SilverSight/python/pist_braid_bridge.py

#!/usr/bin/env python3
"""
PIST + BRAID BRIDGE — Connecting Sprint Results to Lean Formalism
===================================================================

This module bridges the integration_sprint.py results with the Lean 4
formal infrastructure:
  - PIST.Spectral      (Q16_16 fixed-point spectral analysis)
  - BraidEigensolid    (Torus carrier, golden centering, eigensolid)
  - BraidField         (PIST operator B/G/A/P, RG flow)
  - BraidSpherionBridge (Cross-mode ↔ eigensolid correspondence)

Mappings implemented:
  1. Spectral coefficients → Q16_16 → PIST SpectralProfile
  2. Spiral index → TorusWinding (a, b) on T²
  3. 4-mode receipt → PIST field (B, G, A, P)
  4. Cross-mode agreement → Eigensolid convergence check
  5. Φ-corkscrew ↔ Golden centering (φ⁻¹ = 40560/65536)

Author: SilverSight Integration Layer
"""

import json
import math
import struct
from typing import Dict, List, Tuple, Optional
from dataclasses import dataclass, asdict

import numpy as np

# ========================================================================
# §1. Q16_16 FIXED-POINT ARITHMETIC (matches Lean SilverSight.FixedPoint)
# ========================================================================

Q16_SCALE = 65536  # 2^16
Q16_MAX_RAW = 2147483647  # 2^31 - 1
Q16_MIN_RAW = -2147483648  # -2^31


def q16_clamp(x: int) -> int:
    """Saturating clamp to Q16_16 range."""
    if x > Q16_MAX_RAW:
        return Q16_MAX_RAW
    if x < Q16_MIN_RAW:
        return Q16_MIN_RAW
    return x


def float_to_q16(x: float) -> int:
    """Convert float to Q16_16 raw value."""
    return q16_clamp(int(round(x * Q16_SCALE)))


def q16_to_float(raw: int) -> float:
    """Convert Q16_16 raw value to float."""
    return raw / Q16_SCALE


def q16_add(a: int, b: int) -> int:
    return q16_clamp(a + b)


def q16_sub(a: int, b: int) -> int:
    return q16_clamp(a - b)


def q16_mul(a: int, b: int) -> int:
    """Multiply two Q16_16 values, keeping Q16_16 precision."""
    return q16_clamp((a * b) // Q16_SCALE)


def q16_div(a: int, b: int) -> int:
    """Divide two Q16_16 values."""
    if b == 0:
        return Q16_MAX_RAW
    return q16_clamp((a * Q16_SCALE) // b)


def q16_sqrt(raw: int) -> int:
    """Integer square root of Q16_16 value. Returns floor(√x) in Q16_16."""
    if raw <= 0:
        return 0
    # √x in Q16_16 = √(x / 65536) * 65536 = √(x * 65536)
    val = raw if raw >= 0 else 0
    return int(math.isqrt(val * Q16_SCALE))


# Golden centering constant: φ⁻¹ ≈ 0.618033988...
# In Lean: Q16_16.ofRawInt 40560
# 40560 / 65536 = 0.618896484375
PHI_INV_Q16 = 40560
PHI = (1.0 + 5.0 ** 0.5) / 2.0
PSI = 2.0 * math.pi / (PHI ** 2)


# ========================================================================
# §2. PIST.SPECTRAL BRIDGE
# ========================================================================

@dataclass
class PISTSpectralProfile:
    """Python mirror of SilverSight.PIST.Spectral.SpectralProfile."""
    matrix_size: int        # Q16_16 raw
    rank: int              # Q16_16 raw
    spectral_gap: int      # Q16_16 raw
    density: int           # Q16_16 raw
    trace_val: int         # Q16_16 raw
    frobenius_norm: int    # Q16_16 raw
    laplacian_zero_count: int  # Q16_16 raw
    adjacency_eigenvalue_max: int  # Q16_16 raw
    laplacian_eigenvalue_max: int  # Q16_16 raw
    singular_value_max: int    # Q16_16 raw

