Pith Number

pith:35URGC3B

pith:2012:35URGC3B74YPCELRYBBCV6QL6Y

not attested not anchored not stored refs pending

Test elements in torsion-free hyperbolic groups

Daniel Groves

arxiv:1202.3939 v2 · 2012-02-17 · 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{35URGC3B74YPCELRYBBCV6QL6Y}

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	2026-05-18T03:49:11.759868Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df69130b61ff30f11171c0422afa0bf61477bc5ebbb0f1b1cee7053dc32bd44b

Aliases

arxiv: 1202.3939 · arxiv_version: 1202.3939v2 · doi: 10.48550/arxiv.1202.3939 · pith_short_12: 35URGC3B74YP · pith_short_16: 35URGC3B74YPCELR · pith_short_8: 35URGC3B

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/35URGC3B74YPCELRYBBCV6QL6Y \
  | 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: df69130b61ff30f11171c0422afa0bf61477bc5ebbb0f1b1cee7053dc32bd44b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f14c431162ef6b064f3fe6197c6ff3a2a839456582abdeff67e0aa4411b7d58",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-02-17T15:44:20Z",
    "title_canon_sha256": "15735d0447278e0deb0870f8190f44468e41c03b176f17d45d5f85bc62887284"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3939",
    "kind": "arxiv",
    "version": 2
  }
}