trajectory(
+        path, E_exertion=0.5, E_sensory=1.0, eps_trajectory=1e-30, kappa=1.0
+    )
+    assert tight.within_replay_bound is False