Pith Number

pith:4C4WPNZW

pith:2016:4C4WPNZW2ZJDP54YBFNJLW5VNZ

not attested not anchored not stored refs pending

A Direct Proof of the Strong Hanani-Tutte Theorem on the Projective Plane

\'Eric Colin de Verdi\`ere, Martin Tancer, Pavel Pat\'ak, Vojt\v{e}ch Kalu\v{z}a, Zuzana Pat\'akov\'a

arxiv:1608.07855 v2 · 2016-08-28 · cs.CG · 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{4C4WPNZW2ZJDP54YBFNJLW5VNZ}

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	2026-05-18T01:07:19.946694Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0b967b736d65237f798095a95dbb56e762d7b0a8aa8804ed5272266cc9fa6e5

Aliases

arxiv: 1608.07855 · arxiv_version: 1608.07855v2 · doi: 10.48550/arxiv.1608.07855 · pith_short_12: 4C4WPNZW2ZJD · pith_short_16: 4C4WPNZW2ZJDP54Y · pith_short_8: 4C4WPNZW

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/4C4WPNZW2ZJDP54YBFNJLW5VNZ \
  | 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: e0b967b736d65237f798095a95dbb56e762d7b0a8aa8804ed5272266cc9fa6e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "50ec13e2038fbbb477ed8cfd76de2bb164880d53932ca272f7ca1598626c9620",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2016-08-28T21:22:05Z",
    "title_canon_sha256": "1c2471f90ba8880ba6e421188016512cbb8e3badbc55e6d63f5bfd29a74e136f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.07855",
    "kind": "arxiv",
    "version": 2
  }
}