Datasets:

MartialTerran
/

DataScience

"""
PiDataScience_V1.0.py
Standalone Data Science Suite for Substring Collision & Repetition Analysis in Pi (Base 16).
Features:
- Fast Chudnovsky Binary-Splitting Hex Generator (CPU-optimized, zero external libraries).
- Exhaustive Substring Collision Engine for lengths L in [4, 64].
- Exponential Search Expansion: Doubles search horizon N whenever repeats are absent.
- Full Telemetry: Counts, first-incident coordinates, and 0-F digit histograms.
- Safety & Persistence: 30-min checkpoints, auto-download in Colab, resume capability,
  and a hardcoded 3-hour maximum runtime budget.
"""

import os
import sys
import time
import json
import math
from typing import Dict, List, Tuple, Any, Optional

# =====================================================================
# 1. RUNTIME BUDGET & PERSISTENCE CONFIGURATION
# =====================================================================

CONFIG = {
    "min_length": 4,
    "max_length": 64,
    "initial_n": 2000,          # Starting search horizon
    "max_n_limit": 2000000,     # Safety ceiling (2 million hex places)
    "checkpoint_interval_sec": 1800,  # 1800 = 30 minutes
    "max_runtime_sec": 10800,   # 10800 = 3 hours hard ceiling
    "checkpoint_file": "pi_datascience_checkpoint.json",
    "report_txt": "pi_repetition_report.txt",
    "report_md": "pi_repetition_report.md",
    "report_html": "pi_repetition_report.html",
}

HEX_CHARS = "0123456789ABCDEF"

# =====================================================================
# 2. HIGH-SPEED PI HEXADECIMAL ENGINE (CHUDNOVSKY BINARY SPLIT)
# =====================================================================

def chudnovsky_hex_pi(num_hex_digits: int) -> str:
    """
    Computes num_hex_digits of Pi after decimal in Base 16 using binary splitting.
    Pure Python arbitrary-precision integers (extremely fast on standard CPU).
    """
    # Number of decimal digits needed ~ num_hex_digits * 1.204
    digits_dec = int(num_hex_digits * 1.21) + 50
    C = 640320
    C3_OVER_24 = C**3 // 24

    def bs(a, b):
        if b - a == 1:
            if a == 0:
                Pab = 1
                Qab = 1
            else:
                Pab = (6*a - 5) * (2*a - 1) * (6*a - 1)
                Qab = a**3 * C3_OVER_24
            Tab = Pab * (13591409 + 545140134 * a)
            if a & 1:
                Tab = -Tab
            return Pab, Qab, Tab
        else:
            m = (a + b) // 2
            Pam, Qam, Tam = bs(a, m)
            Pmb, Qmb, Tmb = bs(m, b)
            Pab = Pam * Pmb
            Qab = Qam * Qmb
            Tab = Qmb * Tam + Pam * Tmb
            return Pab, Qab, Tab

    # Digits per term ~ 14.18 decimal digits
    terms = int(digits_dec / 14.181647462725477) + 2
    P, Q, T = bs(0, terms)

    one_shift = 1 << (num_hex_digits * 4 + 64)
    # sqrt(10005) via integer Newton-Raphson
    target = 10005 * (1 << (num_hex_digits * 8 + 128))
    x = int(math.isqrt(target))
    sqrt_10005 = x

    pi_val = (Q * 426880 * sqrt_10005) // T
    # Shift right 64 bits of guard precision
    hex_str = f"{pi_val >> 64:x}"
    
    # 3 is the integer part; fractional part follows
    return hex_str[1:num_hex_digits + 1].upper()

# =====================================================================
# 3. REPETITION & DATA SCIENCE ENGINE
# =====================================================================

class PiDataScienceAnalyzer:
    def __init__(self, cfg: Dict[str, Any]):
        self.cfg = cfg
        self.start_time = time.time()
        self.last_checkpoint_time = self.start_time
        self.current_n = cfg["initial_n"]
        self.results: Dict[int, Dict[str, Any]] = {}
        