    def to_float_dict(self) -> Dict[str, float]:
        return {
            "matrix_size": q16_to_float(self.matrix_size),
            "rank": q16_to_float(self.rank),
            "spectral_gap": q16_to_float(self.spectral_gap),
            "density": q16_to_float(self.density),
            "trace_val": q16_to_float(self.trace_val),
            "frobenius_norm": q16_to_float(self.frobenius_norm),
            "laplacian_zero_count": q16_to_float(self.laplacian_zero_count),
            "adjacency_eigenvalue_max": q16_to_float(self.adjacency_eigenvalue_max),
            "laplacian_eigenvalue_max": q16_to_float(self.laplacian_eigenvalue_max),
            "singular_value_max": q16_to_float(self.singular_value_max),
        }


def power_iteration_q16(mat: List[List[int]], max_iter: int = 100,
                        detect_convergence: bool = True) -> Tuple[int, bool]:
    """Dominant eigenvalue via power iteration in Q16_16.

    Matches: SilverSight.PIST.Spectral.powerIteration

    Returns (eigenvalue_q16, converged) where converged=False indicates
    the iteration may have failed (peripheral spectrum, oscillation).

    Known failure mode: matrices with eigenvalues on the unit circle at
    60° angles cause power iteration to oscillate. For these matrices,
    use exact_eigenvalue_q16() instead.
    """
    n = len(mat)
    if n == 0:
        return 0, True

    init_val = Q16_SCALE // n
    v = [init_val] * n
    prev_lam = 0
    oscillation_count = 0

    for iteration in range(max_iter):
        # Matrix-vector multiply
        mv = [0] * n
        for i in range(n):
            s = 0
            for j in range(n):
                s += mat[i][j] * (v[j] if j < len(v) else 0)
            mv[i] = s  # Keep in raw integer space

        # Norm squared
        nm2 = sum(x * x for x in mv)
        if nm2 <= 0:
            break

        nm = int(math.isqrt(nm2))
        if nm == 0:
            break

        # Normalize
        v = [q16_clamp((x * Q16_SCALE) // nm) for x in mv]

        # Convergence check: Rayleigh quotient should stabilize
        if detect_convergence and iteration > 10:
            mv_check = [0] * n
            for i in range(n):
                s = 0
                for j in range(n):
                    s += mat[i][j] * v[j]
                mv_check[i] = s
            num = sum(v[i] * mv_check[i] for i in range(n))
            den = sum(x * x for x in v)
            if den > 0:
                lam = (num * Q16_SCALE) // den
                # Check for oscillation (Rayleigh quotient bouncing between values)
                if abs(lam - prev_lam) < 100:  # Converged
                    pass
                elif iteration > 20 and abs(lam - prev_lam) > Q16_SCALE // 10:
                    oscillation_count += 1
                prev_lam = lam

    # Rayleigh quotient: v^T A v / v^T v
    mv = [0] * n
    for i in range(n):
        s = 0
        for j in range(n):
            s += mat[i][j] * (v[j] if j < len(v) else 0)
        mv[i] = s

    num = sum(v[i] * mv[i] for i in range(n))
    den = sum(x * x for x in v)
    if den <= 0:
        return 0, True

    result = q16_clamp((num * Q16_SCALE) // den)
    converged = oscillation_count < 3
    return result, converged


def exact_eigenvalue_q16(mat: List[List[int]]) -> int:
    """Exact dominant eigenvalue via numpy (characteristic polynomial).

    Use this as fallback when power_iteration_q16 reports non-convergence.
    Returns Q16_16 raw value.

    This is NOT a drop-in replacement for the Lean powerIteration —
    it uses float64 internally. But it's exact for integer matrices
    whose eigenvalues are representable in float64.
    """
    try:
        import numpy as np
        np_mat = np.array(mat, dtype=float)
        evals = np.linalg.eigvals(np_mat)
        spectral_radius = float(max(abs(evals)))
        return q16_clamp(int(spectral_radius * Q16_SCALE))
    except Exception:
        return 0


def compute_pist_spectral(eigenvalues: np.ndarray) -> PISTSpectralProfile:
    """Compute PIST spectral profile from eigenvalues (float → Q16_16).

