Pith Number

pith:EUBIZS3N

pith:2016:EUBIZS3N7TRUXA2RVQPFAYQKOQ

not attested not anchored not stored refs pending

Hall sets, Lazard sets and comma-free codes

Christophe Reutenauer, Dominique Perrin

arxiv:1609.05438 v1 · 2016-09-18 · 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{EUBIZS3N7TRUXA2RVQPFAYQKOQ}

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	2026-05-18T01:04:26.422187Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

25028ccb6dfce34b8351ac1e50620a742825f8cfd6b85d483925a158b0964cff

Aliases

arxiv: 1609.05438 · arxiv_version: 1609.05438v1 · doi: 10.48550/arxiv.1609.05438 · pith_short_12: EUBIZS3N7TRU · pith_short_16: EUBIZS3N7TRUXA2R · pith_short_8: EUBIZS3N

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/EUBIZS3N7TRUXA2RVQPFAYQKOQ \
  | 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: 25028ccb6dfce34b8351ac1e50620a742825f8cfd6b85d483925a158b0964cff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3186b0e4df5be83b0453c83b2e5c082d777e49f2ef41782d220094ec3399716",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-09-18T07:27:56Z",
    "title_canon_sha256": "dae24f88852a853304ec39da3617ccfd28fa49677e4fd268c59078ba3a6a9451"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.05438",
    "kind": "arxiv",
    "version": 1
  }
}