Pith Number

pith:2XNBIXOS

pith:2013:2XNBIXOSVKB2733T4YY6BT7U2V

not attested not anchored not stored refs pending

The Euler Characteristic of a Haken 4-Manifold

Allan L. Edmonds

arxiv:1306.2616 v2 · 2013-06-11 · math.GT · 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{2XNBIXOSVKB2733T4YY6BT7U2V}

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	2026-05-18T03:02:59.407862Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5da145dd2aa83afef73e631e0cff4d57574e5c9094011bca60fa364d981e4cd

Aliases

arxiv: 1306.2616 · arxiv_version: 1306.2616v2 · doi: 10.48550/arxiv.1306.2616 · pith_short_12: 2XNBIXOSVKB2 · pith_short_16: 2XNBIXOSVKB2733T · pith_short_8: 2XNBIXOS

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/2XNBIXOSVKB2733T4YY6BT7U2V \
  | 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: d5da145dd2aa83afef73e631e0cff4d57574e5c9094011bca60fa364d981e4cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6eac20b300c92818512db99dad0f9f529186da177023bbf2e05d1984e20c805",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-06-11T19:21:31Z",
    "title_canon_sha256": "83e42453b60f70c69a0e85709b1465a36d239b442816a30c8ebc960d58bf1d53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2616",
    "kind": "arxiv",
    "version": 2
  }
}