    Mirrors: SilverSight.PIST.Spectral.computeSpectral
    """
    if len(eigenvalues) == 0:
        return PISTSpectralProfile(*([0] * 10))

    k = min(8, len(eigenvalues))
    evals = np.sort(eigenvalues)[::-1][:k]

    # Build 8x8 symmetric matrix from eigenvalues (diagonalization approximation)
    n = 8
    mat = [[0] * n for _ in range(n)]
    for i in range(min(len(evals), n)):
        val = float_to_q16(float(evals[i]))
        mat[i][i] = val
        # Add some off-diagonal coupling for realism
        if i + 1 < n:
            coupling = float_to_q16(float(evals[i]) * 0.1)
            mat[i][i + 1] = coupling
            mat[i + 1][i] = coupling

    # Symmetrize
    sym = [[(mat[i][j] + mat[j][i]) // 2 for j in range(n)] for i in range(n)]

    # Laplacian
    lap = [[0] * n for _ in range(n)]
    for i in range(n):
        deg = sum(sym[i])
        for j in range(n):
            lap[i][j] = deg if i == j else -sym[i][j]

    ev_max, converged = power_iteration_q16(sym)
    if not converged:
        # Fallback to exact eigenvalue computation
        ev_max = exact_eigenvalue_q16(sym)

    # Shift-deflation for second eigenvalue
    shift = (ev_max * 58982) // Q16_SCALE  # 0.9 * ev_max
    shifted = [[sym[i][j] for j in range(n)] for i in range(n)]
    for i in range(n):
        shifted[i][i] = q16_sub(shifted[i][i], shift)
    ev_shift, converged2 = power_iteration_q16(shifted)
    if not converged2:
        ev_shift = exact_eigenvalue_q16(shifted)
    ev_second = q16_sub(ev_max, ev_shift) if ev_shift < ev_max else ev_max
    spectral_gap = q16_sub(ev_max, ev_second)

    lap_max, converged3 = power_iteration_q16(lap)
    if not converged3:
        lap_max = exact_eigenvalue_q16(lap)

    # Density
    total = sum(sum(row) for row in mat)
    density = q16_clamp((total * Q16_SCALE) // (n * n)) if n > 0 else 0

    # Trace
    trace_val = sum(mat[i][i] for i in range(n))

    # Frobenius norm
    frob_sq = sum(sum(x * x for x in row) for row in mat)
    frob_norm = int(math.isqrt(frob_sq))

    # Rank (count non-zero rows)
    rank = sum(1 for row in mat if any(x != 0 for x in row))

    # Laplacian zero count
    lap_zero = sum(1 for i in range(n) if sum(mat[i]) - mat[i][i] == 0)

    # ATA max singular value
    ata = [[0] * n for _ in range(n)]
    for i in range(n):
        for j in range(n):
            s = 0
            for k_idx in range(n):
                s += mat[k_idx][i] * mat[k_idx][j]
            ata[i][j] = s
    ata_ev, converged4 = power_iteration_q16(ata)
    if not converged4:
        ata_ev = exact_eigenvalue_q16(ata)
    sv_max = q16_sqrt(ata_ev)

    return PISTSpectralProfile(
        matrix_size=float_to_q16(n),
        rank=float_to_q16(rank),
        spectral_gap=spectral_gap,
        density=density,
        trace_val=float_to_q16(trace_val),
        frobenius_norm=float_to_q16(frob_norm),
        laplacian_zero_count=float_to_q16(lap_zero),
        adjacency_eigenvalue_max=ev_max,
        laplacian_eigenvalue_max=lap_max,
        singular_value_max=sv_max,
    )


# ========================================================================
# §3. TORUS WINDING ↔ Φ-CORKSCREW
# ========================================================================

@dataclass
class TorusWinding:
    """Torus winding counts: H₁(T²; Z) = Z⟨a⟩ ⊕ Z⟨b⟩.

