#!/usr/bin/env python3
"""
Example 98 — The Emergent Symplectic Substrate
===============================================

Demonstrates the geometry that the TNFR nodal dynamics generates from
itself: a symplectic phase space with canonical conjugate pairs, on which
the nodal equation, conservation laws, and 13 operators all live. The
substrate is not imposed (like the graph) — it EMERGES from the structure.

Physics
-------
The Structural Conservation Theorem gives two canonical conjugate pairs
per node:

    Geometric sector:  (K_φ,  J_φ)       curvature ↔ phase current
    Potential  sector: (Φ_s,  J_ΔNFR)    potential ↔ ΔNFR flux

so the emergent phase space is P = ℝ^{4N} with symplectic 2-form

    ω = Σ_i [ dK_φ(i) ∧ dJ_φ(i) + dΦ_s(i) ∧ dJ_ΔNFR(i) ].

The substrate Hamiltonian H_sub = ½Σ(K_φ²+J_φ²+Φ_s²+J_ΔNFR²) plus the
configuration background ½Σ|∇φ|² equals the canonical energy functional.
The nodal equation ∂EPI/∂t = νf·ΔNFR is the overdamped projection of the
Hamiltonian flow on this substrate.

Experiments
-----------
1. The substrate emerges: extract P = ℝ^{4N} and verify it is a valid
   symplectic manifold (antisymmetric, non-degenerate, closed, canonical
   brackets, Jacobi, Liouville, harmonic flow)
2. Energy consistency: H_sub + background = canonical energy functional
3. Liouville is structural: div(X_H) = tr(J·Hess) = 0 for any Hamiltonian
   (the geometric reason operators preserve phase-space volume)

Honest scope
------------
This makes EXPLICIT and verifies the emergent symplectic structure already
implied by conservation.py and variational.py — a canonical consolidation,
not a new postulate. Field coordinates are delegated to existing canonical
functions. It does NOT, by itself, resolve any open program (Riemann,
Navier–Stokes); it establishes the geometric substrate from which the
canonical structures derive.

References
----------
- src/tnfr/physics/symplectic_substrate.py (this substrate)
- src/tnfr/physics/variational.py (symplectic 2-form ω, Hamiltonian)
- src/tnfr/physics/conservation.py (conjugate pairs, energy functional)
- theory/TNFR_VARIATIONAL_PRINCIPLE.md (full derivation)
- AGENTS.md §"Minimal Structural Degrees of Freedom"
"""

import math
import os
import random
import sys

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

import networkx as nx
import numpy as np

from tnfr.dynamics.dnfr import default_compute_delta_nfr
from tnfr.physics.conservation import compute_energy_functional
from tnfr.physics.symplectic_substrate import (
    background_potential,
    canonical_bracket_table,
    extract_phase_space_point,
    liouville_divergence,
    noether_charges,
    substrate_hamiltonian,
    symplectic_form_matrix,
    verify_canonical_structure,
    verify_hermitian_structure,
    verify_integrability,
    verify_noether_conservation,
    verify_poincare_cartan,
    verify_polarization_symmetry,
    verify_substrate_geometry,
    verify_symplectic_reduction,
)


def _build_graph(n: int = 30, seed: int = 5) -> nx.Graph:
    rng = random.Random(seed)
    G = nx.watts_strogatz_graph(n, 4, 0.3, seed=seed)
    for node in G.nodes():
        G.nodes[node]["theta"] = rng.uniform(0.0, 2.0 * math.pi)
        G.nodes[node]["EPI"] = rng.uniform(0.2, 0.8)
        G.nodes[node]["nu_f"] = rng.uniform(0.5, 1.5)
    default_compute_delta_nfr(G)
    return G


# ============================================================================
# EXPERIMENT 1: The substrate emerges and is a valid symplectic manifold
# ============================================================================
def experiment_1_emergent_substrate():
    """Extract P = ℝ^{4N} and verify the canonical symplectic structure."""
    print("=" * 72)
    print("EXPERIMENT 1: The Emergent Symplectic Substrate")
    print("=" * 72)
    print()
    print("Two canonical conjugate pairs per node emerge from conservation:")
    print("  geometric (K_φ, J_φ)   and   potential (Φ_s, J_ΔNFR)")
    print("→ phase space P = ℝ^{4N} with form ω = Σ dK_φ∧dJ_φ + dΦ_s∧dJ_ΔNFR")
    print()

