feat: migrate milestone4 and prefield_em_emergence from internal/

milestone4: PAC Relativity, Turbulence, and Energy as Collapsed Potential
- 13 experiment scripts (exp_01 through exp_13)
- 30 result JSONs, herniation_research substudy
- source_material/ from energy_equivilance working paper
- Targets Papers 5, 7, 8

prefield_em_emergence: Pre-Field Recursion to 3D EM Field Emergence
- Möbius manifold → Maxwell-like field structure
- E/B = φ^(-4.42w/R + 2.34), R² = 0.9764
- Complete with core/, experiments/, docs/, tests/

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: Peter Groom

foundational/experiments/milestone4/README.md

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+# Milestone 4: PAC Relativity, Turbulence, and Energy as Collapsed Potential
+
+**Version**: 0.1.0  
+**Status**: 🔄 In Progress  
+**Date**: 2026-02-22  
+
+---
+
+## Purpose
+
+Milestone 4 formalizes and rigorously validates three interconnected claims from the exploratory session of February 2026:
+
+1. **PAC Relativity**: The Lorentz factor is the PAC energy partition between internal cascade and propagation
+2. **Turbulence from Cascade**: Kolmogorov -5/3 emerges from PAC cascade mechanics at the physical mode count
+3. **Energy as Collapsed Potential**: Mass is unresolved potential; "energy released" is the Landauer cost of destroyed futures
+
+### Exploratory Source
+
+The `package/` subdirectory contains the original session (Session Journal, simulations, theoretical directions). This milestone reproduces those findings through proper experimental pipeline: error analysis, null tests, falsification conditions, and honest assessment.
+
+### Relationship to Other Milestones
+
+| Milestone | Focus | Status |
+|-----------|-------|--------|
+| milestone1 | PAC/SEC → Standard Model + Gravity | ✅ Complete (40 exp) |
+| milestone2 | Mass derivation + turbulence extension | ✅ Complete (18 + 22 exp) |
+| milestone3 | Energy equivalence + methodology validation | ✅ Complete (32 exp) |
+| **milestone4** | **Relativity + turbulence + nuclear physics** | **🔄 In Progress** |
+
+---
+
+## Experiment Plan
+
+### Block A: PAC Relativity (proposed Paper 7)
+
+| Script | Description | Falsification | Source Connection |
+|--------|-------------|---------------|-------------------|
+| exp_01 | Lorentz factor from PAC partition — exact identity proof | If γ ≠ E_rest/E_internal at any v | pac_relativity_v2.py |
+| exp_02 | Mode collapse at kT ln 2 — photon threshold | If modes persist below kT ln 2 | pac_relativity_v2.py, landauer_erasure exp_01 |
+| exp_03 | Identity conservation under movement — locality | If teleportation preserves identity equally | pac_relativity_v2.py |
+| exp_04 | Gravitational time dilation — functional form | If PAC prediction diverges from Schwarzschild beyond weak field | pac_relativity_v2.py, gravity_from_maxwell_pac |
+
+### Block B: Turbulence from Cascade (feeds Paper 5)
+
+| Script | Description | Falsification | Source Connection |
+|--------|-------------|---------------|-------------------|
+| exp_05 | Mode count → exponent scaling law (2–64 modes) | If no clean functional form mode→exponent | turbulence_pac_v3.py, milestone2 exp_01-04 |
+| exp_06 | Organized fraction convergence ≈ 2/3 | If fraction is parameter-dependent, not universal | turbulence_pac_v3.py |
+| exp_07 | Regularity proof — ξ bounded, no blow-up | If ξ diverges at any injection scale | turbulence_pac_v3.py |
