#!/usr/bin/env python3 """ verify_P148.py -- Addendum 148: provenance as a path in S3. This verifier checks the log-map/tangent encoding claims and flags schema and disambiguation gaps in the proposed provenance amendment. """ from __future__ import annotations import math import sys from pathlib import Path PASS = FAIL = 0 _N = 0 def check(desc, cond): global PASS, FAIL, _N _N += 1 ok = bool(cond) PASS += ok FAIL += not ok print(f" [{'PASS' if ok else 'FAIL'}] {_N:>2}. {desc}") return ok class Verifier: """Same check semantics as verify_common.Verifier; modern output style.""" def __init__(self, name): print(name) def check(self, label, computed, claimed, *, rel=1e-3, abs_tol=None, detail=""): if abs_tol is not None: ok = abs(computed - claimed) <= abs_tol err = abs(computed - claimed) err_detail = f"abs err={err:.6g}, tol={abs_tol:.6g}" else: if claimed == 0: ok = abs(computed) <= (rel or 1e-12) err_detail = f"abs value={abs(computed):.6g}, tol={rel:.6g}" else: err = (computed - claimed) / abs(claimed) ok = abs(err) <= (rel or 0) err_detail = f"rel err={100 * err:+.6g}%, tol={100 * (rel or 0):.6g}%" return self.record(label, ok, computed, claimed, err_detail + (f"; {detail}" if detail else "")) def record(self, label, ok, computed="", claimed="", detail=""): check(label + (f" -- {detail}" if detail else ""), ok) if computed != "" or claimed != "": print(f" computed: {computed}") print(f" claimed : {claimed}") return ok def summary(self): print(f"\n{'='*60}\nRESULT: {PASS} PASS / {FAIL} FAIL") return 1 if FAIL else 0 v = Verifier("P148 -- Provenance Path") ROOT = Path(__file__).resolve().parents[1] TEX = (ROOT / "148_Addendum_ProvenancePath.tex").read_text() def log_norm(q: tuple[float, float, float, float], p: tuple[float, float, float, float]) -> float: dot = sum(a * b for a, b in zip(q, p)) return math.acos(max(-1.0, min(1.0, dot))) q0 = (1.0, 0.0, 0.0, 0.0) q1 = (0.0, 1.0, 0.0, 0.0) q4 = (1.0 / math.sqrt(2.0), 0.0, 0.0, 1.0 / math.sqrt(2.0)) v.record( "proposed tangent lives in a 3D tangent space", "\\TqS \\cong \\mathbb{R}^3" in TEX and "v \\in \\mathbb{R}^3" in TEX, computed="T_q S3 and v in R3 stated", claimed="provenance tangent is three-dimensional", ) v.check("orthogonal quaternion log distance", log_norm(q0, q1), math.pi / 2.0, rel=1e-14) v.check("halfway quaternion log distance", log_norm(q0, q4), math.pi / 4.0, rel=1e-14) v.check("Oscillate k=4 step length", 2.0 * math.pi / 4.0, math.pi / 2.0, rel=1e-14) v.record( "Plateau is identified with zero tangent", "v = 0 \\implies" in TEX and "\\textsc{Plateau}" in TEX, computed="v=0 -> Plateau rule present", claimed="Plateau unique by zero arc length", ) v.record( "Fork/Weld ambiguity is acknowledged", "\\textsc{Fork} or \\textsc{Weld}" in TEX and "h_\\mathrm{prev}" in TEX, computed="needs h_prev / heat sign for Fork-Weld disambiguation", claimed="v alone gives partial provenance", ) v.record( "provenance tangent is deterministic from endpoints", "deterministic function of $(q_\\mathrm{prev},\n q_\\mathrm{curr})$" in TEX, computed="deterministic endpoint function stated", claimed="not a learned parameter", ) v.record( "CanonNode tangent is rejected", "should \\emph{not} gain a tangent field" in TEX, computed="node stays structural, provenance belongs on transitions/edges", claimed="CanonNode unchanged", ) v.record( "log-map formula covers the Plateau case as written", False, computed="the displayed formula excludes p=-q but is also 0/0 at p=q; Plateau uses q_prev=q_curr and needs an explicit v=0 branch", claimed="log_q(p) embeds p != -q into T_q S3", detail="Expected formula-domain fail.", ) v.record( "homotopy class of minimal geodesic arcs distinguishes operators", False, computed="for non-antipodal endpoints the minimal geodesic in S3 is unique, so its homotopy class is not enough to encode Fork/Weld/Oscillate/Perturb without extra heat/length/operator assumptions", claimed="path type is homotopy class plus heat signature", detail="Expected path-type fail.", ) v.record( "v alone gives unambiguous provenance for all five operators", False, computed="the paper itself says v gives only partial provenance: Fork/Weld need h_prev, and Oscillate/Perturb can overlap if zeta R = 2pi/k", claimed="tangent-vector encoding gives unambiguous provenance", detail="Expected disambiguation fail.", ) v.record( "h_prev adds no historical/provenance record", False, computed="h_prev is explicitly a prior-state scalar needed to recover Delta h; whether this is allowed without a second time axis is left to a Wheel invariants audit", claimed="full disambiguation needs only one scalar and no second clock", detail="Expected architecture-status fail.", ) v.record( "amended schema adds two scalar fields", False, computed="v is in R3, so the amendment adds three tangent coordinates plus h_prev, not two scalar fields", claimed="WheelState schema gains two frozen scalar fields (v and h_prev)", detail="Expected schema-count fail.", ) v.record( "existing Wheel tests pass unchanged is verified", False, computed="P148 asserts the 20+ tests do not reference v or h_prev, but no test list or run output is included in the TeX", claimed="existing tests pass unchanged", detail="Expected reproducibility fail.", ) v.record( "full Type-2 self-observation is closed", False, computed="open items remain for Fork/Weld h_prev interpretation, Oscillate/Perturb overlap, typed Mycelium edges, and P18-T2 uniqueness", claimed="Full Type-2 self-observation is achievable without a second time axis", detail="Expected status fail.", ) v.record( "zeta R is guaranteed away from all 2pi/k", False, computed="the paper lists this as an open parameter-discipline constraint rather than proving it from fixed constants", claimed="Oscillate and Perturb are disjoint by magnitude", detail="Expected overlap fail.", ) sys.exit(v.summary())