    G = _build_graph(30)
    cert = verify_canonical_structure(G)

    print(
        f"  Network: N = {cert.n_nodes} nodes  →  phase space dim = "
        f"{cert.dimension}"
    )
    print()
    print(f"  antisymmetric  ωᵀ = −ω        : {cert.is_antisymmetric}")
    print(
        f"  non-degenerate det ω = {cert.determinant:.1f}     : "
        f"{cert.is_nondegenerate}"
    )
    print(f"  closed         dω = 0         : {cert.is_closed}")
    print(f"  canonical Poisson brackets    : {cert.brackets_canonical}")
    print(f"  Jacobi identity               : {cert.jacobi_satisfied}")
    print(
        f"  Liouville div(X_H) = {cert.liouville_divergence:.1e}    : "
        f"{abs(cert.liouville_divergence) < 1e-9}"
    )
    print(f"  harmonic flow q̇=p, ṗ=−q       : {cert.flow_is_harmonic}")
    print()
    print(f"  VALID SYMPLECTIC MANIFOLD: {cert.is_valid_symplectic_manifold}")
    print()

    table = canonical_bracket_table()
    print("  Canonical brackets (one node):")
    print(f"    {{K_φ, J_φ}}   = {table['{qA,pA}']:.1f}   (geometric pair)")
    print(f"    {{Φ_s, J_ΔNFR}} = {table['{qB,pB}']:.1f}   (potential pair)")
    print(f"    cross-sector  = {table['{qA,pB}']:.1f}   (sectors decouple)")
    print()


# ============================================================================
# EXPERIMENT 2: The Hamiltonian is the canonical energy functional
# ============================================================================
def experiment_2_energy_consistency():
    """H_sub + background potential = canonical energy functional."""
    print("=" * 72)
    print("EXPERIMENT 2: The Hamiltonian IS the Energy Functional")
    print("=" * 72)
    print()
    print("H_sub = ½Σ(K_φ²+J_φ²+Φ_s²+J_ΔNFR²)  (symplectic core)")
    print("U     = ½Σ|∇φ|²                       (config. background)")
    print("H_sub + U should equal compute_energy_functional(G).")
    print()

    print(
        f"{'N':>5}  {'H_sub':>10}  {'U_bg':>10}  {'H_sub+U':>10}"
        f"  {'energy E':>10}  {'match':>6}"
    )
    print("-" * 60)
    for n in (10, 20, 30, 50):
        G = _build_graph(n, seed=n)
        pt = extract_phase_space_point(G)
        h_sub = substrate_hamiltonian(pt)
        u_bg = background_potential(pt)
        energy = compute_energy_functional(G)
        match = abs((h_sub + u_bg) - energy) < 1e-9
        print(
            f"{n:>5}  {h_sub:>10.4f}  {u_bg:>10.4f}  {h_sub + u_bg:>10.4f}"
            f"  {energy:>10.4f}  {'OK' if match else 'FAIL':>6}"
        )

    print()
    print("VALIDATED: the substrate Hamiltonian reconstructs the canonical")
    print("energy functional exactly. The substrate is consistent with the")
    print("existing conservation machinery — it is the same physics, seen")
    print("as the geometry the dynamics generates.")
    print()


# ============================================================================
# EXPERIMENT 3: Liouville is structural — the origin of symplectomorphism
# ============================================================================
def experiment_3_liouville_structural():
    """div(X_H) = tr(J·Hess) = 0 for ANY Hamiltonian — volume preserved."""
    print("=" * 72)
    print("EXPERIMENT 3: Liouville is Structural (Operator Volume)")
    print("=" * 72)
    print()
    print("The Hamiltonian flow X_H = J·∇H has divergence tr(J·Hess H).")
    print("Since J is antisymmetric and the Hessian is symmetric,")
    print("tr(J·Hess) = 0 for EVERY Hamiltonian. Phase-space volume is")
    print("preserved — this is why the 13 operators are symplectomorphisms.")
    print()

    G = _build_graph(20)
    pt = extract_phase_space_point(G)
    div = liouville_divergence(pt)
    print(f"  div(X_H) for the substrate Hamiltonian = {div:.3e}")
    print()

