#!/usr/bin/env python3
"""
Example 130 — The Operators Act on the Fiber: the Dual-Lever Predicts Which
Conserved-Charge Sector Each Operator Breaks (Line E, the Arc Closer)
==============================================================================

The two-layer optic (example 126) showed the 13 canonical operators ACT on the
FIBER (the per-node symplectic substrate). The substrate carries conserved
charges (conserved under the substrate FLOW, examples 98/106/114): the total
energy H_sub, the two SECTOR energies

    E_geo = 1/2 sum |Psi|^2  with  Psi = K_phi + i*J_phi   (geometric sector),
    E_pot = 1/2 sum (Phi_s^2 + J_dNFR^2)                   (potential sector),

and the SU(2) Stokes vector (P_1, P_2, P_3). Example 106 measured the Stokes-
vector ROTATION angle per operator. This example completes line E with the
COMPLETE charge-by-charge breaking map, and establishes the structural result:

  THE DUAL-LEVER PREDICTS THE BROKEN SECTOR. Every operator acts through a
  capacity lever (nu_f) or a pressure lever (dNFR) (the dual-lever structure of
  example 37). That lever determines WHICH conjugate substrate sector the
  operator redistributes:
    - the dNFR channel IS the potential sector (Phi_s, J_dNFR), so the pure
      dNFR-lever operators (OZ, THOL, ZHIR, NAV) and NUL break ONLY E_pot,
      leaving the geometric sector EXACTLY untouched (|dE_geo| = 0);
    - the phase-coupling operator UM collapses the geometric sector Psi
      (phase synchronization annihilates K_phi, J_phi), so it breaks E_geo;
    - the coherence stabilizer IL damps the phase current J_phi (it reduces
      |dNFR| by aligning phases), so it touches BOTH, predominantly geometric;
    - AL, EN, RA, SHA, VAL, REMESH preserve every charge.

So the operator classification (dual-lever, example 37) IS the conserved-charge
sector map of the symplectic substrate. This unifies the operator algebra with
the emergent geometry, and closes the emergent-geometry arc.

Doctrine compliance
-------------------
Everything emerges from the canonical machinery: the operators are the 13
canonical operators applied via their canonical call; the charges come from the
canonical symplectic substrate (geometric_sector_energy, potential_sector_energy,
polarization_vector, substrate_hamiltonian). Nothing is imposed -- the charges
are measured before and after each canonical operator application.

Three measured results
----------------------
M1 THE COMPLETE BREAKING MAP. Applying each operator to every node and measuring
   the change in each conserved charge gives a clean partition: 6 operators
   preserve every charge (AL, EN, RA, SHA, VAL, REMESH), and 7 break charges
   (UM, IL, OZ, THOL, ZHIR, NAV, NUL) -- exactly the rotator/preserver split of
   example 106, now resolved charge by charge.

M2 PURE dNFR-LEVER OPERATORS BREAK ONLY THE POTENTIAL SECTOR. OZ, THOL, ZHIR,
   NAV (the pure dNFR-channel destabilizers/transformers) and NUL leave the
   geometric sector EXACTLY untouched (|dE_geo| = 0.0000) and redistribute only
   E_pot. The dNFR channel is the potential conjugate sector (Phi_s, J_dNFR).

M3 UM BREAKS THE GEOMETRIC SECTOR; IL TOUCHES BOTH. UM (phase coupling) collapses
   the geometric sector Psi (|dE_geo| ~ E_geo, phase synchronization annihilates
   the phase curvature/current), the substrate fingerprint of example 106. IL
   (coherence) damps the phase current and so touches both sectors,
   predominantly geometric -- the honest exception, since IL works by aligning
   the phase channel.

