Pith Number

pith:SW3QFLT6

pith:2013:SW3QFLT6T2DXPPENSLA33DAQUW

not attested not anchored not stored refs pending

Congruences concerning Lucas' law of repetition

Zhi-Hong Sun

arxiv:1312.3511 v1 · 2013-12-12 · 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{SW3QFLT6T2DXPPENSLA33DAQUW}

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	2026-05-18T03:04:50.702363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

95b702ae7e9e8777bc8d92c1bd8c10a5a47de65e243bd6c1ad54ff7928fd79fb

Aliases

arxiv: 1312.3511 · arxiv_version: 1312.3511v1 · doi: 10.48550/arxiv.1312.3511 · pith_short_12: SW3QFLT6T2DX · pith_short_16: SW3QFLT6T2DXPPEN · pith_short_8: SW3QFLT6

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/SW3QFLT6T2DXPPENSLA33DAQUW \
  | 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: 95b702ae7e9e8777bc8d92c1bd8c10a5a47de65e243bd6c1ad54ff7928fd79fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17ad34473b5128cd95ee562b0ed1909ff6fde1ebcf705a4c61b636834b55eeb8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-12-12T15:01:02Z",
    "title_canon_sha256": "ff316182988e37cc075702fb56964fdda2218bdcf49bf48457afeb00ec17e90c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3511",
    "kind": "arxiv",
    "version": 1
  }
}