#!/usr/bin/env python3
"""
C_POTENTIAL LANDSCAPE — FREQUENCY BIRTH MODEL
================================================================================
Date: 2026-04-03
Author: Jonathan Shelton (theory), Claude (computation)
Status: OBSERVATIONAL COMPUTATION — no fitting

Build the C_potential landscape from first principles:
  1. The quadratic equation gives boundary energies (floors)
  2. The percolation threshold (29%) gives the bulge point
  3. The frequency floor of each cascade level is BORN from
     the previous level's bulge

Then place each element's Compton frequency on this landscape
and OBSERVE what happens. Do not fit. Do not adjust.

The landscape is NOT flat. It has internal spiral structure
that develops with depth. The spiral at any point is determined
by the floor and bulge of that cascade level.
================================================================================
"""

import numpy as np
import json

# =============================================================================
# CONSTANTS
# =============================================================================
c_light = 2.998e8
h_planck = 6.626e-34
eV_to_J = 1.602e-19
amu_to_kg = 1.6605e-27
phi_c = 0.2895  # percolation threshold

# Dimensional equilibrium spiral ratios
R_eq = {2: 1.500, 3: 1.618034, 4: 1.707}

# =============================================================================
# THE LANDSCAPE: BOUNDARY ENERGIES FROM QUADRATIC
# =============================================================================
def E_boundary_eV(d):
    """Energy at dimensional boundary d (in eV)"""
    log_E = 0.1964 * d**2 + 8.0932 * d - 20.0373
    return 10**log_E

def f_boundary_Hz(d):
    """Frequency at dimensional boundary d (in Hz)"""
    E = E_boundary_eV(d) * eV_to_J
    return E / h_planck

print("=" * 80)
print("C_POTENTIAL LANDSCAPE — DIMENSIONAL BOUNDARIES")
print("=" * 80)
print()

# The cascade floors and ceilings
# Each dimension's floor = previous dimension's overflow frequency
# The overflow fires at the bulge: floor + (ceiling - floor) × capacity
# The ceiling is at r = 0.5 (dimensional equilibrium)
# The bulge is at floor + φ_c × (ceiling - floor)

print("DIMENSIONAL BOUNDARIES (from quadratic):")
print(f"{'Boundary':>12} {'Energy (eV)':>14} {'Frequency (Hz)':>16} {'log₁₀(f)':>10}")
print("-" * 60)
for d in range(1, 6):
    E = E_boundary_eV(d)
    f = f_boundary_Hz(d)
    print(f"  d={d} ({d}D→{d+1}D) {E:14.3e} {f:16.3e} {np.log10(f):10.4f}")

print()
print("WITHIN THE 3D→4D INTERIOR (d = 3.0 to 4.0):")
print("This is where all elements live.")
print()

# The 3D interior spans from f_floor(3D) to f_ceiling(3D)
f_floor_3D = f_boundary_Hz(2)   # 2D→3D boundary = 3D's floor
f_ceiling_3D = f_boundary_Hz(3)  # 3D→4D boundary = 3D's ceiling

print(f"  3D floor (from 2D→3D):   {f_floor_3D:.3e} Hz  (log={np.log10(f_floor_3D):.4f})")
print(f"  3D ceiling (at 3D→4D):   {f_ceiling_3D:.3e} Hz  (log={np.log10(f_ceiling_3D):.4f})")
print(f"  3D frequency range:      {np.log10(f_ceiling_3D) - np.log10(f_floor_3D):.4f} decades")
print()

# The bulge point within 3D
f_bulge_3D_log = np.log10(f_floor_3D) + phi_c * (np.log10(f_ceiling_3D) - np.log10(f_floor_3D))
f_bulge_3D = 10**f_bulge_3D_log

print(f"  3D BULGE (29% of range): {f_bulge_3D:.3e} Hz  (log={f_bulge_3D_log:.4f})")
print(f"  Elements below bulge: in stable 3D (no spiral transition)")
print(f"  Elements above bulge: spiral transitioning toward 4D")
print()

# =============================================================================
# BUT: Within 3D, there are SUB-CASCADES (periods/shells)
# =============================================================================
print("=" * 80)
print("SUB-CASCADES WITHIN 3D — PERIOD SHELLS")
print("=" * 80)
print()
print("""
Within the 3D interior, each PERIOD represents a sub-cascade.
Each period's electron shell is a new cycle on the internal spiral.
The floor of each period = the completion of the previous period.

