Research-Stack/4-Infrastructure/shim/rrc_manifold_assign.py

#!/usr/bin/env python3
"""
rrc_manifold_assign.py — Assign RRC equations to manifold locations using
Anti-Diophantine slack regimes.

Each equation is placed on the 8D braid manifold based on:
1. Route hint from equation semantics (keyword matching)
2. Anti-Diophantine slack from match characteristics
3. Canonical Sidon label assignment

Output: shared-data/data/rrc_manifold_assignment_v1.json
"""
from __future__ import annotations

import json
import re
from collections import Counter, defaultdict
from pathlib import Path

RECEIPT_PATH = Path("archive/experimental-shim-probes/rrc_equation_classifier_receipt.json")
OUT_PATH = Path("shared-data/data/rrc_manifold_assignment_v1.json")

# Manifold route hints with keyword patterns
ROUTE_PATTERNS: list[tuple[str, list[str], str]] = [
    ("thermodynamic_energy", [
        "energy", "entropy", "heat", "carnot", "landauer", "temperature",
        "thermodynamic", "thermal", "dissipation", "efficiency", "joule",
    ], "Anti-Diophantine: high match density, many variant forms"),
    ("geometry_topology", [
        "geodesic", "metric", "stereographic", "euclidean", "manifold",
        "curvature", "riemann", "tensor", "topology", "holonomy",
        "connection", "bundle", "chart",
    ], "Diophantine: tight structural constraints"),
    ("cognitive_load", [
        "cognitive", "load", "emotional", "signal", "attention",
        "salience", "novelty", "surprise", "gate",
    ], "Transition: moderate slack, adaptive"),
    ("compression_route", [
        "compress", "hutter", "encoding", "codec", "entropy",
        "bit", "rate", "distortion", "redundancy",
    ], "Anti-Diophantine: many equivalent compression schemes"),
    ("magnetic_signal", [
        "magnetic", "magneto", "field", "wave", "plasma",
        "flux", "induction", "mhd", "alfven",
    ], "Anti-Diophantine: dense solution space"),
    ("control_signal", [
        "control", "gate", "overflow", "gain", "tuning",
        "cascade", "feedback", "regulator", "threshold",
    ], "Diophantine: precise constraint satisfaction"),
    ("chaotic_couch", [
        "chaotic", "couch", "soliton", "turbulence", "vortex",
        "strange", "attractor", "lyapunov",
    ], "Anti-Diophantine: chaotic regime, dense trajectories"),
    ("number_theory", [
        "prime", "modulo", "congruence", "diophantine", "integer",
        "arithmetic", "logarithm", "lower_bound", "bound",
    ], "Diophantine: Baker-style finiteness bounds"),
]

# Canonical Sidon labels (powers of 2) for address assignment
CANONICAL_LABELS = [1, 2, 4, 8, 16, 32, 64, 128]

# Greek epigenetic state mapping (route → Greek letter)
# Phase angles per Omindirection Principle 3: 360°/8 = 45° sectors
ROUTE_GREEK_MAP: dict[str, dict] = {
    "thermodynamic_energy": {
        "greek": "Φ", "phase": 0, "chirality": "ambidextrous", "direction": "forward",
        "label": "Stable / Fundamental"
    },
    "geometry_topology": {
        "greek": "Λ", "phase": 45, "chirality": "left", "direction": "forward",
        "label": "Ordered attractor / Lattice regime"
    },
    "control_signal": {
        "greek": "Ρ", "phase": 90, "chirality": "ambidextrous", "direction": "forward",
        "label": "Regulated / Spectral radius boundary"
    },
    "cognitive_load": {
        "greek": "Κ", "phase": 135, "chirality": "left", "direction": "forward",
        "label": "Poised / Kappa threshold"
    },
    "chaotic_couch": {
        "greek": "Ω", "phase": 180, "chirality": "ambidextrous", "direction": "reverse",
        "label": "Terminal / Chaotic fixed point"
    },
    "compression_route": {
        "greek": "Σ", "phase": 225, "chirality": "right", "direction": "reverse",
        "label": "Symmetric partner / Compression duality"
    },
    "magnetic_signal": {
        "greek": "Π", "phase": 270, "chirality": "right", "direction": "reverse",
        "label": "Potential / Field effects"
    },
    "number_theory": {
        "greek": "Ζ", "phase": 315, "chirality": "right", "direction": "reverse",
        "label": "Zero-region / Zeta-like boundary"
    },
}

# Regime → Greek fallback (used when route is unclassified)
REGIME_GREEK_MAP: dict[str, str] = {
    "anti_diophantine": "Φ",
    "diophantine": "Λ",
    "transition": "Κ",
    "transition_tight": "Ρ",
}

UNCLASSIFIED_GREEK = "Ζ"

