Pith Number

pith:4OCTKNVH

pith:2015:4OCTKNVH6L5FZUEJKTC7YTUEV6

not attested not anchored not stored refs pending

Pair of pants decomposition of 4-manifolds

Bruno Martelli, Marco Golla

arxiv:1503.05839 v3 · 2015-03-19 · 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{4OCTKNVH6L5FZUEJKTC7YTUEV6}

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	2026-05-18T00:21:00.547910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3853536a7f2fa5cd08954c5fc4e84af9239aa63071fd48007f7e7d2233e08d8

Aliases

arxiv: 1503.05839 · arxiv_version: 1503.05839v3 · doi: 10.48550/arxiv.1503.05839 · pith_short_12: 4OCTKNVH6L5F · pith_short_16: 4OCTKNVH6L5FZUEJ · pith_short_8: 4OCTKNVH

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/4OCTKNVH6L5FZUEJKTC7YTUEV6 \
  | 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: e3853536a7f2fa5cd08954c5fc4e84af9239aa63071fd48007f7e7d2233e08d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ba308b00caf8723687e89fbbf91db51f8e518120032e642bc078782cc671d1c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-03-19T16:49:36Z",
    "title_canon_sha256": "fede835642b7b21901b8977157abfa1e687aeff0c5bbf12d35417a6d1c70c4f0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.05839",
    "kind": "arxiv",
    "version": 3
  }
}