Pith Number

pith:X7M722KK

pith:2015:X7M722KKAIZTB4YNEB3Y2UMDHH

not attested not anchored not stored refs pending

Statistical hyperbolicity of relatively hyperbolic groups

Jeremy Osborne, Wen-yuan Yang

arxiv:1504.01011 v3 · 2015-04-04 · 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{X7M722KKAIZTB4YNEB3Y2UMDHH}

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	2026-05-18T01:04:14.720046Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfd9fd694a023330f30d20778d518339dfe81289de90d270f7439735394beca6

Aliases

arxiv: 1504.01011 · arxiv_version: 1504.01011v3 · doi: 10.48550/arxiv.1504.01011 · pith_short_12: X7M722KKAIZT · pith_short_16: X7M722KKAIZTB4YN · pith_short_8: X7M722KK

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/X7M722KKAIZTB4YNEB3Y2UMDHH \
  | 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: bfd9fd694a023330f30d20778d518339dfe81289de90d270f7439735394beca6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f800f5ec2c527cfbc8aab8b9c69f0a5435018fdb20d9628d705f6444a5e1444e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-04-04T12:34:38Z",
    "title_canon_sha256": "8eef01dc1a6d4317182d31021bab9819b2dfc6189049804330a115682b7419d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01011",
    "kind": "arxiv",
    "version": 3
  }
}