Pith Number

pith:3A726AKI

pith:2011:3A726AKIALVWWLPAMU25XZQSOT

not attested not anchored not stored refs pending

Levels of knotting of spatial handlebodies

Riccardo Benedetti, Roberto Frigerio

arxiv:1101.2151 v3 · 2011-01-11 · math.GT · 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{3A726AKIALVWWLPAMU25XZQSOT}

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	2026-05-18T02:22:58.756935Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d83faf014802eb6b2de06535dbe61274f6519e867a1e7199bb8b6f302dcbf144

Aliases

arxiv: 1101.2151 · arxiv_version: 1101.2151v3 · doi: 10.48550/arxiv.1101.2151 · pith_short_12: 3A726AKIALVW · pith_short_16: 3A726AKIALVWWLPA · pith_short_8: 3A726AKI

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/3A726AKIALVWWLPAMU25XZQSOT \
  | 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: d83faf014802eb6b2de06535dbe61274f6519e867a1e7199bb8b6f302dcbf144

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "18a517477842d39c627dd7b553bd98e6648bd35a3a0df25c5d467eb574befa91",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-01-11T16:08:19Z",
    "title_canon_sha256": "8069725fa141d0c7aea4970a8b58168fce1c82c0279d7feeeee04b0665744a4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.2151",
    "kind": "arxiv",
    "version": 3
  }
}