Pith Number

pith:ZAIUFHBT

pith:2013:ZAIUFHBTHE5QO5OTHRXSYXR4UW

not attested not anchored not stored refs pending

Unimodality of partitions with distinct parts inside Ferrers shapes

Fabrizio Zanello, Richard P. Stanley

arxiv:1305.6083 v3 · 2013-05-27 · 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{ZAIUFHBTHE5QO5OTHRXSYXR4UW}

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	2026-05-18T01:27:37.132701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c811429c33393b0775d33c6f2c5e3ca593f6271ecd5376b8254e6a8db74fd7a2

Aliases

arxiv: 1305.6083 · arxiv_version: 1305.6083v3 · doi: 10.48550/arxiv.1305.6083 · pith_short_12: ZAIUFHBTHE5Q · pith_short_16: ZAIUFHBTHE5QO5OT · pith_short_8: ZAIUFHBT

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/ZAIUFHBTHE5QO5OTHRXSYXR4UW \
  | 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: c811429c33393b0775d33c6f2c5e3ca593f6271ecd5376b8254e6a8db74fd7a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2ac2875ee7f8df1016145f77549fb530ed499cf03bdfcaf9c73a2f0920e5765",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-05-27T00:44:13Z",
    "title_canon_sha256": "8c4a5ed2366b372d41ed74dcf201449b37a0f1383f9c0d0a52484787fcdc50cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.6083",
    "kind": "arxiv",
    "version": 3
  }
}