Pith Number

pith:B4OBKDZN

pith:2018:B4OBKDZNBYHLAM2XRBMHVI6A3Y

not attested not anchored not stored refs pending

Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class group

Juliette Bavard

arxiv:1802.02715 v1 · 2018-02-08 · math.GT · math.DS · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{B4OBKDZNBYHLAM2XRBMHVI6A3Y}

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	2026-05-18T00:24:03.257571Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f1c150f2d0e0eb0335788587aa3c0de1e029137759039727250c460a2af6aba

Aliases

arxiv: 1802.02715 · arxiv_version: 1802.02715v1 · doi: 10.48550/arxiv.1802.02715 · pith_short_12: B4OBKDZNBYHL · pith_short_16: B4OBKDZNBYHLAM2X · pith_short_8: B4OBKDZN

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/B4OBKDZNBYHLAM2XRBMHVI6A3Y \
  | 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: 0f1c150f2d0e0eb0335788587aa3c0de1e029137759039727250c460a2af6aba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3c61a68639f062e54974327ecd8c385dda06590a9834718e1e4f047be234ec15",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2018-02-08T04:46:40Z",
    "title_canon_sha256": "41f9a03fb027acdeaa6f215b4f8cf363461f332ef7ed1fa87b838627f476fbe8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.02715",
    "kind": "arxiv",
    "version": 1
  }
}