Pith Number

pith:5PVJH4ML

pith:2010:5PVJH4MLZMF3G3JDXV7NXKBJU5

not attested not anchored not stored refs pending

Constructions of surface bundles with rank two fundamental groups

Kazuhiro Ichihara, Mitsuhiko Takasawa

arxiv:1012.5401 v1 · 2010-12-24 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5PVJH4MLZMF3G3JDXV7NXKBJU5}

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	2026-05-18T04:32:34.966453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebea93f18bcb0bb36d23bd7edba829a75c82b9b2b0d8b9f001f3d9eb0fedb60d

Aliases

arxiv: 1012.5401 · arxiv_version: 1012.5401v1 · doi: 10.48550/arxiv.1012.5401 · pith_short_12: 5PVJH4MLZMF3 · pith_short_16: 5PVJH4MLZMF3G3JD · pith_short_8: 5PVJH4ML

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/5PVJH4MLZMF3G3JDXV7NXKBJU5 \
  | 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: ebea93f18bcb0bb36d23bd7edba829a75c82b9b2b0d8b9f001f3d9eb0fedb60d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "81e55dec2bf1ebcb87de619eaddd1beff7aaef9975e8953bb31dc84cf60f7e4f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-12-24T14:13:11Z",
    "title_canon_sha256": "0e5bcfccac33375ee005dbf0e16e3d96e22274f57c1b96d1329e8dbe053ef2b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5401",
    "kind": "arxiv",
    "version": 1
  }
}