Pith Number

pith:7EQ5MGO5

pith:2019:7EQ5MGO5USXNLLMHX6ATCMXS7E

not attested not anchored not stored refs pending

On the 2-colored crossing number

Adrian Fuchs, Birgit Vogtenhuber, Carlos Hidalgo-Toscano, Francisco Zaragoza, Irene Parada, Oswin Aichholzer, Ruy Fabila-Monroy

arxiv:1908.06461 v2 · 2019-08-18 · 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{7EQ5MGO5USXNLLMHX6ATCMXS7E}

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	2026-07-05T00:04:10.228556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f921d619dda4aed5ad87bf813132f2f90ad9351e79e939ce834625d1bc6b8748

Aliases

arxiv: 1908.06461 · arxiv_version: 1908.06461v2 · doi: 10.48550/arxiv.1908.06461 · pith_short_12: 7EQ5MGO5USXN · pith_short_16: 7EQ5MGO5USXNLLMH · pith_short_8: 7EQ5MGO5

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/7EQ5MGO5USXNLLMHX6ATCMXS7E \
  | 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: f921d619dda4aed5ad87bf813132f2f90ad9351e79e939ce834625d1bc6b8748

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1315e87d5a1ed82163b118d6d78163a9de0217bf6f221e4c8849caa978858cdd",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2019-08-18T15:18:09Z",
    "title_canon_sha256": "fc0b8c1b7c583d52f509874eacfe987202b5874317e490de300837212c8412f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06461",
    "kind": "arxiv",
    "version": 2
  }
}