Pith Number

pith:Z6H623CR

pith:2011:Z6H623CRC3ZY6XJ5X7B7IK7ML2

not attested not anchored not stored refs pending

Generalized Legendre polynomials and related congruences modulo $p^2$

Zhi-Hong Sun

arxiv:1101.5386 v5 · 2011-01-27 · 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{Z6H623CRC3ZY6XJ5X7B7IK7ML2}

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	2026-05-18T04:03:20.327891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cf8fed6c5116f38f5d3dbfc3f42bec5ea673c7629aa98dd2a28a7e654182ee25

Aliases

arxiv: 1101.5386 · arxiv_version: 1101.5386v5 · doi: 10.48550/arxiv.1101.5386 · pith_short_12: Z6H623CRC3ZY · pith_short_16: Z6H623CRC3ZY6XJ5 · pith_short_8: Z6H623CR

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/Z6H623CRC3ZY6XJ5X7B7IK7ML2 \
  | 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: cf8fed6c5116f38f5d3dbfc3f42bec5ea673c7629aa98dd2a28a7e654182ee25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e184a2aaf118961c6bf876e3d0d7f0985a49e9d42feedc64ade9b0bf3c222b1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-27T20:34:32Z",
    "title_canon_sha256": "7bab9395863577e88f9f5cc777e5a47f36d6ace0f618dcd7d9f04cdf36e1f761"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.5386",
    "kind": "arxiv",
    "version": 5
  }
}