    Matches: SilverSight.BraidEigensolid.TorusWinding
    a = spatial winding (latitude cycle)
    b = phase/torsion winding (longitude cycle)

    The Q16_16 raws are LOSSY above value 32767 (Q16_MAX_RAW clamp);
    a_exact/b_exact carry the plain-ℤ winding with no clamp and are the
    authoritative values when present. BraidEigensolid.lean's
    TorusWinding needs the same widening (Int fields alongside the
    Q16_16 raws) before this exact layer can be mirrored formally.
    """
    a: int  # Q16_16 raw — saturates for values > 32767
    b: int  # Q16_16 raw — saturates for values > 32767
    a_exact: Optional[int] = None  # plain ℤ winding, no clamp
    b_exact: Optional[int] = None  # plain ℤ winding, no clamp

    def to_float(self) -> Tuple[float, float]:
        return q16_to_float(self.a), q16_to_float(self.b)


def spiral_to_torus_winding(spiral_index: int) -> TorusWinding:
    """Map spiral index to torus winding counts.

    The golden spiral f(n) = (√n·cos(nψ), √n·sin(nψ)) with ψ = 2π/φ²
    lives on a torus because ψ/2π = 1/φ² is irrational.

    Winding counts:
      a = spiral_index mod φ_step   (spatial winding)
      b = spiral_index // φ_step    (phase winding)

    where φ_step = round(φ) = 2 (since φ ≈ 1.618)

    ⚠️  SATURATION WARNING: b_raw uses Q16.16 encoding, which clamps at
    Q16_MAX_RAW / 65536 ≈ 32767.99. For spiral_index > 65535, the
    phase winding b silently saturates. The a_exact/b_exact fields carry
    the unclamped integers; torus_to_spiral_index prefers them, so the
    round trip is exact for every spiral_index.

    This mirrors: TorusWinding in BraidEigensolid.lean
    """
    phi_step = int(round(PHI))  # 2
    a_val = spiral_index % phi_step
    b_val = spiral_index // phi_step
    a_raw = float_to_q16(float(a_val))
    b_raw = float_to_q16(float(b_val))
    return TorusWinding(a=a_raw, b=b_raw, a_exact=a_val, b_exact=b_val)


def spiral_to_torus_winding_safe(spiral_index: int) -> Tuple[TorusWinding, bool]:
    """Map spiral index to torus winding with saturation detection.

    Returns (winding, saturated) where saturated=True if the Q16.16
    encoding cannot represent the phase winding losslessly.

    For indices > 65535, the caller should use the raw integer
    spiral_index directly instead of the torus winding.
    """
    phi_step = int(round(PHI))  # 2
    a_val = spiral_index % phi_step
    b_val = spiral_index // phi_step
    max_q16_val = Q16_MAX_RAW // 65536  # ≈ 32767
    saturated = b_val > max_q16_val
    a_raw = float_to_q16(float(a_val))
    b_raw = float_to_q16(float(b_val))
    return TorusWinding(a=a_raw, b=b_raw, a_exact=a_val, b_exact=b_val), saturated


def torus_to_spiral_index(w: TorusWinding) -> int:
    """Inverse: recover spiral index from torus winding.

    n = φ_step · b + a

    Prefers the exact ℤ fields when present (lossless for all n);
    falls back to the Q16.16 raws, which saturate for
    spiral_index > 65535 — use spiral_to_torus_winding_safe() to
    detect that case on legacy windings without exact fields.
    """
    phi_step = int(round(PHI))
    if w.a_exact is not None and w.b_exact is not None:
        return phi_step * w.b_exact + w.a_exact
    b_int = int(round(q16_to_float(w.b)))
    a_int = int(round(q16_to_float(w.a)))
    return phi_step * b_int + a_int


# ========================================================================
# §4. PIST FIELD ↔ 4-MODE SPRINT RECEIPT
# ========================================================================

@dataclass
class PISTField:
    """PIST operator: q_{t+1} = PIST(q_t; B, G, A, P).

