Pith Number

pith:BDDXTJWP

pith:2017:BDDXTJWP6WSSU3F5GUB3T3U2QO

not attested not anchored not stored refs pending

The Catalan numbers have no forbidden residue modulo primes

Rob Burns

arxiv:1703.02705 v1 · 2017-03-08 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BDDXTJWP6WSSU3F5GUB3T3U2QO}

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	2026-05-18T00:49:05.826082Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08c779a6cff5a52a6cbd3503b9ee9a83924c7ac0957f163337c59bb4a3d389bc

Aliases

arxiv: 1703.02705 · arxiv_version: 1703.02705v1 · doi: 10.48550/arxiv.1703.02705 · pith_short_12: BDDXTJWP6WSS · pith_short_16: BDDXTJWP6WSSU3F5 · pith_short_8: BDDXTJWP

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/BDDXTJWP6WSSU3F5GUB3T3U2QO \
  | 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: 08c779a6cff5a52a6cbd3503b9ee9a83924c7ac0957f163337c59bb4a3d389bc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8c2f5e33664aa74af364a2ea98cb6ae39636f5e1da8a09c92c86f86f9e4d355c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2017-03-08T05:09:43Z",
    "title_canon_sha256": "86b4d63ca183392a21277cc7c6d8c8b5f5ffc9114f9e446c09ebf1d7bdf99e2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.02705",
    "kind": "arxiv",
    "version": 1
  }
}