Pith Number

pith:BVBYG77O

pith:2010:BVBYG77OYLW3HRNEEAL2XK4DAV

not attested not anchored not stored refs pending

Congruences concerning Legendre polynomials III

Zhi-Hong Sun

arxiv:1012.4234 v4 · 2010-12-20 · 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{BVBYG77OYLW3HRNEEAL2XK4DAV}

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	2026-05-18T03:42:24.102835Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d43837feec2edb3c5a42017abab8305493062d69d3374ef08cb003dfc353836

Aliases

arxiv: 1012.4234 · arxiv_version: 1012.4234v4 · doi: 10.48550/arxiv.1012.4234 · pith_short_12: BVBYG77OYLW3 · pith_short_16: BVBYG77OYLW3HRNE · pith_short_8: BVBYG77O

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/BVBYG77OYLW3HRNEEAL2XK4DAV \
  | 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: 0d43837feec2edb3c5a42017abab8305493062d69d3374ef08cb003dfc353836

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26205cba73338a93828cd8c8c4fc863caacce47d3e65738621e2ca7abc5e80e9",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-12-20T03:16:57Z",
    "title_canon_sha256": "0f897bd19a33a02fb36a77835dd17dfc6ff57ac36e0bf193733edd61be697b3d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.4234",
    "kind": "arxiv",
    "version": 4
  }
}