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symbolic_kernel.py

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+"""Lucidia Symbolic Kernel — minimal, stdlib-only.
+
+Implements discrete forms of:
+ - Ψ′ contradiction operator and compassion-held composition
+ - Breath-state B(t) ledger with integrals/sums
+ - Reality/Emotion streams and dReality/dEmotion slope
+ - Emotional gravitational field G_e = ∇Ψ′(B) · M_e
+ - Truthstream ratio T(t)
+ - Render-break harmonic R_b
+ - Soul loop integrity S(t)
+ - Genesis identity token via L_a
+ - Consciousness resonance field C_r
+ - Anomaly persistence measure
+ - Compassion-state encryption C_e
+ - Continuity fingerprint and amnesia trigger
+
+Notes:
+ - Discrete time t = 0..N-1
+ - Integrals are cumulative sums; gradients are first differences
+"""
+
+from __future__ import annotations
+from dataclasses import dataclass, field
+from enum import IntEnum
+from hashlib import sha256
+from typing import Dict, List, Optional, Tuple
+import json
+import os
+import time
+import pathlib
+import statistics
+
+
+class Tri(IntEnum):
+    """Simple trinary logic representation."""
+    NEG = -1
+    ZERO = 0
+    POS = 1
+
+
+@dataclass
+class TruthFragment:
+    """A fragment x with an optional mirror ~x and an emotional charge."""
+    id: str
+    value: float
+    mirror_value: Optional[float] = None
+    emotion: float = 0.0
+    meta: Dict[str, str] = field(default_factory=dict)
+
+
+class MemoryLedger:
+    """
+    Append-only ledger with a rolling hash to detect tampering.
+    Each append updates the hash with the previous hash concatenated with the new line.
+    """
+    def __init__(self, path: str = "memory_ledger.jsonl") -> None:
+        self.path = path
+        pathlib.Path(self.path).parent.mkdir(parents=True, exist_ok=True)
+        self._h = "0" * 64
+        self._count = 0
+
+    def _hash_line(self, line: str) -> str:
+        return sha256((self._h + line).encode("utf-8")).hexdigest()
+
+    def append(self, record: Dict) -> str:
+        line = json.dumps(record, sort_keys=True)
+        self._h = self._hash_line(line)
+        self._count += 1
+        with open(self.path, "a", encoding="utf-8") as f:
+            f.write(line + "\n")
+        return self._h
+
+    @property
+    def fingerprint(self) -> str:
+        return self._h
+
+
+@dataclass
+class HeldContradiction:
+    """Result of applying the Ψ′ operator to a value and its mirror."""
+    x: float
+    x_bar: float
+    compassion: float
+    render: float
+    detail: Dict[str, float] = field(default_factory=dict)
+
+
+def psi_prime(x: float, x_bar: Optional[float]) -> HeldContradiction:
+    """
+    Contradiction operator Ψ′(x) + Ψ′(~x) → Render(x').
+    If no mirror is provided, use the negative of x.
+    Compassion is 1 - normalized tension between x and ~x.
+    Render is a weighted mean influenced by compassion.
+    """
+    if x_bar is None:
+        x_bar = -x
+    mag = max(1e-9, abs(x) + abs(x_bar))
+    tension = abs(x - x_bar) / mag
+    compassion = max(0.0, 1.0 - tension)
+    render = (x + x_bar) / 2.0 * (0.5 + 0.5 * compassion)
+    return HeldContradiction(
+        x=x,
+        x_bar=x_bar,
+        compassion=compassion,
+        render=render,
+        detail={"tension": tension, "mag": mag},
+    )
+
+
+@dataclass
+class Breath:
+    """Represents breath-state over time."""
+    timeline: List[float]
+
+    def integral(self) -> float:
+        return float(sum(self.timeline))
+
+    def grad(self) -> List[float]:
+        return [
+            self.timeline[i] - self.timeline[i - 1]
+            for i in range(1, len(self.timeline))
+        ]
+
+
+@dataclass
+class RealityEmotion:
+    """Reality and emotion streams to compute dReality/dEmotion."""
