Pith Number

pith:TRCHXQDO

pith:2004:TRCHXQDOJBOKDNAWLB3IR2SUTE

not attested not anchored not stored refs pending

Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems

D.V. Osin

arxiv:math/0404040 v2 · 2004-04-02 · 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{TRCHXQDOJBOKDNAWLB3IR2SUTE}

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	2026-05-18T02:28:29.744285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9c447bc06e485ca1b416587688ea549933a229d2582cce63f20ca020c683e985

Aliases

arxiv: math/0404040 · arxiv_version: math/0404040v2 · doi: 10.48550/arxiv.math/0404040 · pith_short_12: TRCHXQDOJBOK · pith_short_16: TRCHXQDOJBOKDNAW · pith_short_8: TRCHXQDO

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/TRCHXQDOJBOKDNAWLB3IR2SUTE \
  | 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: 9c447bc06e485ca1b416587688ea549933a229d2582cce63f20ca020c683e985

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0318e7ff402f8d7e25cf12529324c52e147d9c1f91b19ddcb685c963488ec205",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2004-04-02T21:00:14Z",
    "title_canon_sha256": "2db8e19391740157addf1ab9c2018b9d85b31e7c05b74b700d21dd47c0e8d078"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0404040",
    "kind": "arxiv",
    "version": 2
  }
}