Pith Number

pith:J2WXTH7X

pith:2009:J2WXTH7XTOZ62SRUVSXQPELCNB

not attested not anchored not stored refs pending

On the least common multiple of $q$-binomial coefficients

Victor J. W. Guo

arxiv:0907.2870 v1 · 2009-07-16 · 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{J2WXTH7XTOZ62SRUVSXQPELCNB}

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	2026-05-18T04:26:01.570418Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ead799ff79bb3ed4a34acaf079162684ec1a147ce56d25793a7cabc21596a15

Aliases

arxiv: 0907.2870 · arxiv_version: 0907.2870v1 · doi: 10.48550/arxiv.0907.2870 · pith_short_12: J2WXTH7XTOZ6 · pith_short_16: J2WXTH7XTOZ62SRU · pith_short_8: J2WXTH7X

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/J2WXTH7XTOZ62SRUVSXQPELCNB \
  | 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: 4ead799ff79bb3ed4a34acaf079162684ec1a147ce56d25793a7cabc21596a15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8190313d12ce3ac5d341ef3f47a1f2378351c91509ca45d5af845efe4b6dc3a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2009-07-16T15:34:57Z",
    "title_canon_sha256": "980761b8d4eaaf5dfc938700118d31d85582eb660ea31a589bf3a73df5045067"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.2870",
    "kind": "arxiv",
    "version": 1
  }
}