#!/usr/bin/env python3
"""
C_POTENTIAL SPIRAL REMAPPING — COMPTON FREQUENCIES ON GEOMETRIC POTENTIAL
================================================================================
Date: 2026-04-03
Author: Jonathan Shelton (theory), Claude (computation)
Status: OBSERVATIONAL — map and observe, do NOT fit

Map each element's Compton frequency onto C_potential understood as a
geometric object with internal spiral structure. The spiral ratio
interpolates between dimensional equilibrium values:
    2D: 1.500
    3D: 1.618 (phi)
    4D: 1.707

We compute the d_eff for each element and observe where it falls
relative to these equilibria. We DO NOT assume the interpolation shape.

We also compute the FRACTIONAL POSITION within the 3D→4D interior:
    fraction = (d_eff - 3.0) / (4.0 - 3.0) = d_eff - 3.0

This tells us how deep into the 3D interior each element sits.
================================================================================
"""

import numpy as np
import json

# Physical constants
c_light = 2.998e8
h_planck = 6.626e-34
eV_to_J = 1.602e-19
amu_to_kg = 1.6605e-27

# Dimensional equilibrium spiral ratios
R_2D = 1.500
R_3D = 1.618034  # phi
R_4D = 1.707     # from cipher

# Load the sweep results
with open('/root/rhetroiluso/project_prometheus/time_ledger_theory/alchemical_geometry/results/unaudited/BLIND_SWEEP_PREDICTIONS_2026-04-03.json') as f:
    elements = json.load(f)

print("C_POTENTIAL SPIRAL REMAPPING")
print("=" * 100)
print()
print(f"Dimensional equilibria: 2D={R_2D}, 3D={R_3D:.6f}, 4D={R_4D}")
print(f"3D→4D spiral range: {R_4D - R_3D:.6f}")
print()

# For each element, compute:
# 1. d_eff (already in the data)
# 2. Fractional position in 3D→4D interior: (d_eff - 3) / 1
# 3. If we LINEAR interpolate the spiral: r_spiral = R_3D + frac × (R_4D - R_3D)
# 4. The distance from 3D equilibrium in spiral units

print(f"{'Z':>3} {'Sym':>4} {'d_eff':>7} {'frac_3D':>8} {'r_linear':>9} "
      f"{'Δr_from_3D':>11} {'Block':>5} {'Per':>3} {'d_pos':>5} "
      f"{'Archetype':>10} {'Spiral_corr':>11}")
print("-" * 105)

# Collect data for analysis
by_period_dblock = {}
all_data = []

for el in elements:
    Z = el['Z']
    if Z > 118:
        continue

    sym = el['symbol']
    d_eff = el['d_eff']
    block = el['block']
    period = el['period']
    d_pos = el.get('d_pos', 0)
    arch = el['archetype']
    corrected = el['spiral_corrected']

    # Fractional position in 3D→4D interior
    frac_3D = d_eff - 3.0  # 0 = at 3D boundary, 1 = at 4D boundary

    # Linear interpolation of spiral ratio
    if d_eff < 3.0:
        # Below 3D: interpolate between 2D and 3D
        frac_2D = (d_eff - 2.0) / 1.0
        r_spiral = R_2D + frac_2D * (R_3D - R_2D)
    else:
        # Above 3D: interpolate between 3D and 4D
        r_spiral = R_3D + frac_3D * (R_4D - R_3D)

    # Distance from 3D equilibrium
    delta_r = r_spiral - R_3D

    row = {
        'Z': Z, 'sym': sym, 'd_eff': d_eff, 'frac_3D': frac_3D,
        'r_spiral': r_spiral, 'delta_r': delta_r,
        'block': block, 'period': period, 'd_pos': d_pos,
        'arch': arch, 'corrected': corrected,
        'SO_meV': el['SO_meV'],
    }
    all_data.append(row)

    # Only print d-block and interesting elements
    if block == 'd' or Z <= 2 or corrected or Z in [82, 83, 84]:
        print(f"{Z:3d} {sym:>4s} {d_eff:7.4f} {frac_3D:8.4f} {r_spiral:9.6f} "
              f"{delta_r:11.6f} {block:>5s} {period:3d} {d_pos:5d} "
              f"{arch:>10s} {'YES' if corrected else '':>11s}")

    # Collect d-block by period for analysis
    if block == 'd':
        key = f"Period {period}"
        if key not in by_period_dblock:
            by_period_dblock[key] = []
        by_period_dblock[key].append(row)