        # Load existing checkpoint if available
        self.load_checkpoint()

    def load_checkpoint(self):
        ckpt_file = self.cfg["checkpoint_file"]
        if os.path.exists(ckpt_file):
            try:
                with open(ckpt_file, "r") as f:
                    data = json.load(f)
                self.current_n = data.get("current_n", self.cfg["initial_n"])
                self.results = {int(k): v for k, v in data.get("results", {}).items()}
                print(f"[RECOVERY] Loaded checkpoint from {ckpt_file}. Resuming at N={self.current_n}")
            except Exception as e:
                print(f"[WARNING] Could not load checkpoint: {e}. Starting fresh.")

    def save_checkpoint(self, force_download: bool = False):
        ckpt_file = self.cfg["checkpoint_file"]
        data = {
            "current_n": self.current_n,
            "elapsed_sec": time.time() - self.start_time,
            "results": self.results,
            "timestamp": time.strftime("%Y-%m-%d %H:%M:%S")
        }
        with open(ckpt_file, "w") as f:
            json.dump(data, f, indent=2)
        print(f"[CHECKPOINT] Saved state at N={self.current_n} to {ckpt_file}")
        
        # Generate all reports
        self.generate_reports()
        
        # Auto-download in Colab
        if force_download or "google.colab" in sys.modules:
            self.trigger_colab_downloads()

    def trigger_colab_downloads(self):
        try:
            from google.colab import files
            print("[COLAB] Auto-initiating file download...")
            files.download(self.cfg["checkpoint_file"])
            files.download(self.cfg["report_txt"])
            files.download(self.cfg["report_md"])
            files.download(self.cfg["report_html"])
        except Exception:
            pass # Non-colab environments simply retain files on disk

    def analyze_length(self, pi_stream: str, length: int) -> Dict[str, Any]:
        """Examines substring repetitions for a given length L."""
        seen: Dict[str, int] = {}
        repeats: Dict[str, List[int]] = {}
        first_rep_seq = None
        first_rep_idx1 = None
        first_rep_idx2 = None

        total_substrings = len(pi_stream) - length + 1
        for i in range(total_substrings):
            sub = pi_stream[i:i + length]
            if sub in seen:
                if sub not in repeats:
                    repeats[sub] = [seen[sub], i]
                    if first_rep_seq is None:
                        first_rep_seq = sub
                        first_rep_idx1 = seen[sub]
                        first_rep_idx2 = i
                else:
                    repeats[sub].append(i)
            else:
                seen[sub] = i

        has_repeat = len(repeats) > 0
        
        # Compute histogram of hex numerals across repeating sequences
        hist = {c: 0 for c in HEX_CHARS}
        for seq, occurrences in repeats.items():
            mult = len(occurrences)
            for ch in seq:
                hist[ch] += mult

        return {
            "length": length,
            "has_repeat": has_repeat,
            "repeat_sequence_count": len(repeats),
            "total_repeat_events": sum(len(indices) for indices in repeats.values()),
            "first_repeated_sequence": first_rep_seq,
            "first_index": first_rep_idx1,
            "repeat_index": first_rep_idx2,
            "distance": (first_rep_idx2 - first_rep_idx1) if first_rep_idx1 is not None else None,
            "numeral_histogram": hist,
            "evaluated_at_n": len(pi_stream)
        }

    def execute_search(self):
        print("=" * 84)
        print(f"PiDataScience_V1.0 Search Engine Started [Base 16]")
        print(f"Lengths: {self.cfg['min_length']} to {self.cfg['max_length']} | Initial N: {self.current_n}")
        print("=" * 84)

        while True:
            elapsed = time.time() - self.start_time
            if elapsed >= self.cfg["max_runtime_sec"]:
                print(f"[TIMEOUT] Reached hard maximum runtime budget of {self.cfg['max_runtime_sec']}s. Finalizing.")
                self.save_checkpoint(force_download=True)
                break

            if self.current_n > self.cfg["max_n_limit"]:
                print(f"[LIMIT] Reached safety limit N={self.cfg['max_n_limit']}. Stopping search expansion.")
                self.save_checkpoint(force_download=True)
                break

            print(f"\n>>> Generating {self.current_n} hex digits of Pi via Chudnovsky...")
            t0 = time.time()
            pi_stream = chudnovsky_hex_pi(self.current_n)
            print(f">>> Generated {len(pi_stream)} digits in {time.time() - t0:.2f}s. Scanning lengths {self.cfg['min_length']}..{self.cfg['max_length']}...")

