Pith Number

pith:ULFMHVJM

pith:2007:ULFMHVJMSOD36ADOO3ZCMJANYB

not attested not anchored not stored refs pending

Tropical fans and the moduli spaces of tropical curves

Andreas Gathmann, Hannah Markwig, Michael Kerber

arxiv:0708.2268 v2 · 2007-08-16 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ULFMHVJMSOD36ADOO3ZCMJANYB}

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	2026-05-18T03:02:45.133711Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2cac3d52c9387bf006e76f226240dc0695d1e71309cf6b38d000fb37bad5aa7

Aliases

arxiv: 0708.2268 · arxiv_version: 0708.2268v2 · doi: 10.48550/arxiv.0708.2268 · pith_short_12: ULFMHVJMSOD3 · pith_short_16: ULFMHVJMSOD36ADO · pith_short_8: ULFMHVJM

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/ULFMHVJMSOD36ADOO3ZCMJANYB \
  | 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: a2cac3d52c9387bf006e76f226240dc0695d1e71309cf6b38d000fb37bad5aa7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "767160f2f6cfefea146868374d7a5899dfd63b44482076db4122791ff4a15b93",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2007-08-16T19:00:58Z",
    "title_canon_sha256": "4d0f84f4198a10598462329b7c46df458acc654be9d2fcd568cbd2bcaef5850b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.2268",
    "kind": "arxiv",
    "version": 2
  }
}