+| exp_08 | 2D vs 3D turbulence prediction from mode count | If 2D exponent -3 doesn't match framework | milestone2 exp_01-04 |
+
+### Block C: Energy as Collapsed Potential (proposed Paper 8)
+
+| Script | Description | Falsification | Source Connection |
+|--------|-------------|---------------|-------------------|
+| exp_09 | Nuclear config space size vs fission energy release | If no correlation between channel count and energy | NIST nuclear data |
+| exp_10 | Binding energy curve as potential landscape | If Fe-56 doesn't minimize accessible configuration space | Nuclear level density data |
+| exp_11 | Cascade amplification scaling law (modes → amplification) | If amplification doesn't scale with available modes | landauer_erasure exp_09-10, energy_equivilance |
+| exp_12 | Decay rate vs configuration space size | If half-life doesn't correlate with channel count | NNDC nuclear data |
+
+### Block D: Cross-Validation & Integration
+
+| Script | Description | Source Connection |
+|--------|-------------|-------------------|
+| exp_13 | Unify She-Lévêque with PAC cascade | milestone1 exp_21, milestone2 exp_01-04 |
+| exp_14 | Layer 1/2 transition: same entity in vacuum vs medium | internal/maxwell, prefield_maxwell |
+| exp_15 | Comprehensive null tests for all Block A-C results | All above |
+
+---
+
+## Success Criteria
+
+After completion, milestone4 should:
+
+1. [ ] Prove Lorentz factor is mathematical identity from PAC (not just numerical agreement)
+2. [ ] Determine whether the mode count → exponent relationship has an analytical form
+3. [ ] Establish whether binding energy correlates with nuclear configuration space measure
+4. [ ] Resolve gravity: functional form match or flag as unvalidated
+5. [ ] All experiments: error bounds, null tests, falsification conditions
+6. [ ] Honest separation: what's proven vs what's suggestive vs what's speculative
+
+---
+
+## Corpus Connections
+
+### Direct Predecessors (build on these results)
+
+| Experiment | Connection | Key Result |
+|------------|-----------|------------|
+| landauer_erasure_structure | Cascade amplification, kT ln 2 floor | 53× amplification (p = 2.75×10⁻³⁵) |
+| milestone1/exp_14 | c from SEC wave equation | c² = αγ + βδ |
+| milestone1/exp_21,28,39 | She-Lévêque 5/3 from Fibonacci | β = F₃/F₄ = 2/3 |
+| milestone1/exp_23-26 | Gravity hierarchy from F₁₈₃ | 183 = F₇²+F₇+1 |
+| milestone2/exp_01-04 | 2D vs 3D turbulence, mode count | k = d × F_{d+1} |
+| milestone2/mass_derivation | Mass ratios from Fibonacci | μ/e to 5 ppm |
+| milestone3/exp_01,02 | Cascade "why Fibonacci" story | Two-step memory → Fibonacci |
+| milestone3/exp_06 | Θ recycling validation | 3/4 PASS, 36-94% range |
+| navier-stokes | Ξ ≈ 1.0571 from symbolic engine | MED bounds discovered here |
+
+### Related Work (parallel evidence)
+
+| Experiment | Connection |
+|------------|-----------|
+| euclidean_distance_validation | E=mc² in embedding space (R²=1.0, c²≈416) |
+| gravity_from_maxwell_pac | Gravity at depth 183, dark matter at depth 73 |
+| recursive_gravity | Orbits emerge from informational tangle, no Newton |
+| maxwell_from_pac_sec | Maxwell equations from SEC, c from wave equation |
+| internal/maxwell | c from SEC parameters, charge from collapse |
+| pac_dag_fluid | Bidirectional SEC on fluid hierarchies |
+| entropy_information_polarity_field | Black/white hole polarity |
+| internal/energy_equivilance | Full working paper, cascade deep dives |
+
+---
+
+*Dawn Field Institute, 2026*

