Pith Number

pith:SAR5L27Z

pith:2015:SAR5L27ZFUOOJHMBYQK3WVP5AA

not attested not anchored not stored refs pending

Drawings of Kn with the same rotation scheme are the same up to Reidemeister moves. Gioan's Theorem

Alan Arroyo, Dan McQuillan, Gelasio Salazar, R. Bruce Richter

arxiv:1512.09040 v2 · 2015-12-30 · math.CO · 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{SAR5L27ZFUOOJHMBYQK3WVP5AA}

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	2026-05-18T01:21:46.802972Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9023d5ebf92d1ce49d81c415bb55fd001cfb7d6cac4e1c7b5178f83d1fbb490f

Aliases

arxiv: 1512.09040 · arxiv_version: 1512.09040v2 · doi: 10.48550/arxiv.1512.09040 · pith_short_12: SAR5L27ZFUOO · pith_short_16: SAR5L27ZFUOOJHMB · pith_short_8: SAR5L27Z

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/SAR5L27ZFUOOJHMBYQK3WVP5AA \
  | 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: 9023d5ebf92d1ce49d81c415bb55fd001cfb7d6cac4e1c7b5178f83d1fbb490f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb6a9a869e4677aebe627161bfdc2312eb788c5cb03140f360c8d8bad179a1dc",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-30T18:07:21Z",
    "title_canon_sha256": "a0ee3faf0b7d6f4edc309e50811f1e9a92eb8e0b30d02f41af2ae41fa5dea3cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.09040",
    "kind": "arxiv",
    "version": 2
  }
}