Pith Number

pith:2VCDVWW2

pith:2018:2VCDVWW2PQPPASB6B5GT7Y6KYJ

not attested not anchored not stored refs pending

Combinatorial identities related to $2\times 2$ submatrices of recursive matrices

Arthur L.B. Yang, Fangfang Cai, Qing-Hu Hou, Yidong Sun

arxiv:1808.05736 v1 · 2018-08-17 · 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{2VCDVWW2PQPPASB6B5GT7Y6KYJ}

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	2026-05-18T00:07:52.326893Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5443adada7c1ef0483e0f4d3fe3cac26d4eb50ec679b8db07ea88e462c84421

Aliases

arxiv: 1808.05736 · arxiv_version: 1808.05736v1 · doi: 10.48550/arxiv.1808.05736 · pith_short_12: 2VCDVWW2PQPP · pith_short_16: 2VCDVWW2PQPPASB6 · pith_short_8: 2VCDVWW2

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/2VCDVWW2PQPPASB6B5GT7Y6KYJ \
  | 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: d5443adada7c1ef0483e0f4d3fe3cac26d4eb50ec679b8db07ea88e462c84421

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e345642397e3601620fa0932087ad012da800598252589fed16a551ffbf81cdf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-08-17T03:05:53Z",
    "title_canon_sha256": "2e918557e2968dd1eb1ba91240ab9094f098b48ddbaf5d750cf0d968e24d3963"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.05736",
    "kind": "arxiv",
    "version": 1
  }
}