Pith Number

pith:YGLRRWX5

pith:2012:YGLRRWX5SGKTMCSHAXBYER6PYN

not attested not anchored not stored refs pending

A canonical expansion of the product of two Stanley symmetric functions

Nan Li

arxiv:1208.2859 v1 · 2012-08-14 · 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{YGLRRWX5SGKTMCSHAXBYER6PYN}

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	2026-05-18T03:48:47.056924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c19718dafd9195360a4705c38247cfc354085856f37bdd371fd03676e33c9507

Aliases

arxiv: 1208.2859 · arxiv_version: 1208.2859v1 · doi: 10.48550/arxiv.1208.2859 · pith_short_12: YGLRRWX5SGKT · pith_short_16: YGLRRWX5SGKTMCSH · pith_short_8: YGLRRWX5

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/YGLRRWX5SGKTMCSHAXBYER6PYN \
  | 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: c19718dafd9195360a4705c38247cfc354085856f37bdd371fd03676e33c9507

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9d8cc2ff242af6b224b735d9425bf16b8d3fb62175622dd4ade59b5b6a9b49f4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-08-14T13:30:08Z",
    "title_canon_sha256": "f298fefefb50892d6553010c71f8a653ddc2070d83b2fee41578d01ae3f99884"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.2859",
    "kind": "arxiv",
    "version": 1
  }
}