    Matches: SilverSight.BraidField.PISTField
    B = Burden (load, cost, attention)
    G = Geometry (basins, manifolds, gradients)
    A = Adaptation (sorting rate, pacing, convergence)
    P = Protection (compression, thresholding, overload)
    """
    burden: int      # Q16_16 raw
    geometry: int    # Q16_16 raw
    adaptation: int  # Q16_16 raw
    protection: int  # Q16_16 raw

    def to_float_dict(self) -> Dict[str, float]:
        return {
            "burden": q16_to_float(self.burden),
            "geometry": q16_to_float(self.geometry),
            "adaptation": q16_to_float(self.adaptation),
            "protection": q16_to_float(self.protection),
        }


def sprint_receipt_to_pist(result: Dict) -> PISTField:
    """Convert a single sprint mode result to PIST field.

    B = execution_time_ms (how expensive was this mode?)
    G = dominant_eigenvalue + spectral_gap (what did we learn about the graph?)
    A = checks_passed / checks_total (how well did we adapt?)
    P = 1.0 if checks_passed == checks_total else 0.0 (did we protect against errors?)
    """
    B = float_to_q16(result.get("executionTimeMs", 0.0) / 100.0)

    geom = result.get("dominantEigenvalue", 0.0) + result.get("spectralGap", 0.0)
    G = float_to_q16(geom / 10.0)

    checks_total = result.get("checks_total", 7)
    checks_passed = result.get("checks_passed", 7)
    A = float_to_q16(checks_passed / checks_total if checks_total > 0 else 0.0)

    P = Q16_SCALE if checks_passed == checks_total else Q16_SCALE // 2

    return PISTField(burden=B, geometry=G, adaptation=A, protection=P)


def compare_pist_fields(p1: PISTField, p2: PISTField, tolerance: float = 0.05) -> bool:
    """Check if two PIST fields agree within Q16_16 tolerance."""
    for field in ["burden", "geometry", "adaptation", "protection"]:
        v1 = q16_to_float(getattr(p1, field))
        v2 = q16_to_float(getattr(p2, field))
        if abs(v1 - v2) > tolerance:
            return False
    return True


# ========================================================================
# §5. EIGENSOLID CONVERGENCE CHECK
# ========================================================================

def check_eigensolid_convergence(results: List[Dict]) -> Dict:
    """Verify that all modes converge to the same eigensolid.

    Theorem analog: SilverSight.BraidEigensolid.eigensolid_convergence

    All modes should produce:
      - Same dominant eigenvalue (within numerical tolerance)
      - Same spiral index (exact agreement)
      - Same DNA sequence (exact agreement)
      - Same PIST field (within Q16_16 tolerance)
    """
    if len(results) < 2:
        return {"converged": False, "reason": "need_at_least_2_modes"}

    # Check exact agreement on discrete invariants
    spirals = [r.get("spiral_index") for r in results]
    dnas = [r.get("dnaSequence") for r in results]

    spiral_agree = len(set(spirals)) == 1
    dna_agree = len(set(dnas)) == 1

    # Check approximate agreement on continuous invariants
    lambdas = [r.get("dominantEigenvalue", 0.0) for r in results]
    lambda_cv = np.std(lambdas) / np.mean(lambdas) if np.mean(lambdas) > 0 else 0

    gaps = [r.get("spectralGap", 0.0) for r in results]
    gap_cv = np.std(gaps) / np.mean(gaps) if np.mean(gaps) > 0 else 0

    # PIST field agreement
    pist_fields = [sprint_receipt_to_pist(r) for r in results]
    pist_agree = all(
        compare_pist_fields(pist_fields[0], pf) for pf in pist_fields[1:]
    )

    converged = spiral_agree and dna_agree and lambda_cv < 0.01 and gap_cv < 0.01 and pist_agree

    return {
        "converged": converged,
        "spiral_agree": spiral_agree,
        "dna_agree": dna_agree,
        "lambda_cv": float(lambda_cv),
        "gap_cv": float(gap_cv),
        "pist_agree": pist_agree,
        "n_modes": len(results),
        "pist_fields": [pf.to_float_dict() for pf in pist_fields],
    }


# ========================================================================
# §6. GOLDEN CENTERING ↔ Φ-CORKSCREW
# ========================================================================

def golden_centering_compress(q16_val: int) -> int:
    """Apply golden centering contraction: x → φ⁻¹ · x.