    # Demonstrate tr(J·S) = 0 for arbitrary symmetric Hessians.
    omega = symplectic_form_matrix(pt.n_nodes)
    rng = np.random.default_rng(20260613)
    print("  tr(J·Hess) for random symmetric Hessians (any Hamiltonian):")
    for trial in range(3):
        s = rng.standard_normal(omega.shape)
        s = 0.5 * (s + s.T)  # symmetric
        tr = float(np.trace(omega @ s))
        print(f"    trial {trial + 1}: tr(J·S) = {tr:.3e}")

    print()
    print("VALIDATED: volume preservation is a structural identity, not a")
    print("coincidence. The emergent geometry guarantees that grammar-")
    print("compliant evolution conserves the symplectic phase-space volume.")
    print()


# ============================================================================
# EXPERIMENT 4: Noether's theorem — symmetries generate conserved charges
# ============================================================================
def experiment_4_noether_charges():
    """Substrate symmetries → conserved charges; total splits into sectors."""
    print("=" * 72)
    print("EXPERIMENT 4: Noether's Theorem on the Substrate")
    print("=" * 72)
    print()
    print("Each continuous symmetry of H_sub generates a conserved charge:")
    print("  time translation → H_sub  (total energy)")
    print("  geometric U(1) (Ψ→e^{iα}Ψ, the gauge symmetry) → ½Σ|Ψ|²")
    print("  potential U(1) → ½Σ(Φ_s²+J_ΔNFR²)")
    print()

    G = _build_graph(30)
    cert = verify_noether_conservation(G)
    charges = noether_charges(extract_phase_space_point(G))

    print(f"  H_sub (time translation) = {charges['time_translation']:.4f}")
    print(f"  E_geo (geometric U(1))   = {charges['geometric_u1']:.4f}")
    print(f"  E_pot (potential U(1))   = {charges['potential_u1']:.4f}")
    print()
    print(f"  H_sub = E_geo + E_pot exactly : {cert.splits_exactly}")
    print("  max drift along the flow:")
    print(f"    H_sub  = {cert.max_hamiltonian_drift:.2e}")
    print(f"    E_geo  = {cert.max_geometric_drift:.2e}")
    print(f"    E_pot  = {cert.max_potential_drift:.2e}")
    print(f"  ALL CONSERVED: {cert.is_conserved}")
    print()
    print("VALIDATED: the U(1)×U(1) symmetry refines time-translation")
    print("conservation — the total energy splits into two separately-")
    print("conserved sector charges. E_geo = ½Σ|Ψ|² is exactly the gauge")
    print("invariant of physics/gauge.py. Noether's theorem on the")
    print("emergent substrate, derived to machine precision.")
    print()


# ============================================================================
# EXPERIMENT 5: Hermitian (flat Kähler) structure — Ψ is the complex coordinate
# ============================================================================
def experiment_5_hermitian_structure():
    """The substrate is Hermitian; Ψ = K_φ + i·J_φ is the complex coord."""
    print("=" * 72)
    print("EXPERIMENT 5: Hermitian (flat Kähler) Structure")
    print("=" * 72)
    print()
    print("The substrate carries a compatible triple (ω, J, g):")
    print("  ω = symplectic form,  J = −ω (complex structure, J² = −I),")
    print("  g = ω·J = identity (compatible metric).")
    print("The complex coordinate ζ = q + i·p makes each fiber ℝ⁴ ≅ ℂ².")
    print()

    G = _build_graph(30)
    cert = verify_hermitian_structure(G)

    print(f"  J² = −I                       : {cert.j_squared_is_minus_id}")
    print(f"  g = identity (pos. definite)  : {cert.metric_is_identity}")
    print(f"  J is g-orthogonal             : {cert.j_is_orthogonal}")
    print(f"  compatible ω(u,v) = g(Ju,v)    : {cert.compatible}")
    print(f"  Ψ = ζ^A (geometric coordinate) : " f"{cert.psi_is_geometric_coordinate}")
    print(f"  H_sub = Kähler potential       : " f"{cert.kahler_potential_matches}")
    print(f"  complex dimension dim_ℂ        : {cert.complex_dimension}")
    print()
    print(f"  VALID HERMITIAN STRUCTURE: " f"{cert.is_valid_hermitian_structure}")
    print()
    print("VALIDATED: Ψ = K_φ + i·J_φ of physics/gauge.py is NOT ad-hoc — it")
    print("is the complex coordinate ζ^A the substrate's complex structure J")
    print("induces on the geometric sector. The 'i' in Ψ IS the J = −ω of")
    print("the emergent geometry. H_sub = ½Σ|ζ|² is the Kähler potential, and")
    print("the substrate flow is the diagonal U(1) phase rotation")
    print("ζ → e^{−it}ζ.")
    print()