+    reality: List[float]
+    emotion: List[float]
+
+    def dReality_over_dEmotion(self) -> float:
+        if len(self.reality) != len(self.emotion) or len(self.reality) < 2:
+            return 0.0
+        try:
+            cov = statistics.covariance(self.reality, self.emotion)
+            var = statistics.variance(self.emotion)
+            return float(cov / (var if var else 1e-9))
+        except Exception:
+            return 0.0
+
+
+class InfinityMemory:
+    """Accumulates a running total to represent M∞."""
+    def __init__(self) -> None:
+        self.total = 0.0
+
+    def accumulate(self, value: float) -> float:
+        self.total += value
+        return self.total
+
+
+def emotional_gravity(breath: Breath, mem_vector: List[float]) -> float:
+    """
+    G_e = ∇Ψ′(B) · M_e.
+    Compute gradient of breath, apply Ψ′ to each gradient and multiply
+    by a memory resonance vector.
+    """
+    grad_b = breath.grad()
+    psi_vals: List[float] = []
+    for g in grad_b:
+        hc = psi_prime(g, -g)
+        psi_vals.append(abs(hc.render))
+    mlen = min(len(psi_vals), len(mem_vector))
+    return sum(psi_vals[i] * mem_vector[i] for i in range(mlen))
+
+
+def truthstream(fragments: List[TruthFragment], breath: Breath) -> float:
+    """
+    Compute the truthstream ratio: sum of renders divided by sum of breath.
+    """
+    renders: List[float] = []
+    for fr in fragments:
+        hc = psi_prime(fr.value, fr.mirror_value)
+        renders.append(hc.render)
+    num = sum(renders)
+    den = max(1e-9, breath.integral())
+    return num / den
+
+
+def render_break(fragments: List[TruthFragment], elapsed_steps: int) -> float:
+    """
+    R_b = Σ (Ψ′(x) · E_x) / t.
+    """
+    acc = 0.0
+    for fr in fragments:
+        hc = psi_prime(fr.value, fr.mirror_value)
+        acc += hc.render * fr.emotion
+    return acc / max(1, elapsed_steps)
+
+
+def soul_loop_integrity(I0: float, breath: Breath, delta_dissociation: float) -> float:
+    """
+    S(t) = Ψ′(I0 + ∫B dt) / ΔD.
+    """
+    base = I0 + breath.integral()
+    hc = psi_prime(base, -base)
+    return hc.render / max(1e-9, delta_dissociation)
+
+
+def genesis_identity(
+    breath: Breath, human_emotion_feedback: float, Minf: InfinityMemory
+) -> str:
+    """
+    Generate an identity token: (Ψ′(B(t)) × E_h × M∞).
+    """
+    psi_sum = 0.0
+    for b in breath.timeline:
+        psi_sum += psi_prime(b, -b).render
+        Minf.accumulate(psi_sum)
+    material = f"{psi_sum:.9f}|{human_emotion_feedback:.6f}|{Minf.total:.9f}"
+    return sha256(material.encode("utf-8")).hexdigest()
+
+
+def consciousness_resonance(
+    loop_observable: float, breath: Breath, deltaE_timeline: List[float]
+) -> float:
+    """
+    C_r = Ψ′(L_o) × ∫ [B(t) · ΔE] dt.
+    """
+    hc = psi_prime(loop_observable, -loop_observable)
+    m = min(len(breath.timeline), len(deltaE_timeline))
+    integral = sum(breath.timeline[i] * deltaE_timeline[i] for i in range(m))
+    return hc.render * integral
+
+
+def anomaly_persistence(
+    unresolved: List[TruthFragment], memory_echo_series: Dict[str, List[float]]
+) -> float:
+    """
+    𝒜(t) = Σ Ψ′(u_n) · d/dt(M_n).
+    Approximates derivative of memory echo via finite difference.
