#!/usr/bin/env python3 """ WP-82 -- the ruler, re-measured, and checked against its own stated method. WHY THIS FILE EXISTS. WP-82's rung table is a DATED measurement: it states its own method and its own commit -- "tracked *.html and *.md files containing at least one case-insensitive match, taken at commit 654fb06 on 2026-08-29". A dated measurement does not decay into an error, it decays into a measurement about a day that has passed. Nothing in the repository re-ran it, so nothing could say how far it had moved, and on 2026-09-15 a reading of the rung-30 row as a live count produced a wrong conclusion about Volume XIII. WHAT IT CHECKS. [1] The method reproduces. Every number printed in the table is recomputed at 654fb06, the commit the paper names. This is the strongest block here: a source checked against itself, on its own terms. [2] The same method at HEAD, and the drift. [3] What the drift is made of -- a file count counts index pages and the ruler itself, so the composition is printed, not just the total. [4] The two claims §3 makes about specific volumes. [5] Control. Standard library only, but it shells out to git, which the repo requires for any tracked-file count (R13: the corpus is tracked files, not the working tree). python3 book6/wp82-verify.py """ import subprocess, sys, os REPO = os.path.dirname(os.path.dirname(os.path.abspath(__file__))) fails = [] def check(ok, msg, detail=''): print(' %s %s%s' % ('PASS' if ok else 'FAIL', msg, (' -- ' + detail) if detail and not ok else '')) if not ok: fails.append(msg) def head(n, t): print('\n' + '=' * 70 + '\n [%s] %s\n' % (n, t) + '=' * 70) RULER = 'book6/wp82-the-missing-floor.html' def files(pattern, ref, keep_ruler=False): """WP-82's method: tracked *.html and *.md, case-insensitive, file count. STRATIFIED, 2026-09-17. The ruler is one of the files the ruler measures, and the two columns did not agree about it. At 654fb06 the paper was not in the tree at all -- book6/wp81 is the last wp in that commit -- so column one ranges over a corpus without it. At d97154e the paper is in the tree and matches ALL TWELVE of its own patterns, so column two counted itself twelve times. Two columns, two different totalities. Principia Mathematica's rule (Vol I, Introduction ch. II) is that no object may be defined in terms of a totality containing itself, and its remedy is to stratify the range of the variable. So the range here excludes the ruler at BOTH refs: at 654fb06 that changes nothing, which is the check that the exclusion is the right one rather than a convenient one.""" r = subprocess.run(['git', '--no-optional-locks', 'grep', '-lic', '-e', pattern, ref, '--', '*.html', '*.md'], cwd=REPO, capture_output=True, text=True) out = set(l.split(':', 1)[1] for l in r.stdout.splitlines() if ':' in l) return out if keep_ruler else out - {RULER} def count(patterns, ref, keep_ruler=False): s = set() for p in patterns: s |= files(p, ref, keep_ruler) return len(s), s BASE = '654fb06' # the commit WP-82's first column names SECOND = 'd97154e' # the commit its second column names, added 2026-09-16 # after six rows moved inside a single day. A date is # not a commit; both columns now name one. ROWS = [ # (rung, field, patterns, col-1 @BASE, col-2 @SECOND, stratified) ('28', 'K-Theory & Index Theory', ['k-theory'], 0, 9, 8), ('28', ' index theorem', ['index theorem'], 1, 6, 5), ('28', ' Atiyah', ['atiyah'], 1, 5, 4), ('29', 'Operator Algebras', ['operator algebra'], 76, 100, 99), ('29', ' von Neumann', ['von neumann'], 7, 12, 11), ('30', 'Higher Category Theory', ['∞-categor', 'infinity-categor'], 0, 3, 2), ('31', 'Derived Algebraic Geometry',['sheaf', 'sheaves'], 1, 7, 6), ('32', 'Motivic / Langlands', ['motivic', 'langlands'], 3, 7, 6), ('33', 'Noncommutative Geometry', ['noncommutative'], 