Pith Number

pith:WUMK3JMU

pith:2011:WUMK3JMUJ6PAEIVCIHKOJUTKHX

not attested not anchored not stored refs pending

Linear pencils of tropical plane curves

Filip Cools

arxiv:1105.1025 v2 · 2011-05-05 · math.AG · 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{WUMK3JMUJ6PAEIVCIHKOJUTKHX}

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	2026-05-18T04:19:42.996379Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b518ada5944f9e0222a241d4e4d26a3de8638a6ad1606ff3b41e922b1bdf83c4

Aliases

arxiv: 1105.1025 · arxiv_version: 1105.1025v2 · doi: 10.48550/arxiv.1105.1025 · pith_short_12: WUMK3JMUJ6PA · pith_short_16: WUMK3JMUJ6PAEIVC · pith_short_8: WUMK3JMU

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/WUMK3JMUJ6PAEIVCIHKOJUTKHX \
  | 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: b518ada5944f9e0222a241d4e4d26a3de8638a6ad1606ff3b41e922b1bdf83c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df7fd6debe3e38592401ee51b2a2f66d431ea80ce783ab1c44313e0f33fe7eca",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-05-05T10:07:25Z",
    "title_canon_sha256": "2014b3ae2bc15897a67eafa4e83b744c63e60ff134bde549ca57b86055032a16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1025",
    "kind": "arxiv",
    "version": 2
  }
}