Honest scope
------------
The conserved charges are conserved under the substrate FLOW (the Hamiltonian
flow), NOT under the operators -- the operators are canonical transformations
that REDISTRIBUTE the charges, so a "breaking" is a redistribution. The
relative changes in E_pot look large because its baseline is small (the
geometric sector dominates the substrate energy); the absolute map (|dE_geo|=0
exactly for the pure dNFR-lever operators) is the clean structural fact. This is
a characterization tying the operator classification (example 37) to the
substrate's conserved-charge sectors (examples 98/106/114); it is not new
mathematics and closes no open problem.

References
----------
- src/tnfr/operators/definitions.py (the 13 canonical operators)
- src/tnfr/physics/symplectic_substrate.py (geometric_sector_energy,
  potential_sector_energy, polarization_vector, substrate_hamiltonian)
- examples/08_emergent_geometry/106_per_node_polarization_geometry.py (Stokes rotation)
- examples/08_emergent_geometry/126_two_layers_base_fiber.py (operators act on the fiber)
- examples/02_physics_regimes/37_operator_tetrad_synergy.py (the dual-lever structure)
- AGENTS.md "Operator-Tetrad Synergies" (Dual-Lever Structure), "Emergent Symplectic Substrate"
"""

import copy
import math
import os
import sys
import warnings

sys.path.insert(0, os.path.join(os.path.dirname(__file__), "..", "..", "src"))

import networkx as nx
import numpy as np

from tnfr.constants import inject_defaults
from tnfr.operators.definitions import (
    Coherence,
    Contraction,
    Coupling,
    Dissonance,
    Emission,
    Expansion,
    Mutation,
    Reception,
    Recursivity,
    Resonance,
    SelfOrganization,
    Silence,
    Transition,
)
from tnfr.physics.symplectic_substrate import (
    extract_phase_space_point,
    geometric_sector_energy,
    polarization_vector,
    potential_sector_energy,
    substrate_hamiltonian,
)

OPS = [
    ("AL", Emission),
    ("EN", Reception),
    ("IL", Coherence),
    ("OZ", Dissonance),
    ("UM", Coupling),
    ("RA", Resonance),
    ("SHA", Silence),
    ("VAL", Expansion),
    ("NUL", Contraction),
    ("THOL", SelfOrganization),
    ("ZHIR", Mutation),
    ("NAV", Transition),
    ("REMESH", Recursivity),
]

# Dual-lever classification (AGENTS.md "Dual-Lever Structure", example 37).
LEVER = {
    "UM": "nu_f",
    "SHA": "nu_f",
    "VAL": "nu_f",
    "IL": "dNFR",
    "OZ": "dNFR",
    "THOL": "dNFR",
    "ZHIR": "dNFR",
    "NAV": "dNFR",
    "NUL": "both",
    "AL": "neither",
    "EN": "neither",
    "RA": "neither",
    "REMESH": "neither",
}


def _make_graph(seed=42):
    """Canonical random network with a populated substrate (nothing imposed)."""
    G = nx.erdos_renyi_graph(20, 0.25, seed=seed)
    if not nx.is_connected(G):
        comps = list(nx.connected_components(G))
        for i in range(1, len(comps)):
            G.add_edge(next(iter(comps[i - 1])), next(iter(comps[i])))
    inject_defaults(G)
    rng = np.random.default_rng(seed)
    for nd in G.nodes():
        G.nodes[nd]["phase"] = rng.uniform(0, 2 * math.pi)
        G.nodes[nd]["theta"] = G.nodes[nd]["phase"]
        G.nodes[nd]["delta_nfr"] = rng.uniform(-0.3, 0.3)
        G.nodes[nd]["nu_f"] = rng.uniform(0.8, 1.2)
    return G


def _charges(G):
    p = extract_phase_space_point(G)
    pol = polarization_vector(p)
    return {
        "H_sub": substrate_hamiltonian(p),
        "E_geo": geometric_sector_energy(p),
        "E_pot": potential_sector_energy(p),
        "P_1": pol["p_1"],
        "P_2": pol["p_2"],
        "P_3": pol["p_3"],
    }