foundational/experiments/milestone4/core/__init__.py

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+# Milestone 4 core module

foundational/experiments/milestone4/core/constants.py

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+"""
+Milestone 4: Shared constants for all experiments.
+
+Extends milestone3 constants with relativity and nuclear physics values.
+"""
+
+import math
+
+# ============================================================
+# Fundamental mathematical constants
+# ============================================================
+PHI = (1 + math.sqrt(5)) / 2         # Golden ratio: 1.6180339887...
+INV_PHI = 1 / PHI                     # 1/φ: 0.6180339887...
+LN_PHI = math.log(PHI)                # ln(φ): 0.4812118250...
+GAMMA_EM = 0.5772156649015329         # Euler-Mascheroni constant
+
+# Framework constants
+XI_BALANCE = GAMMA_EM + LN_PHI        # Ξ = γ + ln(φ) ≈ 1.0584
+PI_OVER_55 = math.pi / 55             # π/55 ≈ 0.05712
+
+# ============================================================
+# Thermodynamic constants
+# ============================================================
+KT_DEFAULT = 1.0                       # Default thermal energy (natural units)
+LANDAUER_MIN = KT_DEFAULT * math.log(2)  # kT·ln(2) ≈ 0.6931
+K_BOLTZMANN = 1.380649e-23             # J/K (exact, SI 2019)
+
+# ============================================================
+# Physical constants
+# ============================================================
+C_LIGHT = 299792458.0                  # m/s (exact)
+C_LIGHT_SQ = C_LIGHT ** 2             # c² 
+HBAR = 1.054571817e-34                 # J·s (reduced Planck)
+G_NEWTON = 6.67430e-11                 # m³/(kg·s²)
+M_ELECTRON = 9.1093837015e-31         # kg
+M_PROTON = 1.67262192369e-27          # kg
+M_NEUTRON = 1.67492749804e-27         # kg
+AMU = 1.66053906660e-27               # kg (atomic mass unit)
+MEV_TO_JOULE = 1.602176634e-13        # J per MeV
+KEV_TO_JOULE = 1.602176634e-16        # J per keV
+
+# ============================================================
+# Nuclear physics data (NIST/NNDC)
+# ============================================================
+
+# Binding energy per nucleon (MeV) for key nuclides
+# Source: AME2020 (Atomic Mass Evaluation)
+BINDING_ENERGY_PER_NUCLEON = {
+    # (Z, A): BE/A in MeV
+    (1, 1): 0.0,         # H-1 (free proton)
+    (1, 2): 1.112,       # H-2 (deuterium)
+    (1, 3): 2.827,       # H-3 (tritium)
+    (2, 3): 2.573,       # He-3
+    (2, 4): 7.074,       # He-4 (alpha)
+    (3, 6): 5.332,       # Li-6
+    (3, 7): 5.606,       # Li-7
+    (6, 12): 7.680,      # C-12
+    (7, 14): 7.476,      # N-14
+    (8, 16): 7.976,      # O-16
+    (12, 24): 8.261,     # Mg-24
+    (14, 28): 8.448,     # Si-28
+    (20, 40): 8.551,     # Ca-40
+    (26, 56): 8.790,     # Fe-56 (PEAK)
+    (28, 58): 8.732,     # Ni-58
+    (28, 62): 8.795,     # Ni-62 (true peak by total BE)
+    (36, 84): 8.717,     # Kr-84
+    (38, 88): 8.733,     # Sr-88
+    (50, 120): 8.505,    # Sn-120
+    (54, 131): 8.424,    # Xe-131
+    (56, 138): 8.394,    # Ba-138
+    (82, 208): 7.867,    # Pb-208
+    (90, 232): 7.615,    # Th-232
+    (92, 235): 7.591,    # U-235
+    (92, 238): 7.570,    # U-238
+    (94, 239): 7.560,    # Pu-239
+    (94, 244): 7.523,    # Pu-244
+}
+
+# Nuclear magic numbers (closed shells)
+MAGIC_NUMBERS = [2, 8, 20, 28, 50, 82, 126]
+
+# U-235 fission data
+U235_FISSION = {