The sub-cascade floors are determined by the COMPTON FREQUENCIES
of the noble gases (which close each period) and the alkali metals
(which open the next).
""")

# Noble gas Compton frequencies (close each period)
noble_gases = {
    'He': (2, 4.003),
    'Ne': (10, 20.18),
    'Ar': (18, 39.95),
    'Kr': (36, 83.80),
    'Xe': (54, 131.3),
    'Rn': (86, 222.0),
}

# Alkali metals (open each period)
alkalis = {
    'Li': (3, 6.941),
    'Na': (11, 22.99),
    'K': (19, 39.10),
    'Rb': (37, 85.47),
    'Cs': (55, 132.9),
    'Fr': (87, 223.0),
}

def compton_freq(mass_amu):
    """Compton frequency from atomic mass"""
    m_kg = mass_amu * amu_to_kg
    return m_kg * c_light**2 / h_planck

print(f"{'Element':>8} {'Z':>4} {'ν_C (Hz)':>14} {'log₁₀(ν_C)':>12} {'Role':>15}")
print("-" * 60)
for name, (Z, mass) in sorted(noble_gases.items(), key=lambda x: x[1][0]):
    f = compton_freq(mass)
    print(f"{name:>8} {Z:4d} {f:14.3e} {np.log10(f):12.4f} {'period closer':>15}")

print()
for name, (Z, mass) in sorted(alkalis.items(), key=lambda x: x[1][0]):
    f = compton_freq(mass)
    print(f"{name:>8} {Z:4d} {f:14.3e} {np.log10(f):12.4f} {'period opener':>15}")

# =============================================================================
# THE COMPTON FREQUENCY LANDSCAPE
# =============================================================================
print()
print("=" * 80)
print("ALL ELEMENTS ON THE C_POTENTIAL LANDSCAPE")
print("=" * 80)
print()

# Load sweep data
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)

# Compute the position of each element relative to:
# a) The 3D interior (floor to ceiling)
# b) The 3D bulge (29% of range)
# c) Its PERIOD's sub-range

log_floor_3D = np.log10(f_floor_3D)
log_ceiling_3D = np.log10(f_ceiling_3D)
log_range_3D = log_ceiling_3D - log_floor_3D
log_bulge_3D = log_floor_3D + phi_c * log_range_3D

print(f"3D interior: log₁₀(f) from {log_floor_3D:.4f} to {log_ceiling_3D:.4f}")
print(f"3D range: {log_range_3D:.4f} decades")
print(f"3D bulge at: log₁₀(f) = {log_bulge_3D:.4f}")
print()

# Now map each element
print(f"{'Z':>3} {'Sym':>4} {'log₁₀(ν_C)':>12} {'frac_3D':>8} {'past_bulge':>10} "
      f"{'Block':>5} {'Per':>3} {'d_pos':>5} {'Known_corr':>10}")
print("-" * 80)

# Elements known to need spiral correction
need_correction = {43, 44, 45, 62, 75, 76, 77, 80, 84}

# Track sub-ranges by period for d-block
period_ranges = {}

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

    mass = el['mass_amu']
    nu_C = compton_freq(mass)
    log_nu = np.log10(nu_C)

    # Fraction through the 3D interior
    frac_3D = (log_nu - log_floor_3D) / log_range_3D

    # Past the bulge?
    past_bulge = frac_3D > phi_c

    sym = el['symbol']
    block = el['block']
    period = el['period']
    d_pos = el.get('d_pos', 0)
    known_corr = Z in need_correction

