Pith Number

pith:WNU4UEP4

pith:2018:WNU4UEP4IEGLYLGM3JEWJRYPCZ

not attested not anchored not stored refs pending

Upper-triangular linear relations on multiplicities and the Stanley-Stembridge conjecture

Martha Precup, Megumi Harada

arxiv:1812.09503 v2 · 2018-12-22 · math.CO · math.AG · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WNU4UEP4IEGLYLGM3JEWJRYPCZ}

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	2026-05-17T23:46:29.227002Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b369ca11fc410cbc2cccda4964c70f1660c7ffca30d15f05b1bd1eec5735ab09

Aliases

arxiv: 1812.09503 · arxiv_version: 1812.09503v2 · doi: 10.48550/arxiv.1812.09503 · pith_short_12: WNU4UEP4IEGL · pith_short_16: WNU4UEP4IEGLYLGM · pith_short_8: WNU4UEP4

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/WNU4UEP4IEGLYLGM3JEWJRYPCZ \
  | 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: b369ca11fc410cbc2cccda4964c70f1660c7ffca30d15f05b1bd1eec5735ab09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf9d34c86c34709aef6b2a203c70c3f8099b25197722ac912cc86a9ef0f3d3f9",
    "cross_cats_sorted": [
      "math.AG",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-12-22T11:12:23Z",
    "title_canon_sha256": "c2d187bf9c2ed0f9862da8efb58b28a3b3c39f84ea17e2d154f5ec35e37d18c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.09503",
    "kind": "arxiv",
    "version": 2
  }
}