            all_lengths_have_repeats = True

            for L in range(self.cfg["min_length"], self.cfg["max_length"] + 1):
                # If length was already solved and repeated in an earlier smaller N, keep that record
                if L in self.results and self.results[L]["has_repeat"]:
                    continue

                res = self.analyze_length(pi_stream, L)
                self.results[L] = res

                status = "YES" if res["has_repeat"] else "NO"
                info = ""
                if res["has_repeat"]:
                    info = f"Count: {res['repeat_sequence_count']:4d} | First: '{res['first_repeated_sequence']}' @ [{res['first_index']} -> {res['repeat_index']}]"
                else:
                    all_lengths_have_repeats = False
                    info = "No collision detected in current window."

                print(f"  Length {L:02d}: [{status:<3}] {info}")

                # Check 30-min checkpoint cadence
                if time.time() - self.last_checkpoint_time >= self.cfg["checkpoint_interval_sec"]:
                    print("[CADENCE] 30-minute interval elapsed. Triggering intermediate checkpoint & downloads.")
                    self.save_checkpoint(force_download=True)
                    self.last_checkpoint_time = time.time()

            # Save report at current N
            self.save_checkpoint(force_download=False)

            if all_lengths_have_repeats:
                print("\n[SUCCESS] All sequence lengths [4..64] have confirmed repeats!")
                self.save_checkpoint(force_download=True)
                break
            else:
                next_n = self.current_n * 2
                print(f"\n[EXPANSION] Certain lengths have NO repeats in N={self.current_n}. Doubling horizon to N={next_n}...")
                self.current_n = next_n

    # =================================================================
    # 4. REPORT GENERATION (TXT, MD, HTML)
    # =================================================================

    def generate_reports(self):
        # 1. Text Report
        with open(self.cfg["report_txt"], "w") as f:
            f.write("PI HEXADECIMAL SUBSTRING REPETITION REPORT\n")
            f.write(f"Timestamp: {time.strftime('%Y-%m-%d %H:%M:%S')} | Search Horizon N: {self.current_n}\n")
            f.write("=" * 86 + "\n")
            f.write(f"{'Len':<4} | {'Repeat?':<7} | {'Distinct':<8} | {'First Found Sequence':<20} | {'Idx 1':<8} | {'Idx 2':<8}\n")
            f.write("-" * 86 + "\n")
            for L in range(self.cfg["min_length"], self.cfg["max_length"] + 1):
                if L in self.results:
                    r = self.results[L]
                    rep = "YES" if r["has_repeat"] else "NO"
                    seq = r["first_repeated_sequence"] or "NONE"
                    idx1 = str(r["first_index"]) if r["first_index"] is not None else "-"
                    idx2 = str(r["repeat_index"]) if r["repeat_index"] is not None else "-"
                    f.write(f"{L:<4} | {rep:<7} | {r['repeat_sequence_count']:<8} | {seq:<20} | {idx1:<8} | {idx2:<8}\n")

