Pith Number

pith:OIOXG45V

pith:2010:OIOXG45VCGQQDKRTBEJW5CFJBH

not attested not anchored not stored refs pending

On free discrete subgroups of Diff(I)

Azer Akhmedov

arxiv:1004.2060 v1 · 2010-04-12 · math.GR · math.DS · 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{OIOXG45VCGQQDKRTBEJW5CFJBH}

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	2026-05-18T02:41:50.894448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

721d7373b511a101aa3309136e88a909f5c84ed59da7327a0b819612e0bea10f

Aliases

arxiv: 1004.2060 · arxiv_version: 1004.2060v1 · doi: 10.48550/arxiv.1004.2060 · pith_short_12: OIOXG45VCGQQ · pith_short_16: OIOXG45VCGQQDKRT · pith_short_8: OIOXG45V

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/OIOXG45VCGQQDKRTBEJW5CFJBH \
  | 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: 721d7373b511a101aa3309136e88a909f5c84ed59da7327a0b819612e0bea10f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5630f706fdcb4e7768ae6f41775280f184b556d48c48d6c6c553125485d4678b",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-04-12T21:09:59Z",
    "title_canon_sha256": "0ddc8d7c940fd7127d7ec4d3dc575d5ad27cdeabbd6b4e39e45dfa829cec7244"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.2060",
    "kind": "arxiv",
    "version": 1
  }
}