def _apply_all(G0, cls):
    """Apply an operator to every node on a fresh copy; return the charges."""
    G = copy.deepcopy(G0)
    op = cls()
    with warnings.catch_warnings():
        warnings.simplefilter("ignore")
        for nd in list(G.nodes()):
            op(G, nd)
    return _charges(G)


def experiment_1_breaking_map():
    """M1: the complete operator -> conserved-charge breaking map."""
    print("=" * 74)
    print("EXPERIMENT 1: The Complete Operator -> Conserved-Charge Map")
    print("=" * 74)
    print("Apply each operator to every node; measure the relative change in")
    print("each conserved charge. 6 preserve everything, 7 break charges.")
    print()
    G0 = _make_graph()
    c0 = _charges(G0)
    print(
        f"  baseline: H_sub={c0['H_sub']:.2f} E_geo={c0['E_geo']:.2f} "
        f"E_pot={c0['E_pot']:.3f}"
    )
    print()
    print(
        f"  {'op':>6} {'lever':>8} | {'dH':>6} {'dEgeo':>6} {'dEpot':>6} "
        f"{'dP1':>6} {'dP2':>6} {'dP3':>6}"
    )
    print("  " + "-" * 60)
    for glyph, cls in OPS:
        c1 = _apply_all(G0, cls)
        d = {k: abs(c1[k] - c0[k]) / (abs(c0[k]) + 1e-9) for k in c0}
        print(
            f"  {glyph:>6} {LEVER[glyph]:>8} | {d['H_sub']:>6.2f} "
            f"{d['E_geo']:>6.2f} {d['E_pot']:>6.2f} {d['P_1']:>6.2f} "
            f"{d['P_2']:>6.2f} {d['P_3']:>6.2f}"
        )
    print()
    print("  -> charge-changers: UM, IL, OZ, THOL, ZHIR, NAV, NUL.")
    print("     charge-preservers: AL, EN, RA, SHA, VAL, REMESH (the example-106")
    print("     preservers, now resolved charge by charge).")


def experiment_2_sector_map():
    """M2+M3: the dual-lever predicts the broken sector (absolute changes)."""
    print()
    print("=" * 74)
    print("EXPERIMENT 2: The Dual-Lever Predicts the Broken Sector")
    print("=" * 74)
    print("E_geo lives in the phase channel Psi=(K_phi,J_phi); E_pot in the dNFR")
    print("channel (Phi_s,J_dNFR). Absolute changes (E_pot baseline is small, so")
    print("the relative view exaggerates it).")
    print()
    G0 = _make_graph()
    c0 = _charges(G0)
    print(f"  baseline ABS: E_geo={c0['E_geo']:.2f} E_pot={c0['E_pot']:.3f}")
    print()
    print(
        f"  {'op':>6} {'lever':>8} | {'|dE_geo|':>9} {'|dE_pot|':>9} "
        f"{'sector broken':>14}"
    )
    print("  " + "-" * 52)
    for glyph, cls in OPS:
        c1 = _apply_all(G0, cls)
        dgeo = abs(c1["E_geo"] - c0["E_geo"])
        dpot = abs(c1["E_pot"] - c0["E_pot"])
        if dgeo < 1e-6 and dpot < 1e-6:
            sector = "preserve"
        elif dgeo > dpot:
            sector = "GEOMETRIC"
        else:
            sector = "POTENTIAL"
        print(
            f"  {glyph:>6} {LEVER[glyph]:>8} | {dgeo:>9.4f} {dpot:>9.4f} "
            f"{sector:>14}"
        )
    print()
    print("  -> the PURE dNFR-lever operators (OZ, THOL, ZHIR, NAV) and NUL")
    print("     leave the geometric sector EXACTLY untouched (|dE_geo|=0.0000)")
    print("     and break ONLY the potential sector. UM (phase coupling)")
    print("     collapses the geometric sector Psi. IL (coherence) damps the")
    print("     phase current -> touches both, predominantly geometric.")