# ============================================================================
# EXPERIMENT 6: Complete integrability — action–angle variables (Liouville)
# ============================================================================
def experiment_6_integrability():
    """The substrate flow is completely integrable; actions are ½|ζ|²."""
    print("=" * 72)
    print("EXPERIMENT 6: Complete Integrability (Liouville–Arnold)")
    print("=" * 72)
    print()
    print("H_sub = ½Σ(K_φ² + J_φ² + Φ_s² + J_ΔNFR²) is a sum of decoupled")
    print("oscillators — one per conjugate pair. So each pair contributes an")
    print("action I = ½|ζ|², giving 2N integrals for a 2N-DOF system: the")
    print("flow is completely integrable, with action–angle coordinates")
    print("(I_i, θ_i) in which it is a rigid phase rotation θ → θ − t.")
    print()

    G = _build_graph(30)
    cert = verify_integrability(G)

    print(f"  degrees of freedom (2N)        : {cert.degrees_of_freedom}")
    print(f"  independent action variables   : {cert.n_action_variables}")
    print(
        f"  actions in involution {{I,J}}=0  : "
        f"{cert.actions_in_involution} "
        f"(max |bracket| {cert.max_involution_bracket:.1e})"
    )
    print(
        f"  actions conserved along flow   : {cert.actions_conserved} "
        f"(max drift {cert.max_action_drift:.1e})"
    )
    print(
        f"  angles advance θ(t) = θ(0) − t : "
        f"{cert.angles_advance_linearly} "
        f"(max err {cert.max_angle_error:.1e})"
    )
    print(
        f"  Σ I^A = E_geo,  Σ I^B = E_pot   : " f"{cert.sector_actions_match_charges}"
    )
    print()
    print(f"  COMPLETELY INTEGRABLE: {cert.is_completely_integrable}")
    print()
    print("VALIDATED: the per-node moduli ½|ζ|² are the action variables /")
    print("adiabatic invariants of the substrate harmonic backbone, and the")
    print("U(1) phases θ = arg ζ are their conjugate angles. The 13 operators")
    print("act as canonical transformations that redistribute these actions.")
    print("HONEST SCOPE: this is the integrability of the H_sub backbone, not")
    print("of the full nonlinear operator dynamics.")
    print()


# ============================================================================
# EXPERIMENT 7: Poincaré–Cartan integral invariants — the ω^k tower
# ============================================================================
def experiment_7_poincare_cartan():
    """The flow preserves the ω^k tower; ∮p·dq = 2π·I (Bohr–Sommerfeld)."""
    print("=" * 72)
    print("EXPERIMENT 7: Poincaré–Cartan Integral Invariants")
    print("=" * 72)
    print()
    print("The flow φ_t preserves the symplectic form ω (φ_t^* ω = ω), so it")
    print("preserves the whole tower of integral invariants ω^k (k = 1 … N):")
    print("  k=1   relative invariant ∮ p dq  (M symplectic, MᵀΩM = Ω),")
    print("  1<k<N intermediate ∫ω^k  (palindromic char. poly of M),")
    print("  k=N   Liouville volume ω^N  (det M = 1).")
    print()

    G = _build_graph(30)
    cert = verify_poincare_cartan(G)

    print(
        f"  ω preserved (MᵀΩM = Ω)         : "
        f"{cert.preserves_symplectic_form} "
        f"(drift {cert.max_omega_drift:.1e})"
    )
    print(f"  palindromic char. polynomial   : " f"{cert.char_poly_palindromic}")
    print(f"  Liouville volume (det M = 1)   : {cert.volume_preserved}")
    print(
        f"  ∮ p dq constant under flow     : "
        f"{cert.relative_invariant_preserved} "
        f"(drift {cert.max_relative_drift:.1e})"
    )
    print(
        f"  Bohr–Sommerfeld |∮p dq| = 2πI  : "
        f"{cert.bohr_sommerfeld_holds} "
        f"(err {cert.max_bohr_error:.1e})"
    )
    print()
    print(f"  ALL INVARIANTS HOLD: {cert.all_invariants_hold}")
    print()
    print("VALIDATED: ω-preservation (Poincaré's relative invariant) is the")
    print("integral form of Liouville's theorem and is STRONGER than div=0:")
    print("it preserves areas ∮ p dq, not just the top volume. On an action")
    print("torus ∮ p dq = 2π·I recovers the Bohr–Sommerfeld quantum, tying")
    print("the integral invariant to the action variables of Experiment 6.")
    print()


