Pith Number

pith:2HAUPVFC

pith:2013:2HAUPVFCN6GJZZQSMWTIFKTGZE

not attested not anchored not stored refs pending

Zeilberger's KOH theorem and the strict unimodality of q-binomial coefficients

Fabrizio Zanello

arxiv:1311.4480 v2 · 2013-11-18 · math.CO · math.AC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2HAUPVFCN6GJZZQSMWTIFKTGZE}

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	2026-05-18T02:18:31.731493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d1c147d4a26f8c9ce61265a682aa66c93ae08d1cedf9415b3b516e6b6798fcb2

Aliases

arxiv: 1311.4480 · arxiv_version: 1311.4480v2 · doi: 10.48550/arxiv.1311.4480 · pith_short_12: 2HAUPVFCN6GJ · pith_short_16: 2HAUPVFCN6GJZZQS · pith_short_8: 2HAUPVFC

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/2HAUPVFCN6GJZZQSMWTIFKTGZE \
  | 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: d1c147d4a26f8c9ce61265a682aa66c93ae08d1cedf9415b3b516e6b6798fcb2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c09c119bf5c2ee5f99495b0c6edb2ca3a71d2d59c25c1bb9c392b4e16828c571",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-11-18T18:26:38Z",
    "title_canon_sha256": "8b6aad0c48dd8c70beb148c809f44fb421acaec5cb41dfab962b8c3017214916"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.4480",
    "kind": "arxiv",
    "version": 2
  }
}