Pith Number

pith:ROABO2MN

pith:2009:ROABO2MNCAOECJVS2LWAXLDSV6

not attested not anchored not stored refs pending

Enumeration of lifts of commuting elements of a group

Michael Natapov, Vladimir Turaev

arxiv:0904.3902 v1 · 2009-04-24 · 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{ROABO2MNCAOECJVS2LWAXLDSV6}

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	2026-05-18T01:37:45.165396Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b8017698d101c4126b2d2ec0bac72afb76efed802c29577829a663539705ca7

Aliases

arxiv: 0904.3902 · arxiv_version: 0904.3902v1 · doi: 10.48550/arxiv.0904.3902 · pith_short_12: ROABO2MNCAOE · pith_short_16: ROABO2MNCAOECJVS · pith_short_8: ROABO2MN

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/ROABO2MNCAOECJVS2LWAXLDSV6 \
  | 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: 8b8017698d101c4126b2d2ec0bac72afb76efed802c29577829a663539705ca7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d2a79cfa926041f9abb688bc35a062f33bc5b04074f0d0c97c50a57890ed364",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-04-24T16:58:22Z",
    "title_canon_sha256": "a225765ff1a6cac1d0ba5d6f8297bc185d1a7baa23ad63738193cfc2cd3e1761"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0904.3902",
    "kind": "arxiv",
    "version": 1
  }
}