Pith Number

pith:PTCQRMKH

pith:2017:PTCQRMKH5E56XONLF3TFGX5QTH

not attested not anchored not stored refs pending

A Crossing Lemma for Jordan Curves

G\'abor Tardos, J\'anos Pach, Natan Rubin

arxiv:1708.02077 v1 · 2017-08-07 · math.CO · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTCQRMKH5E56XONLF3TFGX5QTH}

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	2026-05-18T00:38:32.368742Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7cc508b147e93bebb9ab2ee6535fb099ea2ffa1f61d62e7ca00cdbeb26cba287

Aliases

arxiv: 1708.02077 · arxiv_version: 1708.02077v1 · doi: 10.48550/arxiv.1708.02077 · pith_short_12: PTCQRMKH5E56 · pith_short_16: PTCQRMKH5E56XONL · pith_short_8: PTCQRMKH

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/PTCQRMKH5E56XONLF3TFGX5QTH \
  | 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: 7cc508b147e93bebb9ab2ee6535fb099ea2ffa1f61d62e7ca00cdbeb26cba287

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afc2b5005ae7a414d78e28950e6d98eb73fd31a861a86996f0e924ca495fde47",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-08-07T11:40:29Z",
    "title_canon_sha256": "0516cd7d725b270ba487318b2bb787a791255ee8df7339cfb52475895ba3ea59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.02077",
    "kind": "arxiv",
    "version": 1
  }
}