#!/usr/bin/env python3 """031 โ€” The Shape Belongs to the Rule: the re-runnable handle. Reproduces the three browser streams and the two live meters with only the standard library. It also guards the page-side constants and formulas, so a later edit cannot silently leave CI checking a different instrument. """ from pathlib import Path import hashlib import math import re N = 900 SEED = 20260828 U32 = 0xFFFFFFFF PI_PREFIX = "31415926535897932384626433832795" E_PREFIX = "27182818284590452353602874713526" RANDOM_PREFIX = "46299884944255105342133945866182" E_JS_SHA256 = "11823f41197921090ff119e17c27bec567407dcdb8448c63cae9583c6a27b46d" PI_JS_SHA256 = "60f9fe202c27a80b9b668b176dea4b9651b56ad131066e35dab4baf0ed738d06" RANDOM_JS_SHA256 = "7dc02abbba208507b8ad114e066c446631cef8865431f0d649a593d2c388130b" GEOMETRY_JS_SHA256 = "969eaaf6e93cc81b8598c163e28880fc2c88b0390e41c7054af23f69a8ea6f29" METERS_JS_SHA256 = "89cf99b52e7128dce3031dcc2b9c7c72f568f773bf8d99133e20131fbf7bf129" MOTION_JS_SHA256 = "462d0efa38720bae8afe2cb32c964edaaeed1550c73cf19419851fb70127281e" class PiSpigot: """Integer port of the page's Rabinowitz-Wagon spigot.""" def __init__(self, n): self.length = 10 * n // 3 + 1 self.a = [2] * self.length self.out = [] self.nines = 0 self.pre = 0 self.first = True self.n = n def emit(self, digit): if self.first: self.first = False return self.out.append(digit) def run(self): for _ in range(self.n): q = 0 for i in range(self.length - 1, -1, -1): x = 10 * self.a[i] + q * (i + 1) self.a[i] = x % (2 * i + 1) q = x // (2 * i + 1) self.a[0] = q % 10 q //= 10 if q == 9: self.nines += 1 elif q == 10: self.emit(self.pre + 1) for _ in range(self.nines): self.emit(0) self.pre = 0 self.nines = 0 else: self.emit(self.pre) self.pre = q for _ in range(self.nines): self.emit(9) self.nines = 0 return self.out def e_digits(n): scale = 10 ** (n + 12) term = scale total = scale k = 1 while term: term //= k total += term k += 1 return [int(c) for c in str(total)[:n]] def imul(a, b): """Low 32 bits of JavaScript Math.imul.""" return ((a & U32) * (b & U32)) & U32 def random_digits(n, seed): """Bit-exact unsigned emulation of the page's mulberry32 stream.""" t = seed & U32 out = [] for _ in range(n): t = (t + 0x6D2B79F5) & U32 r = t r = imul(r ^ (r >> 15), r | 1) r ^= (r + imul(r ^ (r >> 7), r | 61)) & U32 r &= U32 u = (r ^ (r >> 14)) & U32 out.append((u * 10) // 4294967296) return out def directions(): golden_angle = math.pi * (3 - math.sqrt(5)) result = [] for i in range(10): y = 1 - 2 * i / 9 radius = math.sqrt(max(0, 1 - y * y)) theta = golden_angle * i result.append((math.cos(theta) * radius, y, math.sin(theta) * radius)) return result def meters(digits, dirs): point = [0.0, 0.0, 0.0] hist = [0] * 10 for digit in digits[:N]: vector = dirs[digit] point = [point[j] + vector[j] for j in range(3)] hist[digit] += 1 distance = math.sqrt(sum(v * v for v in point)) expected = N / 10 chi2 = sum((count - expected) ** 2 / expected for count in hist) return distance, distance / math.sqrt(N), chi2, hist def main(): failures = [] def check(ok, label, got, want): print(" %-4s %-52s got=%s want=%s" % ("ok" if ok else "FAIL", label, got, want)) if not ok: failures.append(label) page = Path(__file__).with_name("index.html").read_text(encoding="utf-8") print("031 โ€” The Shape Belongs to the Rule ยท handle\n") print("1. the CI handle and the browser still