Pith Number

pith:F5ULKUHC

pith:2015:F5ULKUHCDPR5ZANK5UH2NIYR7X

not attested not anchored not stored refs pending

Quasisymmetric and noncommutative skew Pieri rules

Stephanie van Willigenburg, Vasu Tewari

arxiv:1512.04614 v2 · 2015-12-15 · 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{F5ULKUHCDPR5ZANK5UH2NIYR7X}

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	2026-05-18T00:06:44.819782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f68b550e21be3dc81aaed0fa6a311fde5769d02fea7019b86cb43e2e1e8e8ae

Aliases

arxiv: 1512.04614 · arxiv_version: 1512.04614v2 · doi: 10.48550/arxiv.1512.04614 · pith_short_12: F5ULKUHCDPR5 · pith_short_16: F5ULKUHCDPR5ZANK · pith_short_8: F5ULKUHC

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/F5ULKUHCDPR5ZANK5UH2NIYR7X \
  | 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: 2f68b550e21be3dc81aaed0fa6a311fde5769d02fea7019b86cb43e2e1e8e8ae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6971ecdfb24c1e2f09977c2542cc3776cb6214541012f6e3101616c72fe422d7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-12-15T00:16:36Z",
    "title_canon_sha256": "244139de5dbadedc6e988cf75e9cb8c8533d1529a771871fe4952bb4e29fb612"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.04614",
    "kind": "arxiv",
    "version": 2
  }
}