    # Track d-block ranges by period
    if block == 'd':
        if period not in period_ranges:
            period_ranges[period] = {'min_log': log_nu, 'max_log': log_nu,
                                      'min_Z': Z, 'max_Z': Z}
        else:
            if log_nu < period_ranges[period]['min_log']:
                period_ranges[period]['min_log'] = log_nu
                period_ranges[period]['min_Z'] = Z
            if log_nu > period_ranges[period]['max_log']:
                period_ranges[period]['max_log'] = log_nu
                period_ranges[period]['max_Z'] = Z

    # Print d-block elements and those needing correction
    if block == 'd' or known_corr:
        marker = '←CORR' if known_corr else ''
        bulge_marker = 'YES' if past_bulge else 'no'
        print(f"{Z:3d} {sym:>4s} {log_nu:12.6f} {frac_3D:8.4f} {bulge_marker:>10s} "
              f"{block:>5s} {period:3d} {d_pos:5d} {marker:>10s}")

# =============================================================================
# PERIOD SUB-RANGES IN THE 3D INTERIOR
# =============================================================================
print()
print("=" * 80)
print("PERIOD SUB-RANGES WITHIN 3D (d-block only)")
print("=" * 80)
print()

for per in sorted(period_ranges.keys()):
    pr = period_ranges[per]
    sub_range = pr['max_log'] - pr['min_log']
    sub_floor_frac = (pr['min_log'] - log_floor_3D) / log_range_3D
    sub_ceil_frac = (pr['max_log'] - log_floor_3D) / log_range_3D

    # Where is the bulge relative to this period's sub-range?
    bulge_in_sub = (log_bulge_3D - pr['min_log']) / sub_range if sub_range > 0 else 0

    print(f"  Period {per}:")
    print(f"    log₁₀(ν_C) range: {pr['min_log']:.6f} to {pr['max_log']:.6f} "
          f"(span: {sub_range:.6f})")
    print(f"    Fraction of 3D interior: {sub_floor_frac:.4f} to {sub_ceil_frac:.4f}")
    print(f"    3D bulge at frac = {phi_c:.4f}")
    print(f"    Bulge falls at {bulge_in_sub:.1%} through this period's sub-range")
    print()

# =============================================================================
# THE KEY QUESTION: Does the 29% bulge separate corrected from uncorrected?
# =============================================================================
print("=" * 80)
print("CRITICAL TEST: Does frac_3D = 0.29 separate the corrections?")
print("=" * 80)
print()

corrected_fracs = []
uncorrected_fracs = []

for el in elements:
    Z = el['Z']
    if Z > 118 or el['block'] != 'd':
        continue

    mass = el['mass_amu']
    nu_C = compton_freq(mass)
    log_nu = np.log10(nu_C)
    frac_3D = (log_nu - log_floor_3D) / log_range_3D

    if Z in need_correction:
        corrected_fracs.append((Z, el['symbol'], frac_3D))
    else:
        uncorrected_fracs.append((Z, el['symbol'], frac_3D))

print("Elements NEEDING correction:")
for Z, sym, frac in sorted(corrected_fracs, key=lambda x: x[2]):
    marker = "BELOW 29%" if frac < phi_c else "ABOVE 29%"
    print(f"  {sym:>4s} (Z={Z:3d}): frac_3D = {frac:.6f}  {marker}")

print()
print("d-block elements NOT needing correction:")
for Z, sym, frac in sorted(uncorrected_fracs, key=lambda x: x[2]):
    marker = "BELOW 29%" if frac < phi_c else "ABOVE 29%"
    if frac > 0.27 or frac < 0.31:  # near the boundary
        print(f"  {sym:>4s} (Z={Z:3d}): frac_3D = {frac:.6f}  {marker}")

