Pith Number

pith:Q4HITNW4

pith:2022:Q4HITNW4OEAT4SVSGIRWBJG7YD

not attested not anchored not stored refs pending

On congruences involving Ap\'ery numbers

Wei Xia, Zhi-Wei Sun

arxiv:2212.09455 v2 · 2022-12-19 · 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{Q4HITNW4OEAT4SVSGIRWBJG7YD}

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	2026-07-05T06:11:44.085511Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

870e89b6dc71013e4ab2322360a4dfc0f028c10bebf7c82f47bf7fce7d7137dd

Aliases

arxiv: 2212.09455 · arxiv_version: 2212.09455v2 · doi: 10.48550/arxiv.2212.09455 · pith_short_12: Q4HITNW4OEAT · pith_short_16: Q4HITNW4OEAT4SVS · pith_short_8: Q4HITNW4

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/Q4HITNW4OEAT4SVSGIRWBJG7YD \
  | 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: 870e89b6dc71013e4ab2322360a4dfc0f028c10bebf7c82f47bf7fce7d7137dd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "752a86fa84d3f9599b64b13fde099979dafc42b7f4d6151c1743e3b797e16527",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2022-12-19T13:47:28Z",
    "title_canon_sha256": "ba02ac072f4091017447accdc938eefb24290b539ee69298d7cde28fd7bb6f37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2212.09455",
    "kind": "arxiv",
    "version": 2
  }
}