Pith Number

pith:INJCMO2I

pith:2011:INJCMO2INQGOCUVWPUF6WTLLWE

not attested not anchored not stored refs pending

On sums of Ap\'ery polynomials and related congruences

Zhi-Wei Sun

arxiv:1101.1946 v4 · 2011-01-10 · 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{INJCMO2INQGOCUVWPUF6WTLLWE}

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	2026-05-18T02:53:15.883891Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4352263b486c0ce152b67d0beb4d6bb135037b7085a6ec31022d3b95e9be6788

Aliases

arxiv: 1101.1946 · arxiv_version: 1101.1946v4 · doi: 10.48550/arxiv.1101.1946 · pith_short_12: INJCMO2INQGO · pith_short_16: INJCMO2INQGOCUVW · pith_short_8: INJCMO2I

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/INJCMO2INQGOCUVWPUF6WTLLWE \
  | 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: 4352263b486c0ce152b67d0beb4d6bb135037b7085a6ec31022d3b95e9be6788

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c9030b2add50be5628978516f322e7a1f05fff4584c87b8a5bc5ed762eb17226",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-10T20:44:27Z",
    "title_canon_sha256": "5ef06c555487c8c94491d4bcc2bf51dd581130bc9b3e2116be682c68abd7f080"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.1946",
    "kind": "arxiv",
    "version": 4
  }
}