Pith Number

pith:3QXB2KIC

pith:2011:3QXB2KIC5Y32POAD726UISNDAU

not attested not anchored not stored refs pending

Congruences for Franel numbers

Zhi-Wei Sun

arxiv:1112.1034 v11 · 2011-12-05 · math.NT · 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{3QXB2KIC5Y32POAD726UISNDAU}

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	2026-05-18T02:21:28.003218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dc2e1d2902ee37a7b803febd4449a3051f7fbff4ba34ec7fed7f0236229b5d6e

Aliases

arxiv: 1112.1034 · arxiv_version: 1112.1034v11 · doi: 10.48550/arxiv.1112.1034 · pith_short_12: 3QXB2KIC5Y32 · pith_short_16: 3QXB2KIC5Y32POAD · pith_short_8: 3QXB2KIC

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/3QXB2KIC5Y32POAD726UISNDAU \
  | 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: dc2e1d2902ee37a7b803febd4449a3051f7fbff4ba34ec7fed7f0236229b5d6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a58b18a5821657e15df2b5069b8274ba76533d12aecd5e9c768eec710a5e660",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-12-05T19:38:56Z",
    "title_canon_sha256": "351a5ce4a9674a36889fab453382895869fc5fcca46ff7841789205878743ff0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1034",
    "kind": "arxiv",
    "version": 11
  }
}