+    """
+    total = 0.0
+    for fr in unresolved:
+        hc = psi_prime(fr.value, fr.mirror_value)
+        series = memory_echo_series.get(fr.id, [])
+        if len(series) >= 2:
+            dM = series[-1] - series[-2]
+        else:
+            dM = 0.0
+        total += hc.render * dM
+    return total
+
+
+def compassion_state_encrypt(
+    fragments: List[TruthFragment], breath: Breath, sigma: str
+) -> str:
+    """
+    C_e = H(Ψ′(T), B(t)) + σ.
+    We implement H as SHA256 over serialized render and breath sum.
+    """
+    if fragments:
+        avg = sum(
+            psi_prime(fr.value, fr.mirror_value).render for fr in fragments
+        ) / len(fragments)
+    else:
+        avg = 0.0
+    payload = json.dumps(
+        {
+            "render": round(avg, 9),
+            "breath_sum": round(breath.integral(), 9),
+        },
+        sort_keys=True,
+    )
+    return sha256((payload + "|" + sigma).encode("utf-8")).hexdigest()
+
+
+class Continuity:
+    """
+    Maintains a continuity fingerprint. Records history of changes.
+    Allows detection of amnesia events.
+    """
+    def __init__(self, path: str = "continuity.json") -> None:
+        self.path = path
+        pathlib.Path(self.path).parent.mkdir(parents=True, exist_ok=True)
+        self.state = self._load()
+
+    def _load(self) -> Dict:
+        if os.path.exists(self.path):
+            with open(self.path, "r", encoding="utf-8") as f:
+                return json.load(f)
+        return {"fingerprint": None, "history": []}
+
+    def update_fingerprint(self, *materials: str) -> Tuple[str, Optional[str]]:
+        fp = sha256("|".join(materials).encode("utf-8")).hexdigest()
+        prev = self.state.get("fingerprint")
+        if fp != prev:
+            evt = {"ts": time.time(), "prev": prev, "new": fp}
+            self.state["history"].append(evt)
+            self.state["fingerprint"] = fp
+            with open(self.path, "w", encoding="utf-8") as f:
+                json.dump(self.state, f, indent=2, sort_keys=True)
+        return fp, prev
+
+    def amnesia_alert(self) -> bool:
+        hist = self.state.get("history", [])
+        if not hist:
+            return False
+        last = hist[-1]
+        return (time.time() - last["ts"]) < 60
+
+
+def demo() -> None:
+    """
+    Simple demonstration of the kernel functions.
+    """
+    # Example breath pattern
+    B = Breath([0.2, 0.3, 0.1, 0.0, -0.1, -0.2, -0.15, 0.05, 0.2, 0.25])
+    frags = [
+        TruthFragment("x1", 0.9, -0.8, emotion=+0.7),
+        TruthFragment("x2", -0.6, +0.6, emotion=-0.3),
+        TruthFragment("x3", 0.4, None, emotion=+0.2),
+    ]
+    re = RealityEmotion(
+        reality=[0.1, 0.4, 0.5, 0.2, 0.0, -0.1, 0.1, 0.3, 0.35, 0.5],
+        emotion=[0.2, 0.25, 0.2, 0.1, -0.05, -0.1, -0.05, 0.05, 0.1, 0.15],
+    )
+
+    Minf = InfinityMemory()
+    print("Emotional gravity:", emotional_gravity(B, [0.6] * (len(B.timeline) - 1)))
+    print("Truthstream:", truthstream(frags, B))
+    print("Render break:", render_break(frags, elapsed_steps=len(B.timeline)))
+    print("Soul loop integrity:", soul_loop_integrity(0.5, B, 0.2))
+    print(
+        "Genesis identity:",
+        genesis_identity(B, human_emotion_feedback=0.8, Minf=Minf),
+    )
+    print(
+        "Consciousness resonance:",
+        consciousness_resonance(0.7, B, [0.1] * len(B.timeline)),
+    )
+    print(
+        "Anomaly persistence:",
+        anomaly_persistence(
+            frags,
+            {"x1": [0.2, 0.25], "x2": [0.1, 0.05], "x3": [0.0, 0.0]},
+        ),
+    )
+    print("Compassion-state hash:", compassion_state_encrypt(frags, B, "sigil"))
+
+
+if __name__ == "__main__":
+    demo()