Pith Number

pith:4DBKLJ5Q

pith:2004:4DBKLJ5QTOFHY576UPADNV52ZQ

not attested not anchored not stored refs pending

Limit groups for relatively hyperbolic groups, I: The basic tools

Daniel Groves

arxiv:math/0412492 v2 · 2004-12-24 · 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{4DBKLJ5QTOFHY576UPADNV52ZQ}

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	2026-05-18T01:22:19.360167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e0c2a5a7b09b8a7c77fea3c036d7bacc3bfc84bd120987f451833b870dc34f4e

Aliases

arxiv: math/0412492 · arxiv_version: math/0412492v2 · doi: 10.48550/arxiv.math/0412492 · pith_short_12: 4DBKLJ5QTOFH · pith_short_16: 4DBKLJ5QTOFHY576 · pith_short_8: 4DBKLJ5Q

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/4DBKLJ5QTOFHY576UPADNV52ZQ \
  | 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: e0c2a5a7b09b8a7c77fea3c036d7bacc3bfc84bd120987f451833b870dc34f4e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f1d00c1f787136bf137c5b48928d6d12fbe01c11935fa0183578e03a073d7d96",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2004-12-24T17:49:23Z",
    "title_canon_sha256": "63abfd5724d95572d5c60f69bf307631b532847136d2059afe4f06d89f476557"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412492",
    "kind": "arxiv",
    "version": 2
  }
}