# Analysis: do the spiral corrections correlate with spiral position?
print()
print("=" * 100)
print("ANALYSIS: SPIRAL DEVIATION vs KNOWN CORRECTIONS")
print("=" * 100)
print()

print("Elements that NEED spiral correction (from cipher document):")
print("(Tc, Ru, Rh in P5; Re, Os, Ir, Sm, Hg, Po in P6)")
print()

need_correction = {43, 44, 45, 75, 76, 77, 62, 80, 84}

for el in all_data:
    if el['Z'] in need_correction:
        print(f"  {el['sym']:>4s} (Z={el['Z']:3d}): d_eff={el['d_eff']:.4f}, "
              f"frac_3D={el['frac_3D']:.4f}, Δr={el['delta_r']:.6f}, "
              f"SO={el['SO_meV']:.0f} meV, "
              f"predicted={el['arch']}, corrected={'YES' if el['corrected'] else 'NO (should be)'}")

print()
print("Elements that DON'T need correction (same d-positions, earlier periods):")
need_no_correction = {25, 26, 27, 24, 30}  # Mn, Fe, Co, Cr, Zn (Period 4 analogs)

for el in all_data:
    if el['Z'] in need_no_correction:
        print(f"  {el['sym']:>4s} (Z={el['Z']:3d}): d_eff={el['d_eff']:.4f}, "
              f"frac_3D={el['frac_3D']:.4f}, Δr={el['delta_r']:.6f}, "
              f"SO={el['SO_meV']:.0f} meV, predicted={el['arch']}")

# Key comparison: Period 4 vs Period 5 vs Period 6 at same d-positions
print()
print("=" * 100)
print("PERIOD COMPARISON AT SAME d-POSITIONS")
print("=" * 100)
print()

# d_pos 5 (Group 7): Mn / Tc / Re
# d_pos 6 (Group 8): Fe / Ru / Os
# d_pos 7 (Group 9): Co / Rh / Ir
# d_pos 10 (Group 12): Zn / Cd / Hg

comparisons = [
    ("d_pos=5 (Group 7)", [(25, 'Mn'), (43, 'Tc'), (75, 'Re')]),
    ("d_pos=6 (Group 8)", [(26, 'Fe'), (44, 'Ru'), (76, 'Os')]),
    ("d_pos=7 (Group 9)", [(27, 'Co'), (45, 'Rh'), (77, 'Ir')]),
    ("d_pos=10 (Group 12)", [(30, 'Zn'), (48, 'Cd'), (80, 'Hg')]),
]

for label, group in comparisons:
    print(f"  {label}:")
    for Z, sym in group:
        el = next(e for e in all_data if e['Z'] == Z)
        needs = Z in need_correction
        print(f"    {sym:>2s} (P{el['period']}, Z={Z:2d}): "
              f"d_eff={el['d_eff']:.4f}, "
              f"Δr={el['delta_r']:.6f}, "
              f"SO_est={el['SO_meV']:.0f} meV  "
              f"{'← NEEDS CORRECTION' if needs else ''}")
    print()

# The critical question: is there a Δr threshold?
print("=" * 100)
print("THRESHOLD ANALYSIS")
print("=" * 100)
print()
print("Is there a Δr value below which no correction is needed,")
print("and above which correction IS needed?")
print()

corrected_deltas = [el['delta_r'] for el in all_data if el['Z'] in need_correction]
uncorrected_deltas = [el['delta_r'] for el in all_data
                      if el['block'] == 'd' and el['Z'] not in need_correction
                      and el['Z'] <= 80]

if corrected_deltas and uncorrected_deltas:
    print(f"  Δr for elements NEEDING correction:")
    print(f"    min: {min(corrected_deltas):.6f}")
    print(f"    max: {max(corrected_deltas):.6f}")
    print(f"    mean: {np.mean(corrected_deltas):.6f}")
    print()
    print(f"  Δr for d-block elements NOT needing correction:")
    print(f"    min: {min(uncorrected_deltas):.6f}")
    print(f"    max: {max(uncorrected_deltas):.6f}")
    print(f"    mean: {np.mean(uncorrected_deltas):.6f}")
    print()

    # Is there separation?
    gap = min(corrected_deltas) - max(uncorrected_deltas)
    print(f"  GAP between groups: {gap:.6f}")
    if gap > 0:
        print(f"  CLEAN SEPARATION — threshold between {max(uncorrected_deltas):.6f} "
              f"and {min(corrected_deltas):.6f}")
    else:
        print(f"  OVERLAP — no clean threshold in linear Δr")
        print(f"  The spiral interpolation may not be LINEAR.")
        print(f"  The internal topology may create non-linear structure.")