#!/usr/bin/env python3 """Independent rational audit of the first Target Lens reading-drift tie. Input is a validated Target Lens v1 receipt. The edge is derived afresh from its readings and target interval; the receipt's selected drift is not used. """ import argparse from fractions import Fraction import json from pathlib import Path import sys from verify_target_lens import verify SCALE = 1_000_000 MAXIMUM = 100 * SCALE def median(readings): return sorted(readings)[2] def display(value): """Reduce a rational in millionth units to ordinary reading units.""" fraction = value / SCALE return str(fraction.numerator) + ("/" + str(fraction.denominator) if fraction.denominator != 1 else "") def audit_edge(readings, low, high, mask=31): """Return exact first roots of both factors under a clipped L-infinity box.""" if (len(readings) != 5 or any(type(r) is not int or r < 0 or r > MAXIMUM for r in readings) or type(low) is not int or type(high) is not int or not 0 <= low <= high <= MAXIMUM or type(mask) is not int or not 0 <= mask <= 31): raise ValueError("Invalid audit inputs") total = sum(readings) estimate = total - 5 * median(readings) reference_low = total + 5 * median(readings) - 10 * high reference_high = total + 5 * median(readings) - 10 * low if estimate == 0 or reference_low <= 0 <= reference_high: return {"kind": "no-baseline"} signs = {"estimate": 1 if estimate > 0 else -1, "reference": 1 if reference_low > 0 else -1} winner = "Median" if signs["estimate"] == signs["reference"] else "Mean" movable = [bool(mask & (1 << i)) for i in range(5)] stops = {Fraction(0), Fraction(MAXIMUM)} for i, reading in enumerate(readings): if movable[i]: stops.update((Fraction(reading), Fraction(MAXIMUM - reading))) for j in range(i): if movable[i] or movable[j]: stops.add(Fraction(abs(reading - readings[j]), 2 if movable[i] and movable[j] else 1)) stops = sorted(stops) def box(radius): return ([max(Fraction(0), r - radius) if moves else Fraction(r) for r, moves in zip(readings, movable)], [min(Fraction(MAXIMUM), r + radius) if moves else Fraction(r) for r, moves in zip(readings, movable)]) groups = [] for middle in range(5): other = [index for index in range(5) if index != middle] for a in range(3): for b in range(a + 1, 4): below = (other[a], other[b]) groups.append((middle, below, tuple(i for i in other if i not in below))) def signed_estimate(bounds, group): lower, upper = bounds middle, below, above = group floor = max(lower[i] for i in (middle, *below)) ceiling = min(upper[i] for i in (middle, *above)) if floor > ceiling: return None if signs["estimate"] > 0: # Minimum of sum(x)-5m: below at lower bounds, above at # max(lower,m), and the largest feasible median m. return sum(lower[i] for i in below) + sum(max(lower[i], ceiling) for i in above) - 4 * ceiling # Maximum of sum(x)-5m, negated to give a positive baseline margin. return -(sum(upper[i] for i in above) + sum(min(upper[i], floor) for i in below) - 4 * floor) def signed_reference(bounds): lower, upper = bounds if signs["reference"] > 0: return sum(lower) + 5 * median(lower) - 10 * high return -(sum(upper) + 5 * median(upper) - 10 * low) roots = {"estimate": None, "reference": None} def consider(kind, group, left, right, at_left, at_right): if at_left is None or at_right is None: return if at_left <= 0: root = left elif at_right <= 0: root = left + (right - left) * at_left / (at_left - at_right) else: return if roots[kind] is None or root < roots[kind][0]: roots[kind] = (root, group) for left, right in zip(stops, stops[1:]): first, last = box(left), box(right) consider("reference", None, left, right, signed_reference(first), signed_reference(last)) for group in groups: consider("estimate", group, left, right, signed_estimate(first, group), signed_estimate(last, group)) def witness(kind, route): radius, group = route lower, upper = box(radius) if kind == "reference": arrangement = lower if signs[kind] > 0 else upper target = Fraction(high if signs[kind] > 0 else low) else: middle, below, above = group if signs[kind] > 0: pivot = min(upper[i] for i in (middle, *above)) arrangement = [pivot if i == middle else max(lower[i], pivot) if i in above else lower[i] for i in range(5)] else: pivot = max(lower[i] for i in (middle, *below)) arrangement = [pivot if i == middle else min(upper[i], pivot) if i in below else upper[i] for i in range(5)] target = Fraction(low) mean = sum(arrangement) / 5 middle_value = median(arrangement) error = abs(mean - target) if error != abs(middle_value - target) or any(x < a or x > b for x, a, b in zip(arrangement, lower, upper)): raise ArithmeticError("Computed boundary witness is not admissible") return {"readings": [display(x) for x in arrangement], "target": display(target), "mean": display(mean), "median": display(middle_value), "equalError": display(error)} if not any(roots.values()): return {"kind": "unreachable", "winner": winner, "mask": mask, "routes": {"estimate": None, "reference": None}} first_kind = min((kind for kind in ("reference", "estimate") if roots[kind] is not None), key=lambda kind: roots[kind][0]) radius = roots[first_kind][0] routes = {kind: None if route is None else {"radius": display(route[0]), "witness": witness(kind, route)} for kind, route in roots.items()} return {"kind": "edge", "winner": winner, "mask": mask, "firstRoute": first_kind, "radius": display(radius), "firstTieUnits": -(-radius.numerator // radius.denominator), "routes": routes} def main(): parser = argparse.ArgumentParser(description=__doc__) parser.add_argument("receipt", type=Path, help="Target Lens v1 JSON receipt") parser.add_argument("--mask", type=int, default=31, help="movable reading bitmask 0–31 (default: all five)") parser.add_argument("--json", action="store_true", help="emit machine-readable result") args = parser.parse_args() try: if args.receipt.stat().st_size > 1_000_000: raise ValueError("Receipt too large") receipt = json.loads(args.receipt.read_text(encoding="utf-8")) verify(receipt) inputs = receipt["inputs"] result = audit_edge(inputs["readings"], inputs["low"], inputs["high"], args.mask) if args.json: print(json.dumps(result, separators=(",", ":"))) elif result["kind"] == "edge": print(f"First tie at ε = {result['radius']} (route: {result['firstRoute']}); " f"first selectable setting {result['firstTieUnits'] / SCALE:.6f}") for kind, route in result["routes"].items(): if route is not None: proof = route["witness"] print(f"{kind}: ε = {route['radius']}; readings {proof['readings']}; " f"target {proof['target']}; mean {proof['mean']}; median {proof['median']}; " f"both errors {proof['equalError']}") else: print(result["kind"] + (" · " + result.get("winner", "") if result.get("winner") else "")) except (OSError, ValueError, KeyError, TypeError, ArithmeticError) as error: print(f"Audit failed: {error}", file=sys.stderr) return 1 return 0 if __name__ == "__main__": sys.exit(main())