print()
# Count
corr_above = sum(1 for _, _, f in corrected_fracs if f > phi_c)
corr_below = sum(1 for _, _, f in corrected_fracs if f <= phi_c)
uncorr_above = sum(1 for _, _, f in uncorrected_fracs if f > phi_c)
uncorr_below = sum(1 for _, _, f in uncorrected_fracs if f <= phi_c)

print(f"SEPARATION ANALYSIS:")
print(f"  Corrected elements above 29%:    {corr_above}/{len(corrected_fracs)}")
print(f"  Corrected elements below 29%:    {corr_below}/{len(corrected_fracs)}")
print(f"  Uncorrected elements above 29%:  {uncorr_above}/{len(uncorrected_fracs)}")
print(f"  Uncorrected elements below 29%:  {uncorr_below}/{len(uncorrected_fracs)}")
print()

if corr_above == len(corrected_fracs) and uncorr_below == len(uncorrected_fracs):
    print("  CLEAN SEPARATION — the 29% bulge perfectly divides corrected from uncorrected")
elif corr_below == len(corrected_fracs) and uncorr_above == 0:
    print("  ALL BELOW 29% — the bulge is above all elements (not the threshold)")
else:
    print(f"  MIXED — the 29% line does not cleanly separate")
    print(f"  But this is frac of the FULL 3D interior (floor to ceiling)")
    print(f"  The relevant fraction may be within each PERIOD's sub-range")

# =============================================================================
# WITHIN-PERIOD BULGE TEST
# =============================================================================
print()
print("=" * 80)
print("WITHIN-PERIOD TEST: 29% of each period's sub-range")
print("=" * 80)
print()

for per in sorted(period_ranges.keys()):
    pr = period_ranges[per]
    sub_range = pr['max_log'] - pr['min_log']
    sub_bulge_log = pr['min_log'] + phi_c * sub_range

    print(f"Period {per} d-block:")
    print(f"  Sub-range: {pr['min_log']:.6f} to {pr['max_log']:.6f}")
    print(f"  29% bulge at: log₁₀(ν) = {sub_bulge_log:.6f}")
    print()

    for el in elements:
        Z = el['Z']
        if Z > 118 or el['block'] != 'd' or el['period'] != per:
            continue

        mass = el['mass_amu']
        nu_C = compton_freq(mass)
        log_nu = np.log10(nu_C)
        frac_in_period = (log_nu - pr['min_log']) / sub_range if sub_range > 0 else 0
        past_sub_bulge = frac_in_period > phi_c

        known_corr = Z in need_correction
        marker = '←CORR' if known_corr else ''
        bulge_m = 'PAST' if past_sub_bulge else 'before'

        print(f"    {el['symbol']:>4s} (Z={Z:3d}, d{el.get('d_pos',0):d}): "
              f"frac_in_period={frac_in_period:.4f}  {bulge_m:>6s}  {marker}")

    # Count separations for this period
    corr_past = 0
    corr_before = 0
    uncorr_past = 0
    uncorr_before = 0

    for el in elements:
        Z = el['Z']
        if Z > 118 or el['block'] != 'd' or el['period'] != per:
            continue
        mass = el['mass_amu']
        log_nu = np.log10(compton_freq(mass))
        frac = (log_nu - pr['min_log']) / sub_range if sub_range > 0 else 0

        if Z in need_correction:
            if frac > phi_c:
                corr_past += 1
            else:
                corr_before += 1
        else:
            if frac > phi_c:
                uncorr_past += 1
            else:
                uncorr_before += 1

    total_corr = corr_past + corr_before
    total_uncorr = uncorr_past + uncorr_before
    print(f"\n    Corrected past bulge: {corr_past}/{total_corr}  "
          f"Uncorrected before bulge: {uncorr_before}/{total_uncorr}")
    if total_corr > 0 and corr_past == total_corr and uncorr_before == total_uncorr:
        print(f"    *** CLEAN SEPARATION IN PERIOD {per} ***")
    print()