Pith Number

pith:4XCGSI3R

pith:2010:4XCGSI3RIIRDGALQOLIFECVC24

not attested not anchored not stored refs pending

Cobham's theorem for substitutions

Fabien Durand (LAMFA)

arxiv:1010.4009 v1 · 2010-10-19 · math.CO · cs.DM · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4XCGSI3RIIRDGALQOLIFECVC24}

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	2026-05-18T04:38:59.934460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5c4692371422233017072d0520aa2d7146020f315d019022e28a29291d65249

Aliases

arxiv: 1010.4009 · arxiv_version: 1010.4009v1 · doi: 10.48550/arxiv.1010.4009 · pith_short_12: 4XCGSI3RIIRD · pith_short_16: 4XCGSI3RIIRDGALQ · pith_short_8: 4XCGSI3R

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/4XCGSI3RIIRDGALQOLIFECVC24 \
  | 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: e5c4692371422233017072d0520aa2d7146020f315d019022e28a29291d65249

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1088f4f3720434ea6e9893cf5a95cc665e3a67fbb3ed8ff35fe413329dc97e76",
    "cross_cats_sorted": [
      "cs.DM",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-10-19T19:10:38Z",
    "title_canon_sha256": "55ca9760dda1579f125595822fd16c2255912915289d51a70a6efe6dc50238ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4009",
    "kind": "arxiv",
    "version": 1
  }
}