        # 2. Markdown Report
        with open(self.cfg["report_md"], "w") as f:
            f.write("# $\\pi$ Hexadecimal Substring Repetition Audit\n\n")
            f.write(f"- **Current Search Horizon ($N$):** {self.current_n:,} digits\n")
            f.write(f"- **Generated At:** {time.strftime('%Y-%m-%d %H:%M:%S')}\n\n")
            f.write("| Length | Repeat Detected? | Unique Repeated Strings | Total Events | First Repeated Substring | First Index | Repeat Index | Distance |\n")
            f.write("| :--- | :---: | :---: | :---: | :--- | :---: | :---: | :---: |\n")
            for L in range(self.cfg["min_length"], self.cfg["max_length"] + 1):
                if L in self.results:
                    r = self.results[L]
                    rep = "**YES**" if r["has_repeat"] else "NO"
                    seq = f"`{r['first_repeated_sequence']}`" if r["first_repeated_sequence"] else "—"
                    i1 = r["first_index"] if r["first_index"] is not None else "—"
                    i2 = r["repeat_index"] if r["repeat_index"] is not None else "—"
                    dist = r["distance"] if r["distance"] is not None else "—"
                    f.write(f"| {L} | {rep} | {r['repeat_sequence_count']} | {r['total_repeat_events']} | {seq} | {i1} | {i2} | {dist} |\n")

        # 3. HTML Report with Interactive Styling
        with open(self.cfg["report_html"], "w") as f:
            f.write("""<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8">
<title>Pi Repetition Analysis</title>
<style>
body { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif; margin: 30px; background: #0d1117; color: #c9d1d9; }
h1, h2 { color: #58a6ff; }
table { border-collapse: collapse; width: 100%; margin-top: 20px; background: #161b22; }
th, td { border: 1px solid #30363d; padding: 10px; text-align: left; }
th { background: #21262d; color: #f0f6fc; }
tr:nth-child(even) { background: #1c2128; }
.yes { color: #3fb950; font-weight: bold; }
.no { color: #f85149; font-weight: bold; }
.code { font-family: monospace; background: #2b313a; padding: 2px 6px; border-radius: 4px; color: #ff7b72; }
.hist { display: flex; gap: 2px; height: 16px; align-items: flex-end; }
.bar { width: 8px; background: #58a6ff; }
</style>
</head>
<body>
<h1>&pi; Hexadecimal Substring Repetition Audit</h1>
<p>Search Horizon: <strong>""" + f"{self.current_n:,}" + """ digits</strong> | Checkpointed at: """ + time.strftime("%Y-%m-%d %H:%M:%S") + """</p>
<table>
<tr>
  <th>Length (L)</th>
  <th>Repeated?</th>
  <th>Distinct Repeats</th>
  <th>First Repeated Sequence</th>
  <th>First Index</th>
  <th>Repeat Index</th>
  <th>Numeral Histogram (0 to F)</th>
</tr>""")
            for L in range(self.cfg["min_length"], self.cfg["max_length"] + 1):
                if L in self.results:
                    r = self.results[L]
                    rep_cls = "yes" if r["has_repeat"] else "no"
                    rep_txt = "YES" if r["has_repeat"] else "NO"
                    seq = f'<span class="code">{r["first_repeated_sequence"]}</span>' if r["first_repeated_sequence"] else "—"
                    i1 = str(r["first_index"]) if r["first_index"] is not None else "—"
                    i2 = str(r["repeat_index"]) if r["repeat_index"] is not None else "—"
                    
                    # Mini bar-chart for 0-F
                    hist_bars = ""
                    max_h = max(r["numeral_histogram"].values()) if r["has_repeat"] and max(r["numeral_histogram"].values()) > 0 else 1
                    for ch in HEX_CHARS:
                        val = r["numeral_histogram"].get(ch, 0)
                        h_px = int((val / max_h) * 16)
                        hist_bars += f'<div class="bar" style="height:{max(1, h_px)}px;" title="{ch}: {val}"></div>'

                    f.write(f"""
<tr>
  <td><strong>{L}</strong></td>
  <td class="{rep_cls}">{rep_txt}</td>
  <td>{r['repeat_sequence_count']:,}</td>
  <td>{seq}</td>
  <td>{i1}</td>
  <td>{i2}</td>
  <td><div class="hist">{hist_bars}</div></td>
</tr>""")
            f.write("""
</table>
</body>
</html>""")

if __name__ == "__main__":
    analyzer = PiDataScienceAnalyzer(CONFIG)
    analyzer.execute_search()

	"""
	PiDataScience_V1.0.py
	Standalone Data Science Suite for Substring Collision & Repetition Analysis in Pi (Base 16).