    Matches: goldenCentering in BraidEigensolid.lean
    Uses the fixed-point constant 40560 = φ⁻¹ in Q16_16.

    This is the compressor's contraction envelope — it keeps all crossing
    weights in the Q0_2 range [0, 16384] after finite iteration.
    """
    return q16_mul(q16_val, PHI_INV_Q16)


def phi_corkscrew_to_q16(spiral_index: int, n_coeffs: int = 9) -> List[int]:
    """Convert spiral index to Q16_16 spectral coefficients.

    The Φ-corkscrew packs spectral info into a single integer.
    Unpack: recover coefficients via base-φ decomposition.
    """
    coeffs = []
    n = spiral_index
    for i in range(n_coeffs):
        digit = n % 8  # Hachimoji base-8
        coeffs.append(float_to_q16(digit / 8.0))
        n //= 8
    return coeffs


def q16_to_phi_corkscrew(coeffs: List[int]) -> int:
    """Pack Q16_16 spectral coefficients into spiral index (inverse)."""
    spiral = 0
    for i, c in enumerate(coeffs):
        digit = int(round(q16_to_float(c) * 8)) % 8
        spiral += digit * (8 ** i)
    return spiral


# ========================================================================
# §7. OCTAGONAL NORM ↔ FISHER-RAO BOUND
# ========================================================================

def octagonal_norm(x: float, y: float) -> float:
    """Octagonal norm: κ ≈ max(|x|,|y|) + 3/8·min(|x|,|y|).

    Matches: PhaseVec.normApprox in BraidBracket.lean
    """
    ax, ay = abs(x), abs(y)
    hi, lo = max(ax, ay), min(ax, ay)
    return hi + (3.0 / 8.0) * lo


def fisher_rao_distance(p: np.ndarray, q: np.ndarray) -> float:
    """Fisher-Rao distance on probability simplex: arccos(Σ√(pᵢqᵢ))."""
    bc = np.sum(np.sqrt(p * q))
    bc = np.clip(bc, -1.0, 1.0)
    return np.arccos(bc)


def octagonal_fisher_bound(braid_state_8d: np.ndarray) -> float:
    """Show that octagonal norm upper-bounds Fisher-Rao distance.

    For an 8-strand braid state interpreted as a point on Δ₇,
    the octagonal norm of the phase vector upper-bounds the
    Fisher-Rao distance from the uniform distribution.

    Returns: ratio octagonal_norm / fisher_rao_distance (should be ≥ 1)
    """
    # Normalize to probability simplex
    s = braid_state_8d.sum()
    if s <= 0:
        return float('inf')
    p = braid_state_8d / s
    uniform = np.ones(8) / 8.0

    fisher_dist = fisher_rao_distance(p, uniform)

    # Octagonal norm on first two coordinates (phase vector)
    x, y = p[0] - 1.0 / 8.0, p[1] - 1.0 / 8.0
    oct_norm = octagonal_norm(x, y)

    ratio = oct_norm / fisher_dist if fisher_dist > 1e-12 else float('inf')
    return float(ratio)


# ========================================================================
# §8. MAIN — Load sprint receipt and run full bridge
# ========================================================================

def run_bridge(sprint_receipt_path: str = "sprint_receipt.json") -> Dict:
    """Load sprint receipt and run all bridge analyses."""
    try:
        with open(sprint_receipt_path, 'r') as f:
            receipt = json.load(f)
    except FileNotFoundError:
        return {"error": f"Receipt not found: {sprint_receipt_path}"}

    results = receipt.get("results", [])
    if not results:
        return {"error": "No results in receipt"}

    output = {
        "quimb_backend": receipt.get("quimb_backend", "unknown"),
        "n_modes": len(results),
        "bridge_analyses": {},
    }

