Pith Number

pith:7JIL7Z3Q

pith:2013:7JIL7Z3QHPFKN36APF446PZBVL

not attested not anchored not stored refs pending

Knots in collapsible and non-collapsible balls

Bruno Benedetti, Frank H. Lutz

arxiv:1303.2070 v2 · 2013-03-08 · math.CO · cs.CG · 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{7JIL7Z3QHPFKN36APF446PZBVL}

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	2026-05-18T02:53:56.444617Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa50bfe7703bcaa6efc07979cf3f21aae44bce98ae20ed6824ffb13b3f4ceca5

Aliases

arxiv: 1303.2070 · arxiv_version: 1303.2070v2 · doi: 10.48550/arxiv.1303.2070 · pith_short_12: 7JIL7Z3QHPFK · pith_short_16: 7JIL7Z3QHPFKN36A · pith_short_8: 7JIL7Z3Q

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/7JIL7Z3QHPFKN36APF446PZBVL \
  | 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: fa50bfe7703bcaa6efc07979cf3f21aae44bce98ae20ed6824ffb13b3f4ceca5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a507fb9cb64458f62b8cedad8b2dfa79039c2ccb0696ce8afd9eeb13d9f485d",
    "cross_cats_sorted": [
      "cs.CG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-03-08T18:13:22Z",
    "title_canon_sha256": "084c11421976e08561408ef59b6d072b30187114d868fac69b313d2198cdb86f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.2070",
    "kind": "arxiv",
    "version": 2
  }
}