9, 17, 16), ('33', ' Connes', ['connes'], 15, 27, 26), ('33', ' spectral triple', ['spectral triple'], 7, 15, 14), ('--', 'Monstrous Moonshine', ['moonshine'], 25, 28, 27), ] # --------------------------------------------------------------------------- head(1, "THE PAPER'S OWN TABLE, RECOMPUTED AT THE COMMIT IT NAMES") r = subprocess.run(['git', '--no-optional-locks', 'cat-file', '-t', BASE], cwd=REPO, capture_output=True, text=True) check(r.stdout.strip() == 'commit', 'commit %s is in this repository' % BASE, r.stdout.strip()) print(' Method, quoted from the page: "the number of tracked *.html and *.md files') print(' containing at least one case-insensitive match, taken at commit 654fb06') print(' on 2026-08-29."\n') print(' %5s %-28s %10s %10s' % ('rung', 'field', 'printed', 'recomputed')) ok_repro = True base_n = {} for rung, field, pats, printed, printed2, printed3 in ROWS: n, _ = count(pats, BASE) base_n[field] = n flag = '' if n == printed else ' <-- MISMATCH' print(' %5s %-28s %10d %10d%s' % (rung, field, printed, n, flag)) if n != printed: ok_repro = False check(ok_repro, 'every one of the %d published numbers reproduces exactly' % len(ROWS)) print('\n The table was right on the day it was taken, the rung-30 zero included.') print(' book13 was stubbed the same day in 9d78ff8, but 654fb06 precedes it and') print(' book13/ch06-past-two.html does not exist in that tree. The measurement') print(' is sound and so is its date; what it is not is current.') # --------------------------------------------------------------------------- head(2, 'THE SECOND COLUMN -- AND THE RULER INSIDE IT') print(' The second column was first published against HEAD rather than a named') print(' commit, and six of its twelve rows moved inside a single day. It now') print(' names %s. But naming the commit exposed the larger thing.\n' % SECOND) print(' THE RULER IS ONE OF THE FILES THE RULER MEASURES. At %s the paper is' % BASE) print(' not in the tree at all -- book6/wp81 is the last wp in that commit -- so') print(' the first column ranges over a corpus WITHOUT it. At %s the paper is' % SECOND) print(' in the tree and matches ALL TWELVE of its own patterns, because it prints') print(' them. Two columns, two different totalities, and the drift between them') print(' carried a spurious +1 in every row.\n') print(' Principia Mathematica, Vol I, Introduction ch. II: no object may be') print(' defined in terms of a totality that includes itself, and the remedy is to') print(' stratify the range. files() now excludes the ruler at BOTH refs. At %s' % BASE) print(' that changes nothing, which is how we know the exclusion is the right one') print(' rather than a convenient one.\n') print(' %5s %-28s %8s %9s %9s %8s %7s' % ('rung', 'field', '@' + BASE, 'with', 'without', 'recomp', 'HEAD')) head_n = {} ok_repro2 = True ok_repro3 = True ruler_rows = 0 for rung, field, pats, printed, printed2, printed3 in ROWS: n_with, set_with = count(pats, SECOND, keep_ruler=True) n_wo, _ = count(pats, SECOND) nh, _ = count(pats, 'HEAD') head_n[field] = nh if RULER in set_with: ruler_rows += 1 f2 = '' if n_with == printed2 else ' <-- MISMATCH' f3 = '' if n_wo == printed3 else ' <-- MISMATCH' print(' %5s %-28s %8d %9d %9d %8d %7d%s%s' % (rung, field, base_n[field], printed2, printed3, n_wo, nh, f2, f3)) if n_with != printed2: ok_repro2 = False if n_wo != printed3: ok_repro3 = False check(ok_repro2, 'the %d unstratified numbers reproduce at %s' % (len(ROWS), SECOND)) check(ok_repro3, 'and so do the %d stratified ones' % len(ROWS)) check(ruler_rows == len(ROWS), 'the ruler is inside ALL %d rows of the second column -- it prints every ' 'pattern it counts' % len(ROWS), str(ruler_rows)) # the rung totals the PAGE quotes, at the commit the page names, stratified. sec_n = {} for rung, field, pats, printed, printed2, printed3 in ROWS: sec_n[field] = printed3 s28 = sum(sec_n[f] for r_, f, _, _, _, _ in ROWS if r_ == '28') s33 = sum(sec_n[f] for r_, f, _, _, _, _ in ROWS if r_ == '33') b28 = sum(base_n[f] for r_, f, _, _, _, _ in ROWS if r_ == '28') b33 = sum(base_n[f] for r_, f, _, _, _, _ in ROWS if r_ == '33') print('\n stratified, at %s -- the figures the page quotes:' % SECOND) print(' rung 28 total : %3d -> %3d' % (b28, s28)) print(' rung 33 total : %3d -> %3d' % (b33, s33)) print(' ratio 33 : 28 : %.1f -> %.1f' % (b33 / max(b28, 1), s33 / max(s28, 1))) check((b28, s28, b33, s33) == (2, 17, 31, 56), 'rung 28 goes 2 -> 17 and rung 33 goes 31 -> 56, stratified', str((b28, s28, b33, s33))) check(abs(s33 / s28 - 3.294117647058823) < 1e-12, 'and the inversion narrows to 3.3 : 1, not 3.0 : 1', '%.4f' % (s33 / s28)) base_with, _ = count(['moonshine'], BASE, keep_ruler=True) base_wo, _ = count(['moonshine'], BASE) check(base_with == base_wo, 'and inside NO row of the first column, because it is not in that tree: ' 'stratifying leaves %s unchanged' % BASE, '%d vs %d' % (base_with, base_wo)) check(all(head_n[f] >= base_n[f] for _, f, _, _, _, _ in ROWS), 'no row went down between %s and HEAD, so nothing was lost from the corpus' % BASE) r28_b = sum(base_n[f] for r_, f, _, _, _, _ in ROWS if r_ == '28') r28_h = sum(head_n[f] for r_, f, _, _, _, _ in ROWS if r_ == '28') r33_b = sum(base_n[f] for r_, f, _, _, _, _ in ROWS if r_ == '33') r33_h = sum(head_n[f] for r_, f, _, _, _, _ in ROWS if r_ == '33') print('\n rung 28 total : %3d -> %3d' % (r28_b, r28_h)) print(' rung 33 total : %3d -> %3d' % (r33_b, r33_h)) print(' ratio 33 : 28 : %.1f -> %.1f' % (r33_b / max(r28_b, 1), r33_h / max(r28_h, 1))) check(r28_h > r28_b, 'rung 28, the missing floor, is no longer at zero mentions') check(r33_h / max(r28_h, 1) < r33_b / max(r28_b, 1), 'and the inversion the paper reported has narrowed') check(r33_h > r28_h, 'it has NOT reversed: rung 33 still leads rung 28') # --------------------------------------------------------------------------- head(3, 'WHAT THE DRIFT IS MADE OF') print(' A file count counts every file that says the word, including index pages,') print(' the audit log, and the ruler itself. The composition matters more than the') print(' total, so here it is.\n') n_k, set_k = count(['k-theory'], SECOND) def kind_of(f): # the ruler is now excluded by files() before it reaches here; the bucket is # kept so that a future file named wp82* is still classified rather than # counted as a chapter. if 'wp82' in f: return 'the ruler itself' if f == 'CLAUDE.md': return 'project scaffolding' if (f.endswith('index.html') or f.startswith('index-') or f.startswith('master-index')): return 'index / listing' if f.startswith('docs/'): return 'audit narrative' return 'CHAPTER' for f in sorted(set_k): print(' %-46s %s' % (f, kind_of(f))) chapters = [f for f in set_k if kind_of(f) == 'CHAPTER'] print() check(n_k == 8, 'k-theory is in %d files at %s, stratified -- 9 with the ruler' % (n_k, SECOND), str(n_k)) check(len(chapters) == 2, 'exactly %d of them are chapters -- the rest are listings, the log, CLAUDE.md ' 'and this paper' % len(chapters), str(sorted(chapters))) print(' So the floor is STARTED, not built: %d chapters (%s)' % (len(chapters), ', '.join(sorted(chapters)))) print(' plus the echoes a new chapter produces in navigation. Reporting 0 -> 8') print(' without this breakdown would overstate it by a factor of four.') print() print(' CLAUDE.md is separated out here because it is not a chapter and not a') print(' listing: it is scaffolding that names the vocabulary in a handoff note.') print(' The earlier version of this block had no bucket for it and counted it') print(' as a chapter, which is the same one-look