Pith Number

pith:IYKTN4H6

pith:2012:IYKTN4H6QVIGTNQSXK2KGDOPIE

not attested not anchored not stored refs pending

On the end depth and ends of groups

Martha Giannoudovardi

arxiv:1207.0941 v1 · 2012-07-04 · 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{IYKTN4H6QVIGTNQSXK2KGDOPIE}

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	2026-05-18T03:51:47.915786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

461536f0fe855069b612bab4a30dcf4119e23c35260ef43e67c97188ad14b7f1

Aliases

arxiv: 1207.0941 · arxiv_version: 1207.0941v1 · doi: 10.48550/arxiv.1207.0941 · pith_short_12: IYKTN4H6QVIG · pith_short_16: IYKTN4H6QVIGTNQS · pith_short_8: IYKTN4H6

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/IYKTN4H6QVIGTNQSXK2KGDOPIE \
  | 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: 461536f0fe855069b612bab4a30dcf4119e23c35260ef43e67c97188ad14b7f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "913a8401446ab1afc01b31d7a69b615e7db621fdf52a25336c00d342370c19cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-07-04T11:12:22Z",
    "title_canon_sha256": "8a1820e8a196e33b5f0fa0f555986145ef609de93ba41cabb9e6e30b71b1c95d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0941",
    "kind": "arxiv",
    "version": 1
  }
}