	Features:
	- Fast Chudnovsky Binary-Splitting Hex Generator (CPU-optimized, zero external libraries).
	- Exhaustive Substring Collision Engine for lengths L in [4, 64].
	- Exponential Search Expansion: Doubles search horizon N whenever repeats are absent.
	- Full Telemetry: Counts, first-incident coordinates, and 0-F digit histograms.
	- Safety & Persistence: 30-min checkpoints, auto-download in Colab, resume capability,
	and a hardcoded 3-hour maximum runtime budget.
	"""

	import os
	import sys
	import time
	import json
	import math
	from typing import Dict, List, Tuple, Any, Optional

	# =====================================================================
	# 1. RUNTIME BUDGET & PERSISTENCE CONFIGURATION
	# =====================================================================

	CONFIG = {
	"min_length": 4,
	"max_length": 64,
	"initial_n": 2000, # Starting search horizon
	"max_n_limit": 2000000, # Safety ceiling (2 million hex places)
	"checkpoint_interval_sec": 1800, # 1800 = 30 minutes
	"max_runtime_sec": 10800, # 10800 = 3 hours hard ceiling
	"checkpoint_file": "pi_datascience_checkpoint.json",
	"report_txt": "pi_repetition_report.txt",
	"report_md": "pi_repetition_report.md",
	"report_html": "pi_repetition_report.html",
	}

	HEX_CHARS = "0123456789ABCDEF"

	# =====================================================================
	# 2. HIGH-SPEED PI HEXADECIMAL ENGINE (CHUDNOVSKY BINARY SPLIT)
	# =====================================================================

	def chudnovsky_hex_pi(num_hex_digits: int) -> str:
	"""
	Computes num_hex_digits of Pi after decimal in Base 16 using binary splitting.
	Pure Python arbitrary-precision integers (extremely fast on standard CPU).
	"""
	# Number of decimal digits needed ~ num_hex_digits * 1.204
	digits_dec = int(num_hex_digits * 1.21) + 50
	C = 640320
	C3_OVER_24 = C**3 // 24

	def bs(a, b):
	if b - a == 1:
	if a == 0:
	Pab = 1
	Qab = 1
	else:
	Pab = (6a - 5) (2a - 1) (6*a - 1)
	Qab = a*3 C3_OVER_24
	Tab = Pab * (13591409 + 545140134 * a)
	if a & 1:
	Tab = -Tab
	return Pab, Qab, Tab
	else:
	m = (a + b) // 2
	Pam, Qam, Tam = bs(a, m)
	Pmb, Qmb, Tmb = bs(m, b)
	Pab = Pam * Pmb
	Qab = Qam * Qmb
	Tab = Qmb * Tam + Pam * Tmb
	return Pab, Qab, Tab

	# Digits per term ~ 14.18 decimal digits
	terms = int(digits_dec / 14.181647462725477) + 2
	P, Q, T = bs(0, terms)

	one_shift = 1 << (num_hex_digits * 4 + 64)
	# sqrt(10005) via integer Newton-Raphson
	target = 10005 * (1 << (num_hex_digits * 8 + 128))
	x = int(math.isqrt(target))
	sqrt_10005 = x

	pi_val = (Q * 426880 * sqrt_10005) // T
	# Shift right 64 bits of guard precision
	hex_str = f"{pi_val >> 64:x}"

	# 3 is the integer part; fractional part follows
	return hex_str[1:num_hex_digits + 1].upper()

	# =====================================================================
	# 3. REPETITION & DATA SCIENCE ENGINE
	# =====================================================================

	class PiDataScienceAnalyzer:
	def __init__(self, cfg: Dict[str, Any]):
	self.cfg = cfg
	self.start_time = time.time()
	self.last_checkpoint_time = self.start_time
	self.current_n = cfg["initial_n"]
	self.results: Dict[int, Dict[str, Any]] = {}