+    'energy_mev': 200.0,           # Average total energy per fission (MeV)
+    'kinetic_mev': 170.0,          # Kinetic energy of products
+    'gamma_mev': 7.0,              # Prompt gamma rays
+    'beta_mev': 8.0,               # Beta decay energy
+    'neutrino_mev': 12.0,          # Neutrinos (lost)
+    'delayed_gamma_mev': 3.0,      # Delayed gammas
+    'mass_defect_fraction': 0.001, # Δm/m
+    'neutrons_per_fission': 2.43,  # Average prompt neutrons
+    'primary_channels': 60,         # Approximate distinct fission channels
+    'daughter_count': 800,          # Approximate distinct fission products
+}
+
+# Known nuclide data for configuration space analysis
+# decay_modes: number of energetically accessible decay channels
+NUCLIDE_DECAY_DATA = {
+    # (Z, A): {'half_life_s': t, 'decay_modes': n, 'name': str}
+    (1, 3):   {'half_life_s': 3.888e8, 'decay_modes': 1, 'name': 'H-3'},
+    (6, 14):  {'half_life_s': 1.808e11, 'decay_modes': 1, 'name': 'C-14'},
+    (11, 22): {'half_life_s': 8.211e7, 'decay_modes': 2, 'name': 'Na-22'},
+    (19, 40): {'half_life_s': 3.938e16, 'decay_modes': 3, 'name': 'K-40'},
+    (27, 60): {'half_life_s': 1.663e8, 'decay_modes': 2, 'name': 'Co-60'},
+    (38, 90): {'half_life_s': 9.08e8, 'decay_modes': 1, 'name': 'Sr-90'},
+    (53, 131): {'half_life_s': 6.95e5, 'decay_modes': 2, 'name': 'I-131'},
+    (55, 137): {'half_life_s': 9.49e8, 'decay_modes': 2, 'name': 'Cs-137'},
+    (84, 210): {'half_life_s': 1.196e7, 'decay_modes': 2, 'name': 'Po-210'},
+    (86, 222): {'half_life_s': 3.304e5, 'decay_modes': 1, 'name': 'Rn-222'},
+    (88, 226): {'half_life_s': 5.049e10, 'decay_modes': 2, 'name': 'Ra-226'},
+    (90, 232): {'half_life_s': 4.42e17, 'decay_modes': 2, 'name': 'Th-232'},
+    (92, 235): {'half_life_s': 2.22e16, 'decay_modes': 3, 'name': 'U-235'},
+    (92, 238): {'half_life_s': 1.41e17, 'decay_modes': 3, 'name': 'U-238'},
+    (94, 239): {'half_life_s': 7.61e11, 'decay_modes': 2, 'name': 'Pu-239'},
+}
+
+# Comprehensive excited state / level density data
+# Cumulative number of known levels below given energy
+# Source: RIPL-3 (Reference Input Parameter Library)
+NUCLEAR_LEVEL_DENSITY = {
+    # (Z, A): {'levels_below_5MeV': n, 'levels_below_10MeV': n}
+    (26, 56): {'levels_below_5MeV': 25, 'levels_below_10MeV': 180},
+    (28, 62): {'levels_below_5MeV': 20, 'levels_below_10MeV': 150},
+    (50, 120): {'levels_below_5MeV': 60, 'levels_below_10MeV': 800},
+    (82, 208): {'levels_below_5MeV': 35, 'levels_below_10MeV': 400},
+    (92, 235): {'levels_below_5MeV': 200, 'levels_below_10MeV': 5000},
+    (92, 238): {'levels_below_5MeV': 150, 'levels_below_10MeV': 4000},
+}
+
+# ============================================================
+# Fibonacci sequence
+# ============================================================
+def fibonacci(n):
+    """Return the nth Fibonacci number (0-indexed: F(0)=0, F(1)=1, ...)."""
+    if n < 0:
+        raise ValueError(f"Negative index: {n}")
+    if n <= 1:
+        return n
+    a, b = 0, 1
+    for _ in range(2, n + 1):
+        a, b = b, a + b
+    return b
+
+FIB = [fibonacci(i) for i in range(21)]
+
+# ============================================================
+# Turbulence reference values
+# ============================================================
+KOLMOGOROV_EXPONENT = -5/3            # Kolmogorov -5/3 law
+SHE_LEVEQUE_BETA = 2/3               # She-Lévêque β = F₃/F₄
+ORGANIZED_FRACTION_TARGET = 1 - 2**(-5/3)  # ≈ 0.685 for exact -5/3

