Pith Number

pith:CJKB7PPO

pith:2014:CJKB7PPON35H6O3YV3GQ4WDOTT

not attested not anchored not stored refs pending

Proof of the middle levels conjecture

Torsten M\"utze

arxiv:1404.4442 v3 · 2014-04-17 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CJKB7PPON35H6O3YV3GQ4WDOTT}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:23:19.634512Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12541fbdee6efa7f3b78aecd0e586e9cf1b1ce493738b3fe7e0c7971aab31aaa

Aliases

arxiv: 1404.4442 · arxiv_version: 1404.4442v3 · doi: 10.48550/arxiv.1404.4442 · pith_short_12: CJKB7PPON35H · pith_short_16: CJKB7PPON35H6O3Y · pith_short_8: CJKB7PPO

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CJKB7PPON35H6O3YV3GQ4WDOTT \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 12541fbdee6efa7f3b78aecd0e586e9cf1b1ce493738b3fe7e0c7971aab31aaa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0a9f42835cda02fa1cf681a1cf38508c12fb1fb99966c5cd90e2fcbe0ff2b63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-04-17T08:03:04Z",
    "title_canon_sha256": "f5e2f4817abc94630c04b6a8d12c0625a6de217e6a57ad26703e344ff57c9d41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1404.4442",
    "kind": "arxiv",
    "version": 3
  }
}