Pith Number

pith:I2MULLIN

pith:2007:I2MULLINJ3TQWONG72DYGVB5DK

not attested not anchored not stored refs pending

Generalizations of Swierczkowski's lemma and the arity gap of finite functions

Erkko Lehtonen, Miguel Couceiro

arxiv:0712.1753 v2 · 2007-12-11 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I2MULLINJ3TQWONG72DYGVB5DK}

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	2026-05-18T00:57:38.807749Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

469945ad0d4ee70b39a6fe8783543d1a9d6d1b4d585d0513215b1fd00f6bc8c1

Aliases

arxiv: 0712.1753 · arxiv_version: 0712.1753v2 · doi: 10.48550/arxiv.0712.1753 · pith_short_12: I2MULLINJ3TQ · pith_short_16: I2MULLINJ3TQWONG · pith_short_8: I2MULLIN

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/I2MULLINJ3TQWONG72DYGVB5DK \
  | 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: 469945ad0d4ee70b39a6fe8783543d1a9d6d1b4d585d0513215b1fd00f6bc8c1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fdf216fb3ceaac5aa6689fc0b3da6249e0cea3bdb0f378c9d90ecd671fcdb3f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2007-12-11T16:12:59Z",
    "title_canon_sha256": "ed93c7c082106a8a9797246329c9836e80e48004f38775cbabb7ab15571102e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.1753",
    "kind": "arxiv",
    "version": 2
  }
}