foundational/experiments/milestone4/core/utils.py

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+"""
+Milestone 4: Shared utilities for experiment scripts.
+"""
+
+import json
+import os
+import time
+import math
+import numpy as np
+from datetime import datetime, timezone
+
+
+def save_results(results, experiment_name, results_dir=None):
+    """Save experiment results to timestamped JSON file."""
+    if results_dir is None:
+        results_dir = os.path.join(
+            os.path.dirname(os.path.dirname(os.path.abspath(__file__))),
+            'results'
+        )
+    os.makedirs(results_dir, exist_ok=True)
+
+    timestamp = datetime.now(timezone.utc).strftime('%Y%m%d_%H%M%S')
+    filename = f"{experiment_name}_{timestamp}.json"
+    filepath = os.path.join(results_dir, filename)
+
+    with open(filepath, 'w') as f:
+        json.dump(results, f, indent=2, default=str)
+
+    print(f"\nResults saved: {filepath}")
+    return filepath
+
+
+def timer():
+    """Simple context-manager timer."""
+    class Timer:
+        def __enter__(self):
+            self.start = time.perf_counter()
+            return self
+        def __exit__(self, *args):
+            self.elapsed = time.perf_counter() - self.start
+    return Timer()
+
+
+def bootstrap_ci(data, statistic=np.mean, n_bootstrap=10000, ci=0.95, seed=42):
+    """
+    Compute bootstrap confidence interval for a statistic.
+    
+    Returns
+    -------
+    dict with 'estimate', 'ci_lower', 'ci_upper', 'std_error'
+    """
+    rng = np.random.default_rng(seed)
+    data = np.asarray(data)
+    n = len(data)
+    
+    estimates = np.empty(n_bootstrap)
+    for i in range(n_bootstrap):
+        sample = data[rng.integers(0, n, size=n)]
+        estimates[i] = statistic(sample)
+    
+    alpha = (1 - ci) / 2
+    return {
+        'estimate': statistic(data),
+        'ci_lower': float(np.percentile(estimates, 100 * alpha)),
+        'ci_upper': float(np.percentile(estimates, 100 * (1 - alpha))),
+        'std_error': float(np.std(estimates)),
+    }
+
+
+def monte_carlo_null(observed, generator_fn, n_trials=10000, seed=42):
+    """
+    Monte Carlo null test: what fraction of random trials match or exceed observed?
+    
+    Parameters
+    ----------
+    observed : float
+        The observed statistic.
+    generator_fn : callable
+        Function(rng) → random statistic under null hypothesis.
+    n_trials : int
+        Number of Monte Carlo trials.
+    seed : int
+        Random seed.
+    
+    Returns
+    -------
+    dict with 'observed', 'null_mean', 'null_std', 'p_value', 'z_score'
+    """
+    rng = np.random.default_rng(seed)
+    null_dist = np.array([generator_fn(rng) for _ in range(n_trials)])
+    
+    p_value = np.mean(null_dist >= observed)
+    null_mean = np.mean(null_dist)
+    null_std = np.std(null_dist)
+    z_score = (observed - null_mean) / null_std if null_std > 0 else float('inf')
+    
+    return {
+        'observed': float(observed),
+        'null_mean': float(null_mean),
+        'null_std': float(null_std),
+        'p_value': float(p_value),
+        'z_score': float(z_score),
+        'n_trials': n_trials,
+    }
+
+
+def print_header(title, subtitle=None):
+    """Print formatted experiment header."""
+    print("\n" + "=" * 70)
+    print(title)
+    if subtitle:
+        print(subtitle)
+    print("=" * 70)
+
+
+def print_table(headers, rows, col_widths=None):
+    """Print a formatted table."""
+    if col_widths is None:
+        col_widths = [max(len(str(h)), max(len(str(r[i])) for r in rows)) + 2 
+                      for i, h in enumerate(headers)]
+    
+    header_line = "".join(str(h).ljust(w) for h, w in zip(headers, col_widths))
+    print(header_line)
+    print("-" * sum(col_widths))
+    for row in rows:
+        print("".join(str(v).ljust(w) for v, w in zip(row, col_widths)))