	# Load existing checkpoint if available
	self.load_checkpoint()

	def load_checkpoint(self):
	ckpt_file = self.cfg["checkpoint_file"]
	if os.path.exists(ckpt_file):
	try:
	with open(ckpt_file, "r") as f:
	data = json.load(f)
	self.current_n = data.get("current_n", self.cfg["initial_n"])
	self.results = {int(k): v for k, v in data.get("results", {}).items()}
	print(f"[RECOVERY] Loaded checkpoint from {ckpt_file}. Resuming at N={self.current_n}")
	except Exception as e:
	print(f"[WARNING] Could not load checkpoint: {e}. Starting fresh.")

	def save_checkpoint(self, force_download: bool = False):
	ckpt_file = self.cfg["checkpoint_file"]
	data = {
	"current_n": self.current_n,
	"elapsed_sec": time.time() - self.start_time,
	"results": self.results,
	"timestamp": time.strftime("%Y-%m-%d %H:%M:%S")
	}
	with open(ckpt_file, "w") as f:
	json.dump(data, f, indent=2)
	print(f"[CHECKPOINT] Saved state at N={self.current_n} to {ckpt_file}")

	# Generate all reports
	self.generate_reports()

	# Auto-download in Colab
	if force_download or "google.colab" in sys.modules:
	self.trigger_colab_downloads()

	def trigger_colab_downloads(self):
	try:
	from google.colab import files
	print("[COLAB] Auto-initiating file download...")
	files.download(self.cfg["checkpoint_file"])
	files.download(self.cfg["report_txt"])
	files.download(self.cfg["report_md"])
	files.download(self.cfg["report_html"])
	except Exception:
	pass # Non-colab environments simply retain files on disk

	def analyze_length(self, pi_stream: str, length: int) -> Dict[str, Any]:
	"""Examines substring repetitions for a given length L."""
	seen: Dict[str, int] = {}
	repeats: Dict[str, List[int]] = {}
	first_rep_seq = None
	first_rep_idx1 = None
	first_rep_idx2 = None

	total_substrings = len(pi_stream) - length + 1
	for i in range(total_substrings):
	sub = pi_stream[i:i + length]
	if sub in seen:
	if sub not in repeats:
	repeats[sub] = [seen[sub], i]
	if first_rep_seq is None:
	first_rep_seq = sub
	first_rep_idx1 = seen[sub]
	first_rep_idx2 = i
	else:
	repeats[sub].append(i)
	else:
	seen[sub] = i

	has_repeat = len(repeats) > 0

	# Compute histogram of hex numerals across repeating sequences
	hist = {c: 0 for c in HEX_CHARS}
	for seq, occurrences in repeats.items():
	mult = len(occurrences)
	for ch in seq:
	hist[ch] += mult

	return {
	"length": length,
	"has_repeat": has_repeat,
	"repeat_sequence_count": len(repeats),
	"total_repeat_events": sum(len(indices) for indices in repeats.values()),
	"first_repeated_sequence": first_rep_seq,
	"first_index": first_rep_idx1,
	"repeat_index": first_rep_idx2,
	"distance": (first_rep_idx2 - first_rep_idx1) if first_rep_idx1 is not None else None,
	"numeral_histogram": hist,
	"evaluated_at_n": len(pi_stream)
	}

	def execute_search(self):
	print("=" * 84)
	print(f"PiDataScience_V1.0 Search Engine Started [Base 16]")
	print(f"Lengths: {self.cfg['min_length']} to {self.cfg['max_length']} \| Initial N: {self.current_n}")
	print("=" * 84)

	while True:
	elapsed = time.time() - self.start_time
	if elapsed >= self.cfg["max_runtime_sec"]:
	print(f"[TIMEOUT] Reached hard maximum runtime budget of {self.cfg['max_runtime_sec']}s. Finalizing.")
	self.save_checkpoint(force_download=True)
	break

	if self.current_n > self.cfg["max_n_limit"]:
	print(f"[LIMIT] Reached safety limit N={self.cfg['max_n_limit']}. Stopping search expansion.")
	self.save_checkpoint(force_download=True)
	break

	print(f"\n>>> Generating {self.current_n} hex digits of Pi via Chudnovsky...")
	t0 = time.time()
	pi_stream = chudnovsky_hex_pi(self.current_n)
	print(f">>> Generated {len(pi_stream)} digits in {time.time() - t0:.2f}s. Scanning lengths {self.cfg['min_length']}..{self.cfg['max_length']}...")

