Pith Number

pith:67F4DZF5

pith:2015:67F4DZF5MPDPDVUOIIUX4ASGEM

not attested not anchored not stored refs pending

A Lucas-type congruence for q-Delannoy numbers

Hao Pan

arxiv:1508.02046 v1 · 2015-08-09 · math.CO · 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{67F4DZF5MPDPDVUOIIUX4ASGEM}

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	2026-05-18T01:35:34.398545Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7cbc1e4bd63c6f1d68e42297e0246231d02913d797e6a9d827b6d89a861f022

Aliases

arxiv: 1508.02046 · arxiv_version: 1508.02046v1 · doi: 10.48550/arxiv.1508.02046 · pith_short_12: 67F4DZF5MPDP · pith_short_16: 67F4DZF5MPDPDVUO · pith_short_8: 67F4DZF5

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/67F4DZF5MPDPDVUOIIUX4ASGEM \
  | 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: f7cbc1e4bd63c6f1d68e42297e0246231d02913d797e6a9d827b6d89a861f022

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8cc1d590b2a0f40399c51029ba983fc621d7d23dc8b667950a6fe99d93c78d5e",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-09T16:30:01Z",
    "title_canon_sha256": "030ef0831614feff9129ef23eb37a92159d64c97cea3b1fca2d80283dc3fe193"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02046",
    "kind": "arxiv",
    "version": 1
  }
}