Pith Number

pith:LN2JOK4L

pith:2012:LN2JOK4LFJ5E5GX4OKL5XMHFWR

not attested not anchored not stored refs pending

Proof of two conjectures of Z.-W. Sun on congruences for Franel numbers

Victor J. W. Guo

arxiv:1201.0617 v3 · 2012-01-03 · 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{LN2JOK4LFJ5E5GX4OKL5XMHFWR}

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	2026-05-18T03:50:25.553715Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b74972b8b2a7a4e9afc7297dbb0e5b44e691cdc0ef2be8c3a4b23ee7ad25b62

Aliases

arxiv: 1201.0617 · arxiv_version: 1201.0617v3 · doi: 10.48550/arxiv.1201.0617 · pith_short_12: LN2JOK4LFJ5E · pith_short_16: LN2JOK4LFJ5E5GX4 · pith_short_8: LN2JOK4L

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/LN2JOK4LFJ5E5GX4OKL5XMHFWR \
  | 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: 5b74972b8b2a7a4e9afc7297dbb0e5b44e691cdc0ef2be8c3a4b23ee7ad25b62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efebd10db83944ad125d08c849ee1a71cf07b120c56e68d389e7fa3be11fb3a0",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-01-03T12:40:50Z",
    "title_canon_sha256": "d60a98edc7259fa9bd7afbcbff13e9e5eb7c38a6b203c6b6e0b4d3cee32e4f69"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.0617",
    "kind": "arxiv",
    "version": 3
  }
}