ROUTE_ORDER = ["Φ", "Λ", "Ρ", "Κ", "Ω", "Σ", "Π", "Ζ"]


def compute_antidiophantine_slack(match_count: int | None, stage: str | None) -> tuple[int, str]:
    """Compute Anti-Diophantine slack from match characteristics."""
    mc = match_count or 0
    if mc >= 100:
        slack = 128  # Anti-Diophantine: many matches, dense
        regime = "anti_diophantine"
    elif mc >= 20:
        slack = 64   # Transition: moderate
        regime = "transition"
    elif mc >= 5:
        slack = 16   # Transition: tighter
        regime = "transition_tight"
    else:
        slack = 4    # Diophantine: few matches, tight
        regime = "diophantine"
    # Adjust for kernel stage quality
    if stage == "kernel_refine_v1":
        slack = max(slack // 2, 2)  # Keyword match is weaker
    elif stage == "kernel_refine_v4":
        slack = min(slack * 2, 256)  # Dataset match is stronger
    return slack, regime


def classify_route(name: str, eq_text: str) -> str:
    """Classify an equation into a manifold route by name + text keywords."""
    combined = (name + " " + str(eq_text)).lower()
    best_route = "unclassified"
    best_score = 0
    for route, keywords, _ in ROUTE_PATTERNS:
        score = sum(3 for kw in keywords if kw in combined)
        if score > best_score:
            best_score = score
            best_route = route
    return best_route


def assign_canonical_label(route: str, index: int) -> int:
    """Assign a canonical Sidon label (power of 2) based on route and index."""
    return CANONICAL_LABELS[hash(route + str(index)) % len(CANONICAL_LABELS)]


def route_to_greek(route: str) -> dict:
    """Map a manifold route to its Greek epigenetic state."""
    g = ROUTE_GREEK_MAP.get(route)
    if g is not None:
        return dict(g)
    return {"greek": UNCLASSIFIED_GREEK, "phase": 315, "chirality": "right",
            "direction": "reverse", "label": "Unclassified / Boundary"}


def regime_fallback_greek(regime: str) -> str:
    """Fallback Greek state from regime when route is unclassified."""
    return REGIME_GREEK_MAP.get(regime, UNCLASSIFIED_GREEK)


def main():
    d = json.loads(RECEIPT_PATH.read_text())
    eqs = d["compiled_equations"]
    N = len(eqs)

    manifold = {
        "schema": "rrc_manifold_assignment_v1",
        "description": "RRC equations assigned to 8D braid manifold locations with Anti-Diophantine slack regimes",
        "strands": 8,
        "canonical_labels": CANONICAL_LABELS,
        "route_counts": {},
        "regime_counts": Counter(),
        "equations": [],
    }

    route_registry: dict[str, int] = Counter()

    for e in eqs:
        rec = e["equation_record"]
        name = rec.get("name", "unknown")
        eq_text = str(rec.get("equation", ""))
        match_count = rec.get("arxiv_match_count")
        stage = rec.get("arxiv_match_stage")

        # 1. Classify route
        route = rec.get("route_hint", "unclassified")
        if route == "?" or route == "unclassified":
            route = classify_route(name, eq_text)
            if route == "unclassified" and not route:
                route = "unclassified"

        route_registry[route] += 1

        # 2. Compute slack and regime
        slack, regime = compute_antidiophantine_slack(match_count, stage)
        manifold["regime_counts"][regime] += 1

        # 3. Assign canonical Sidon label
        label_idx = route_registry[route] - 1
        sidon_label = assign_canonical_label(route, label_idx)

        # 4. Compute address budget M = slack + label
        M = slack + sidon_label

        # 5. Compute strand position (0-7)
        strand = sidon_label.bit_length() - 1

        # 6. Assign Greek epigenetic state
        greek_info = route_to_greek(route)
        if greek_info["greek"] == UNCLASSIFIED_GREEK:
            greek_info["greek"] = regime_fallback_greek(regime)
            # Recalculate phase for fallback
            fallback_idx = ROUTE_ORDER.index(greek_info["greek"]) if greek_info["greek"] in ROUTE_ORDER else 7
            greek_info["phase"] = fallback_idx * 45

        manifold["equations"].append({
            "name": name,
            "route": route,
            "regime": regime,
            "greek_state": greek_info["greek"],
            "greek_phase": greek_info["phase"],
            "greek_chirality": greek_info["chirality"],
            "greek_direction": greek_info["direction"],
            "slack": slack,
            "sidon_label": sidon_label,
            "address_budget": M,
            "strand": strand,
            "match_count": match_count,
            "match_stage": stage,
        })

    manifold["route_counts"] = dict(route_registry)
    manifold["greek_counts"] = Counter(e["greek_state"] for e in manifold["equations"])

    OUT_PATH.parent.mkdir(parents=True, exist_ok=True)
    OUT_PATH.write_text(json.dumps(manifold, indent=2, ensure_ascii=False))
    print(f"=== Manifold Assignment ({N} equations) ===")
    print(f"Routes:")
    for route, count in sorted(manifold["route_counts"].items(), key=lambda x: -x[1]):
        print(f"  {route:30s} {count:4d}")
    print(f"\nRegimes:")
    for regime, count in sorted(manifold["regime_counts"].items(), key=lambda x: -x[1]):
        print(f"  {regime:25s} {count:4d}")
    print(f"\nGreek Epigenetic States:")
    for greek in ROUTE_ORDER:
        count = sum(1 for e in manifold["equations"] if e["greek_state"] == greek)
        label = ROUTE_GREEK_MAP.get(
            next((r for r, v in ROUTE_GREEK_MAP.items() if v["greek"] == greek), ""), {}
        ).get("label", "")
        if count > 0:
            phase = next((e["greek_phase"] for e in manifold["equations"] if e["greek_state"] == greek), 0)
            print(f"  {greek} ({phase:3d}°): {count:4d}  — {label}")
    print(f"\nWritten to {OUT_PATH}")


if __name__ == "__main__":
    main()