Pith Number

pith:IVI5VTLY

pith:2018:IVI5VTLYPJLJGZ4UJEMTFIIM5K

not attested not anchored not stored refs pending

Boolean product polynomials and Schur-positivity

Louis J. Billera, Sara C. Billey, Vasu Tewari

arxiv:1806.02943 v1 · 2018-06-08 · 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{IVI5VTLYPJLJGZ4UJEMTFIIM5K}

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	2026-05-18T00:13:54.216629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4551dacd787a56936794491932a10ceaa2bf2413c4e329ceafcae2f6ca29c620

Aliases

arxiv: 1806.02943 · arxiv_version: 1806.02943v1 · doi: 10.48550/arxiv.1806.02943 · pith_short_12: IVI5VTLYPJLJ · pith_short_16: IVI5VTLYPJLJGZ4U · pith_short_8: IVI5VTLY

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/IVI5VTLYPJLJGZ4UJEMTFIIM5K \
  | 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: 4551dacd787a56936794491932a10ceaa2bf2413c4e329ceafcae2f6ca29c620

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e322f8c2202713894807a34cbdbcedd9f5ef6906681cc3628e2082fd086533b4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-06-08T02:12:15Z",
    "title_canon_sha256": "1d0fa4b67f0863c88f29d85072cf2fccf153e6346b94c10ea3444e104a10afc5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.02943",
    "kind": "arxiv",
    "version": 1
  }
}