	all_lengths_have_repeats = True

	for L in range(self.cfg["min_length"], self.cfg["max_length"] + 1):
	# If length was already solved and repeated in an earlier smaller N, keep that record
	if L in self.results and self.results[L]["has_repeat"]:
	continue

	res = self.analyze_length(pi_stream, L)
	self.results[L] = res

	status = "YES" if res["has_repeat"] else "NO"
	info = ""
	if res["has_repeat"]:
	info = f"Count: {res['repeat_sequence_count']:4d} \| First: '{res['first_repeated_sequence']}' @ [{res['first_index']} -> {res['repeat_index']}]"
	else:
	all_lengths_have_repeats = False
	info = "No collision detected in current window."

	print(f" Length {L:02d}: [{status:<3}] {info}")

	# Check 30-min checkpoint cadence
	if time.time() - self.last_checkpoint_time >= self.cfg["checkpoint_interval_sec"]:
	print("[CADENCE] 30-minute interval elapsed. Triggering intermediate checkpoint & downloads.")
	self.save_checkpoint(force_download=True)
	self.last_checkpoint_time = time.time()

	# Save report at current N
	self.save_checkpoint(force_download=False)

	if all_lengths_have_repeats:
	print("\n[SUCCESS] All sequence lengths [4..64] have confirmed repeats!")
	self.save_checkpoint(force_download=True)
	break
	else:
	next_n = self.current_n * 2
	print(f"\n[EXPANSION] Certain lengths have NO repeats in N={self.current_n}. Doubling horizon to N={next_n}...")
	self.current_n = next_n

	# =================================================================
	# 4. REPORT GENERATION (TXT, MD, HTML)
	# =================================================================

	def generate_reports(self):
	# 1. Text Report
	with open(self.cfg["report_txt"], "w") as f:
	f.write("PI HEXADECIMAL SUBSTRING REPETITION REPORT\n")
	f.write(f"Timestamp: {time.strftime('%Y-%m-%d %H:%M:%S')} \| Search Horizon N: {self.current_n}\n")
	f.write("=" * 86 + "\n")
	f.write(f"{'Len':<4} \| {'Repeat?':<7} \| {'Distinct':<8} \| {'First Found Sequence':<20} \| {'Idx 1':<8} \| {'Idx 2':<8}\n")
	f.write("-" * 86 + "\n")
	for L in range(self.cfg["min_length"], self.cfg["max_length"] + 1):
	if L in self.results:
	r = self.results[L]
	rep = "YES" if r["has_repeat"] else "NO"
	seq = r["first_repeated_sequence"] or "NONE"
	idx1 = str(r["first_index"]) if r["first_index"] is not None else "-"
	idx2 = str(r["repeat_index"]) if r["repeat_index"] is not None else "-"
	f.write(f"{L:<4} \| {rep:<7} \| {r['repeat_sequence_count']:<8} \| {seq:<20} \| {idx1:<8} \| {idx2:<8}\n")

