Pith Number

pith:CYKXNTKC

pith:2016:CYKXNTKCLM7P4PYTFKYDXOTACG

not attested not anchored not stored refs pending

Supercongruences involving Lucas sequences

Zhi-Wei Sun

arxiv:1610.03384 v8 · 2016-10-11 · 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{CYKXNTKCLM7P4PYTFKYDXOTACG}

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	2026-07-05T01:59:07.771594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

161576cd425b3efe3f132ab03bba6011b04edbee65e772a4deb8b9da45a9af89

Aliases

arxiv: 1610.03384 · arxiv_version: 1610.03384v8 · doi: 10.48550/arxiv.1610.03384 · pith_short_12: CYKXNTKCLM7P · pith_short_16: CYKXNTKCLM7P4PYT · pith_short_8: CYKXNTKC

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/CYKXNTKCLM7P4PYTFKYDXOTACG \
  | 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: 161576cd425b3efe3f132ab03bba6011b04edbee65e772a4deb8b9da45a9af89

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6babda5cb4875cef29299eda4b81d3bb570ed2ca24eea65b0a29547d1fb3e6bf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-10-11T18:17:12Z",
    "title_canon_sha256": "cd2e1cf1f222761104d6b84344fadf851631cb56782fa6e24edf1c3fd08eb497"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.03384",
    "kind": "arxiv",
    "version": 8
  }
}