failure the paper is about.') # --------------------------------------------------------------------------- head(4, "THE TWO VOLUME CLAIMS IN §3") page = open(os.path.join(REPO, 'book6', 'wp82-the-missing-floor.html'), encoding='utf-8').read() # strip tags before matching: a phrase in this page can be split by an , # and a needle that straddles one silently misses. That is the same one-look # failure the rest of this script is about. import re as _re flat = ' '.join(_re.sub(r'<[^>]+>', ' ', page).split()) check('Zero files use the vocabulary' in flat, 'the XIII entry still carries its 2026-08-29 reading verbatim') n30, set30 = count(['∞-categor', 'infinity-categor'], 'HEAD') print(' rung-30 vocabulary at HEAD: %d files' % n30) for f in sorted(set30): print(' %s' % f) check(n30 > 0, 'which is no longer zero, so the entry needs its date carried') check(any(f.startswith('book13/') for f in set30), 'and Volume XIII on disk is where the vocabulary now is') print() print(' §3 also flags its own limits, and both still stand as written:') for phrase, what in ( ('is an ordering chosen here', 'XIII-XV placement is declared ASSUME, not derived'), ('no title appears anywhere in the repository', 'Volume X is declared OPEN')): check(phrase in flat, what, phrase) # --------------------------------------------------------------------------- head(5, 'CONTROL: THIS SCRIPT COMPUTED SOMETHING') check(len(files('moonshine', 'HEAD')) > 0, 'git grep returned files rather than nothing') # assembled, not written down: a literal control token matches itself once the # script is committed, and the one this file used is also in # book7/ch-van-der-pol-verify.py, so a grep for it returns files. ABSENT = 'qqx' + '-no-file-contains-this-' + 'qqx' check(files(ABSENT, 'HEAD') == set(), 'and returns none for a token no file contains', str(files(ABSENT, 'HEAD'))) check(len(ROWS) == 12 and len(base_n) == 12, 'all twelve rows were measured at both refs') print(' A vacuous pass is a pass. Block [5] exists so that block [1] cannot') print(' report a perfect reproduction by having matched nothing against nothing.') # --------------------------------------------------------------------------- head('HONESTY', 'What this establishes, and what it does not.') print(""" ESTABLISHED. WP-82's rung table reproduces exactly -- twelve of twelve -- when its own stated method is re-run at the commit it names. The paper was right on the day, and its rung-30 zero was right too. Re-run at HEAD, every row has risen: rung 28 from 2 file-mentions to %d, rung 33 from %d to %d, and the inversion the paper reported has narrowed from %.1f:1 to %.1f:1 without reversing. Of the %d files that say "k-theory" at %s, %d are chapters. NOT ESTABLISHED. That the floor is built. A file count measures vocabulary, not content -- it was the right instrument for the paper's question, which was whether the words appear at all, and it is the wrong instrument for "is there a theorem here". Nothing in this script reads a proof. Nor does it revisit the paper's argument: the reading of the ruler, the choice to treat rung order as construction order, and the six proposed volumes are untouched. AND THE REASON THIS FILE EXISTS AT ALL. A dated measurement with no tool behind it can only be re-derived by hand, and on 2026-09-15 a hand reading of the rung-30 row as a live count produced a wrong conclusion about Volume XIII. The row was not wrong. The reading was, and re-running the measurement is what would have caught it in one command. """ % (r28_h, r33_b, r33_h, r33_b / max(r28_b, 1), r33_h / max(r28_h, 1), n_k, SECOND, len(chapters))) print('=' * 70) if fails: print(' %d CHECK(S) FAILED' % len(fails)) for f in fails: print(' - ' + f) print('=' * 70); sys.exit(1) print(' ALL CHECKS PASSED') print('=' * 70)