Pith Number

pith:4LWS4XVR

pith:2014:4LWS4XVROKVWOMTPRTW3OFDPR4

not attested not anchored not stored refs pending

Hyperbolicit\'e du graphe des rayons et quasi-morphismes sur un gros groupe modulaire

Juliette Bavard

arxiv:1409.6566 v1 · 2014-09-23 · math.DS · math.GR · 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{4LWS4XVROKVWOMTPRTW3OFDPR4}

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	2026-05-18T01:19:30.665903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2ed2e5eb172ab67326f8cedb7146f8f2110198ed1f0576b831ff5586667fd74

Aliases

arxiv: 1409.6566 · arxiv_version: 1409.6566v1 · doi: 10.48550/arxiv.1409.6566 · pith_short_12: 4LWS4XVROKVW · pith_short_16: 4LWS4XVROKVWOMTP · pith_short_8: 4LWS4XVR

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/4LWS4XVROKVWOMTPRTW3OFDPR4 \
  | 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: e2ed2e5eb172ab67326f8cedb7146f8f2110198ed1f0576b831ff5586667fd74

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d33b21b55b5967253698903aad68ad136d3c86c5e7a60cb7611c78be6a5fea8d",
    "cross_cats_sorted": [
      "math.GR",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-09-23T14:56:06Z",
    "title_canon_sha256": "5a20366ca395c238d7711b31890b29aa8f24bcbc5a9798f534b37abaefb17eca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.6566",
    "kind": "arxiv",
    "version": 1
  }
}