Pith Number

pith:V7FYCAJS

pith:2010:V7FYCAJS57HIXRIK3R43LIXDA6

not attested not anchored not stored refs pending

Congruences concerning Legendre polynomials II

Zhi-Hong Sun

arxiv:1012.3898 v2 · 2010-12-17 · 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{V7FYCAJS57HIXRIK3R43LIXDA6}

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	2026-05-18T03:49:33.050393Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afcb810132efce8bc50adc79b5a2e307abd4ba993131f389147e3d900bfbe765

Aliases

arxiv: 1012.3898 · arxiv_version: 1012.3898v2 · doi: 10.48550/arxiv.1012.3898 · pith_short_12: V7FYCAJS57HI · pith_short_16: V7FYCAJS57HIXRIK · pith_short_8: V7FYCAJS

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/V7FYCAJS57HIXRIK3R43LIXDA6 \
  | 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: afcb810132efce8bc50adc79b5a2e307abd4ba993131f389147e3d900bfbe765

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40a4ac93549d99ceb60336f72871f426989df7365894c19252c0f0df11d575d3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-12-17T15:00:29Z",
    "title_canon_sha256": "7cd7df6853bf013b4c11aebec832c5d81aad77bbb88794b5256ffd7b092fb962"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3898",
    "kind": "arxiv",
    "version": 2
  }
}