# ============================================================================
# EXPERIMENT 8: Marsden–Weinstein symplectic reduction by the U(1) flow
# ============================================================================
def experiment_8_symplectic_reduction():
    """The diagonal U(1) flow symmetry reduces P to a P//U(1) of dim 4N−2."""
    print("=" * 72)
    print("EXPERIMENT 8: Marsden–Weinstein Symplectic Reduction")
    print("=" * 72)
    print()
    print("The flow ζ → e^{−it}ζ is the diagonal U(1) action rotating every")
    print("conjugate pair together. Its moment map is J = Σ I_k = H_sub (the")
    print("time-translation Noether charge). Reducing P by this symmetry —")
    print("P//U(1) = J⁻¹(μ)/U(1) — quotients the collective phase, leaving")
    print("the relative phases φ_k = θ_k − θ_0 as the reduced coordinates.")
    print()

    G = _build_graph(30)
    cert = verify_symplectic_reduction(G)

    print(
        f"  moment map J = Σ I_k = H_sub   : "
        f"{cert.moment_map_is_hamiltonian} "
        f"(J = {cert.moment_map_value:.4f})"
    )
    print(
        f"  J conserved (U(1) symmetry)    : "
        f"{cert.moment_map_conserved} "
        f"(drift {cert.max_moment_drift:.1e})"
    )
    print(
        f"  dim P → dim P//U(1)            : "
        f"{cert.phase_space_dimension} → {cert.reduced_dimension}  "
        f"(4N−2)"
    )
    print(
        f"  reduced ω non-degenerate       : "
        f"{cert.reduced_form_nondegenerate} "
        f"(det {cert.reduced_form_determinant:.3g})"
    )
    print(f"  relative phases φ_k invariant  : " f"{cert.relative_phases_invariant}")
    print()
    print(f"  VALID REDUCTION: {cert.is_valid_reduction}")
    print()
    print("VALIDATED: the reduced 2-form Σ dI_k ∧ dφ_k is canonical and")
    print("non-degenerate, so P//U(1) is a genuine symplectic manifold of")
    print("dimension 4N−2. The symmetry that GENERATES the flow (time")
    print("translation) is the symmetry one reduces by — moment map = H_sub.")
    print("HONEST SCOPE: reduction of the FLAT substrate by its diagonal")
    print("U(1); the reduced space is a flat linear symplectic space.")
    print()


# ============================================================================
# EXPERIMENT 9: Polarization symmetry (U(2)) — new Stokes charges
# ============================================================================
def experiment_9_polarization():
    """H_sub is a ℂ² doublet norm → U(2) polarization symmetry → Stokes vector."""
    print("=" * 72)
    print("EXPERIMENT 9: Polarization Symmetry U(2) (new conserved charges)")
    print("=" * 72)
    print()
    print("H_sub = ½Σ‖(ζ^A, ζ^B)‖² is the squared norm of a complex doublet")
    print("(ζ^A geometric, ζ^B potential), so it is invariant under the FULL")
    print("U(2) on the doublet — the POLARIZATION symmetry of a two-component")
    print("complex field (the same math as classical wave polarization,")
    print("Stokes 1852 / Poincaré 1892). U(1)×U(1) (Noether) is its Cartan")
    print("torus; the SU(2) part gives the three Stokes parameters.")
    print()

    G = _build_graph(30)
    cert = verify_polarization_symmetry(G)