    # 1. PIST Spectral for each mode
    spectral_profiles = []
    for r in results:
        # Create synthetic 8x8 from the eigenvalues
        ev_max = r.get("eigenvalue_max", 1.0)
        ev_min = r.get("eigenvalue_min", 0.0)
        gap = r.get("spectralGap", 0.0)
        # Create a spectrum: dominant, dominant-gap, and the rest
        spectrum = np.array([ev_max, ev_max - gap] + [ev_min] * 6)
        profile = compute_pist_spectral(spectrum)
        spectral_profiles.append(profile)

    output["bridge_analyses"]["pist_spectral"] = {
        "profiles": [p.to_float_dict() for p in spectral_profiles],
        "mean_gap_q16": q16_to_float(
            sum(p.spectral_gap for p in spectral_profiles) // len(spectral_profiles)
        ),
    }

    # 2. Torus winding for each mode
    torus_windings = []
    for r in results:
        tw = spiral_to_torus_winding(r.get("spiral_index", 0))
        torus_windings.append(tw)

    output["bridge_analyses"]["torus_winding"] = {
        "windings": [{"a": tw.to_float()[0], "b": tw.to_float()[1]}
                      for tw in torus_windings],
        "inverse_check": [
            torus_to_spiral_index(tw) == r.get("spiral_index", 0)
            for tw, r in zip(torus_windings, results)
        ],
    }

    # 3. PIST field for each mode
    pist_fields = [sprint_receipt_to_pist(r) for r in results]
    output["bridge_analyses"]["pist_field"] = {
        "fields": [pf.to_float_dict() for pf in pist_fields],
        "all_agree": all(compare_pist_fields(pist_fields[0], pf)
                         for pf in pist_fields[1:]),
    }

    # 4. Eigensolid convergence check
    output["bridge_analyses"]["eigensolid_convergence"] = \
        check_eigensolid_convergence(results)

    # 5. Golden centering compression check
    max_eigenvalue_q16 = float_to_q16(
        max(r.get("dominantEigenvalue", 0.0) for r in results)
    )
    compressed = golden_centering_compress(max_eigenvalue_q16)
    output["bridge_analyses"]["golden_centering"] = {
        "original_q16": max_eigenvalue_q16,
        "compressed_q16": compressed,
        "phi_inv": PHI_INV_Q16,
        "phi_inv_float": q16_to_float(PHI_INV_Q16),
    }

    # 6. Φ-corkscrew ↔ Q16_16 roundtrip
    if results:
        spiral = results[0].get("spiral_index", 0)
        coeffs = phi_corkscrew_to_q16(spiral)
        recovered = q16_to_phi_corkscrew(coeffs)
        output["bridge_analyses"]["phi_corkscrew_roundtrip"] = {
            "original": spiral,
            "recovered": recovered,
            "match": spiral == recovered,
            "n_coeffs": len(coeffs),
        }

    # Overall verdict
    conv = output["bridge_analyses"]["eigensolid_convergence"]
    pist_agree = output["bridge_analyses"]["pist_field"]["all_agree"]
    corkscrew_ok = output["bridge_analyses"]["phi_corkscrew_roundtrip"]["match"]
    output["bridge_verdict"] = {
        "all_checks_pass": conv.get("converged", False) and pist_agree and corkscrew_ok,
        "eigensolid_converged": conv.get("converged", False),
        "pist_fields_agree": pist_agree,
        "corkscrew_roundtrip_ok": corkscrew_ok,
        "formal_backing": [
            "BraidEigensolid.eigensolid_convergence",
            "BraidEigensolid.receipt_invertible",
            "BraidSpherionBridge.receipt_correspondence",
            "BraidSpherionBridge.braidCross_merge_correspondence",
        ],
    }

    return output


if __name__ == "__main__":
    import os
    receipt_path = os.path.join(os.path.dirname(__file__), "sprint_receipt.json")
    result = run_bridge(receipt_path)
    print(json.dumps(result, indent=2, default=str))