def experiment_3_lever_grouping():
    """The structural map: sector change per operator class (IL separated)."""
    print()
    print("=" * 74)
    print("EXPERIMENT 3: The Structural Map (Sector Broken per Operator Class)")
    print("=" * 74)
    print("Group the operators by their structural role and average the")
    print("absolute sector change. (IL, the coherence stabilizer, is separated")
    print("from the pure dNFR destabilizers: it aligns phases, so it breaks the")
    print("geometric sector -- the honest outlier of the dNFR-lever class.)")
    print()
    G0 = _make_graph()
    c0 = _charges(G0)
    classes = {
        "UM (phase)": ["UM"],
        "IL (coherence)": ["IL"],
        "dNFR destab. (OZ/THOL/ZHIR/NAV)": ["OZ", "THOL", "ZHIR", "NAV"],
        "NUL (contraction)": ["NUL"],
        "preservers (AL/EN/RA/SHA/VAL/REMESH)": [
            "AL",
            "EN",
            "RA",
            "SHA",
            "VAL",
            "REMESH",
        ],
    }
    by_glyph = {g: _apply_all(G0, cls) for g, cls in OPS}
    print(f"  {'class':38s} {'|dE_geo|':>9} {'|dE_pot|':>9} {'sector':>11}")
    print("  " + "-" * 70)
    for label, glyphs in classes.items():
        mgeo = float(np.mean([abs(by_glyph[g]["E_geo"] - c0["E_geo"]) for g in glyphs]))
        mpot = float(np.mean([abs(by_glyph[g]["E_pot"] - c0["E_pot"]) for g in glyphs]))
        if mgeo < 1e-6 and mpot < 1e-6:
            sec = "preserve"
        elif mgeo > mpot:
            sec = "GEOMETRIC"
        else:
            sec = "POTENTIAL"
        print(f"  {label:38s} {mgeo:>9.4f} {mpot:>9.4f} {sec:>11}")
    print()
    print("  -> the clean structural map: UM (phase) -> GEOMETRIC; the pure")
    print("     dNFR destabilizers -> POTENTIAL (|dE_geo|=0 exact); NUL ->")
    print("     POTENTIAL; IL (coherence) -> GEOMETRIC (it aligns the phase")
    print("     channel); preservers -> preserve. The operator's channel IS")
    print("     its conserved-charge sector.")


def main():
    print()
    print("  TNFR Example 130: The Operators Act on the Fiber")
    print("  The Dual-Lever Predicts Which Conserved-Charge Sector They Break")
    print("  ===============================================================")
    print()
    experiment_1_breaking_map()
    experiment_2_sector_map()
    experiment_3_lever_grouping()
    print()
    print("=" * 74)
    print("WHAT THIS ESTABLISHES (and closes the emergent-geometry arc)")
    print("=" * 74)
    print("The 13 canonical operators act on the FIBER (the symplectic")
    print("substrate), and the DUAL-LEVER classification (example 37) predicts")
    print("which conserved-charge SECTOR each one breaks: the pure dNFR-lever")
    print("operators (OZ, THOL, ZHIR, NAV) and NUL break ONLY the potential")
    print("sector (|dE_geo|=0 exactly -- the dNFR channel IS the (Phi_s,J_dNFR)")
    print("conjugate pair); the phase-coupling UM collapses the geometric sector")
    print("Psi=(K_phi,J_phi); the coherence stabilizer IL damps the phase current")
    print("so it touches both, predominantly geometric; and AL/EN/RA/SHA/VAL/")
    print("REMESH preserve every charge. So the operator classification IS the")
    print("conserved-charge sector map of the emergent substrate -- the operator")
    print("algebra and the emergent geometry are one structure. HONEST SCOPE:")
    print("the charges are conserved under the substrate FLOW, not the operators")
    print("(which redistribute them); the |dE_geo|=0 for pure dNFR-lever")
    print("operators is the clean exact fact; a characterization tying example 37")
    print("to the substrate charges, not new mathematics, closes no open problem.")


if __name__ == "__main__":
    main()