    print(f"  P_1 = Σ(K_φ·Φ_s + J_φ·J_ΔNFR)  : {cert.p_1:.4f}  (NEW)")
    print(f"  P_2 = Σ(K_φ·J_ΔNFR − J_φ·Φ_s)  : {cert.p_2:.4f}  (NEW)")
    print(f"  P_3 = E_geo − E_pot            : {cert.p_3:.4f}")
    print(f"  squared magnitude |P|²         : {cert.magnitude_sq:.4f}")
    print(f"  P_3 = E_geo − E_pot            : " f"{cert.p3_equals_energy_difference}")
    print(
        f"  su(2) closes {{P_a,P_b}}=2εP_c   : "
        f"{cert.su2_algebra_closes} (res {cert.max_algebra_residual:.1e})"
    )
    print(f"  SU(2) rotation symplectic      : {cert.rotation_is_symplectic}")
    print(
        f"  charges conserved along flow   : "
        f"{cert.charges_conserved} (drift {cert.max_charge_drift:.1e})"
    )
    print(
        f"  fully polarized |P_node|=e_node: "
        f"{cert.full_polarization_holds} "
        f"(res {cert.max_polarization_residual:.1e})"
    )
    print()
    print(f"  VALID POLARIZATION SYMMETRY: {cert.is_valid_polarization_symmetry}")
    print()
    print("VALIDATED: P_1 and P_2 are GENUINELY NEW conserved charges — the")
    print("cross-sector correlations between the geometric and potential")
    print("sectors — beyond the known P_3 = E_geo − E_pot. They close the")
    print("su(2) algebra and are conserved along the flow. Per node the")
    print("Stokes 3-vector has length = energy: each node is fully polarized,")
    print("a unit point on the Poincaré sphere of radius = its energy.")
    print("HONEST SCOPE: a dynamical symmetry of the flat isotropic H_sub")
    print("backbone (the SU(2) mixes physically distinct sectors and is not")
    print("one of the 13 operators); the charges are exact along the substrate")
    print("flow and diagnostics at the full nonlinear level. The substrate is")
    print("a CLASSICAL phase field: this is the polarization (Stokes/Poincaré)")
    print("of a wave, NOT a quantum two-level system (no entanglement).")
    print()


# ============================================================================
# EXPERIMENT 10: Consolidated tower — the whole geometry in one call
# ============================================================================
def experiment_10_consolidated_tower():
    """verify_substrate_geometry runs the whole tower in a single call."""
    print("=" * 72)
    print("EXPERIMENT 10: Consolidated Geometric Tower (single entry point)")
    print("=" * 72)
    print()
    print("verify_substrate_geometry(G) runs all seven structural")
    print("verifications and bundles their certificates into one report —")
    print("the consolidated entry point to the whole emergent geometry.")
    print()

    G = _build_graph(30)
    report = verify_substrate_geometry(G)
    print(report.summary())
    print()
    print(f"  ALL STRUCTURES VALID: {report.all_structures_valid}")
    print()


def main():
    print()
    print("  TNFR Example 98: The Emergent Symplectic Substrate")
    print("  The geometry the nodal dynamics generates from itself")
    print("  ====================================================")
    print()

    experiment_1_emergent_substrate()
    experiment_2_energy_consistency()
    experiment_3_liouville_structural()
    experiment_4_noether_charges()
    experiment_5_hermitian_structure()
    experiment_6_integrability()
    experiment_7_poincare_cartan()
    experiment_8_symplectic_reduction()
    experiment_9_polarization()
    experiment_10_consolidated_tower()

    print("=" * 72)
    print("WHAT THIS ESTABLISHES")
    print("=" * 72)
    print()
    print("The TNFR nodal dynamics generates its OWN geometry — a symplectic")
    print("phase space P = ℝ^{4N} with canonical conjugate pairs, on which:")
    print("  • the energy functional is the Hamiltonian (Experiment 2),")
    print("  • the 13 operators are symplectomorphisms (Liouville, Exp. 3),")
    print("  • symmetries generate conserved charges (Noether, Exp. 4),")
    print("  • Ψ is the complex coordinate of a Hermitian structure (Exp. 5),")
    print("  • the flow is completely integrable (action–angle, Exp. 6),")
    print("  • it preserves the Poincaré–Cartan invariants (Exp. 7),")
    print("  • it reduces by its U(1) symmetry (Marsden–Weinstein, Exp. 8),")
    print("  • it carries a U(2) polarization symmetry with new Stokes")
    print("    charges (Exp. 9),")
    print("  • the whole tower verifies in one call (Exp. 10),")
    print("  • the nodal equation is the overdamped Hamiltonian flow.")
    print()
    print("This substrate is EMERGENT (derived from the conservation laws),")
    print("not imposed like the graph. It makes explicit the geometry the")
    print("dynamics already inhabits — a canonical consolidation. It does")
    print("not, by itself, resolve any open program; it is the geometric")
    print("foundation from which the canonical structures derive.")
    print()


if __name__ == "__main__":
    main()