describe one instrument") for fragment in ( "var N = 900;", "digits:rndDigits(N+6, 20260828)", "var exp = n/10", "dist/Math.sqrt(w.n)", "y = 1 - (i/(K-1))*2;", "if (d <= 1) return null;", "var running = !reduced, acc = 0;", "if (!reduced || running || dragging) scheduleFrame();", "if (reduced) piGen.step(piGen.n);", 'cv.addEventListener("pointercancel", endDrag);', 'cv.addEventListener("lostpointercapture", endDrag);', 'class="lab blind" id="lab"', 'id="blind" aria-pressed="true"', ".lab.blind .meters,.lab.blind .ribbons,.lab.blind .stream-toggle{visibility:hidden}", "ctx.strokeStyle = blind ? BLIND_COL : COL[s];", 'blind = true;', "if (!blind) return;", "elBlind.disabled = true;", 'el.textContent = digits.length ? digits[0] : "";', ".wrap{max-width:1080px", ".intro{max-width:780px", ".why p{max-width:780px", ".guide{max-width:780px", "if (reduced && running && walks[0].n >= N && walks[1].n >= N && walks[2].n >= N)", ): check(fragment in page, "page contract: %s" % fragment, fragment in page, True) browser_contracts = ( ("e", r"function eDigits\(n\)\{.*?\n\}(?=\nfunction PiSpigot)", E_JS_SHA256), ("pi", r"function PiSpigot\(n\)\{.*?PiSpigot\.prototype\.step = function\(count\)\{.*?\n\};(?=\n/\* mulberry32)", PI_JS_SHA256), ("control", r"function rndDigits\(n, seed\)\{.*?\n\}(?=\n\nvar piGen)", RANDOM_JS_SHA256), ("geometry", r"function tenDirections\(\)\{.*?function advance\(w, d\)\{.*?\n\}", GEOMETRY_JS_SHA256), ("meters", r"function chi2\(h, n\)\{.*?function meters\(\)\{.*?\n\}", METERS_JS_SHA256), ("motion", r"var running = !reduced, acc = 0;.*?scheduleFrame\(\);(?=\n\}\)\(\);)", MOTION_JS_SHA256), ) for name, pattern, expected_hash in browser_contracts: implementation = re.search(pattern, page, re.S) implementation_hash = ( hashlib.sha256(implementation.group(0).encode()).hexdigest() if implementation else None ) check(implementation_hash == expected_hash, "browser %s implementation hash" % name, implementation_hash, expected_hash) streams = ( ("pi", PiSpigot(N + 6).run()), ("e", e_digits(N + 6)), ("rnd", random_digits(N + 6, SEED)), ) print("\n2. the named streams reproduce their independently known openings") check("".join(map(str, streams[0][1][:32])) == PI_PREFIX, "pi first 32 digits", "".join(map(str, streams[0][1][:32])), PI_PREFIX) check("".join(map(str, streams[1][1][:32])) == E_PREFIX, "e first 32 digits", "".join(map(str, streams[1][1][:32])), E_PREFIX) random_prefix = "".join(map(str, streams[2][1][:32])) check(random_prefix == RANDOM_PREFIX, "seeded control first 32 digits", random_prefix, RANDOM_PREFIX) dirs = directions() print("\n3. all ten digit directions have unit length") for i, vector in enumerate(dirs): length = math.sqrt(sum(v * v for v in vector)) check(abs(length - 1) < 1e-12, "direction %d" % i, "%.12f" % length, "1.000000000000") print("\n4. the page's two live witnesses, re-derived at n=900") for name, digits in streams: distance, scaled, chi2, hist = meters(digits, dirs) print(" %-3s |d|=%7.3f |d|/sqrt(n)=%5.3f chi2=%5.2f hist=%s" % (name, distance, scaled, chi2, hist)) check(sum(hist) == N, "%s histogram total" % name, sum(hist), N) check(chi2 < 16.9, "%s chi2 below stated 5%% guide" % name, "%.2f" % chi2, "<16.9") print("\n%s โ€” %d checks failed" % ("FAILED" if failures else "ALL HANDLES HOLD", len(failures))) return 1 if failures else 0 if __name__ == "__main__": raise SystemExit(main())