	# 2. Markdown Report
	with open(self.cfg["report_md"], "w") as f:
	f.write("# $\\pi$ Hexadecimal Substring Repetition Audit\n\n")
	f.write(f"- Current Search Horizon ($N$): {self.current_n:,} digits\n")
	f.write(f"- Generated At: {time.strftime('%Y-%m-%d %H:%M:%S')}\n\n")
	f.write("\| Length \| Repeat Detected? \| Unique Repeated Strings \| Total Events \| First Repeated Substring \| First Index \| Repeat Index \| Distance \|\n")
	f.write("\| :--- \| :---: \| :---: \| :---: \| :--- \| :---: \| :---: \| :---: \|\n")
	for L in range(self.cfg["min_length"], self.cfg["max_length"] + 1):
	if L in self.results:
	r = self.results[L]
	rep = "YES" if r["has_repeat"] else "NO"
	seq = f"`{r['first_repeated_sequence']}`" if r["first_repeated_sequence"] else "—"
	i1 = r["first_index"] if r["first_index"] is not None else "—"
	i2 = r["repeat_index"] if r["repeat_index"] is not None else "—"
	dist = r["distance"] if r["distance"] is not None else "—"
	f.write(f"\| {L} \| {rep} \| {r['repeat_sequence_count']} \| {r['total_repeat_events']} \| {seq} \| {i1} \| {i2} \| {dist} \|\n")

	# 3. HTML Report with Interactive Styling
	with open(self.cfg["report_html"], "w") as f:
	f.write("""<!DOCTYPE html>
	<html>
	<head>
	<meta charset="utf-8">
	<title>Pi Repetition Analysis</title>
	<style>
	body { font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif; margin: 30px; background: #0d1117; color: #c9d1d9; }
	h1, h2 { color: #58a6ff; }
	table { border-collapse: collapse; width: 100%; margin-top: 20px; background: #161b22; }
	th, td { border: 1px solid #30363d; padding: 10px; text-align: left; }
	th { background: #21262d; color: #f0f6fc; }
	tr:nth-child(even) { background: #1c2128; }
	.yes { color: #3fb950; font-weight: bold; }
	.no { color: #f85149; font-weight: bold; }
	.code { font-family: monospace; background: #2b313a; padding: 2px 6px; border-radius: 4px; color: #ff7b72; }
	.hist { display: flex; gap: 2px; height: 16px; align-items: flex-end; }
	.bar { width: 8px; background: #58a6ff; }
	</style>
	</head>
	<body>
	<h1>π Hexadecimal Substring Repetition Audit</h1>
	<p>Search Horizon: <strong>""" + f"{self.current_n:,}" + """ digits</strong> \| Checkpointed at: """ + time.strftime("%Y-%m-%d %H:%M:%S") + """</p>
	<table>
	<tr>
	<th>Length (L)</th>
	<th>Repeated?</th>
	<th>Distinct Repeats</th>
	<th>First Repeated Sequence</th>
	<th>First Index</th>
	<th>Repeat Index</th>
	<th>Numeral Histogram (0 to F)</th>
	</tr>""")
	for L in range(self.cfg["min_length"], self.cfg["max_length"] + 1):
	if L in self.results:
	r = self.results[L]
	rep_cls = "yes" if r["has_repeat"] else "no"
	rep_txt = "YES" if r["has_repeat"] else "NO"
	seq = f'<span class="code">{r["first_repeated_sequence"]}</span>' if r["first_repeated_sequence"] else "—"
	i1 = str(r["first_index"]) if r["first_index"] is not None else "—"
	i2 = str(r["repeat_index"]) if r["repeat_index"] is not None else "—"

	# Mini bar-chart for 0-F
	hist_bars = ""
	max_h = max(r["numeral_histogram"].values()) if r["has_repeat"] and max(r["numeral_histogram"].values()) > 0 else 1
	for ch in HEX_CHARS:
	val = r["numeral_histogram"].get(ch, 0)
	h_px = int((val / max_h) * 16)
	hist_bars += f'<div class="bar" style="height:{max(1, h_px)}px;" title="{ch}: {val}"></div>'

	f.write(f"""
	<tr>
	<td><strong>{L}</strong></td>
	<td class="{rep_cls}">{rep_txt}</td>
	<td>{r['repeat_sequence_count']:,}</td>
	<td>{seq}</td>
	<td>{i1}</td>
	<td>{i2}</td>
	<td><div class="hist">{hist_bars}</div></td>
	</tr>""")
	f.write("""
	</table>
	</body>
	</html>""")

	if __name__ == "__main__":
	analyzer = PiDataScienceAnalyzer(CONFIG)
	analyzer.execute_search()