Pith Number

pith:6237OTQV

pith:2015:6237OTQVNPR2BAUAL7QEUWZZWP

not attested not anchored not stored refs pending

Variations on a Theorem of Birman and Series

Anna Lenzhen, Juan Souto

arxiv:1512.04360 v1 · 2015-12-14 · 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{6237OTQVNPR2BAUAL7QEUWZZWP}

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	2026-05-18T01:24:22.382865Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f6b7f74e156be3a082805fe04a5b39b3f3e217567af44aef85cd9afef5aceee2

Aliases

arxiv: 1512.04360 · arxiv_version: 1512.04360v1 · doi: 10.48550/arxiv.1512.04360 · pith_short_12: 6237OTQVNPR2 · pith_short_16: 6237OTQVNPR2BAUA · pith_short_8: 6237OTQV

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/6237OTQVNPR2BAUAL7QEUWZZWP \
  | 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: f6b7f74e156be3a082805fe04a5b39b3f3e217567af44aef85cd9afef5aceee2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee5bebc4c377f40befc9491c4f0e17b7d72728b1272743cb44a598c2a7103b2b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-12-14T15:21:33Z",
    "title_canon_sha256": "a85658ce5584dec41b368b20b85e82eef21d0a3c5b1f928bedf9f48c4b0bc526"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04360",
    "kind": "arxiv",
    "version": 1
  }
}