Pith Number

pith:543X2R6A

pith:2015:543X2R6AXDA5QOO6RPBMATKK2A

not attested not anchored not stored refs pending

Schur-positive sets of permutations via products of grid classes

Sergi Elizalde, Yuval Roichman

arxiv:1509.00045 v2 · 2015-08-31 · 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{543X2R6AXDA5QOO6RPBMATKK2A}

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	2026-05-18T01:00:53.779931Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef377d47c0b8c1d839de8bc2c04d4ad03e706b5f398af3ef671db076d558f700

Aliases

arxiv: 1509.00045 · arxiv_version: 1509.00045v2 · doi: 10.48550/arxiv.1509.00045 · pith_short_12: 543X2R6AXDA5 · pith_short_16: 543X2R6AXDA5QOO6 · pith_short_8: 543X2R6A

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/543X2R6AXDA5QOO6RPBMATKK2A \
  | 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: ef377d47c0b8c1d839de8bc2c04d4ad03e706b5f398af3ef671db076d558f700

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c484c070232a97be99e59e71477f104f89e6f5562b6c9a2c29f09d130a92f13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-08-31T20:24:35Z",
    "title_canon_sha256": "1181fae60b4808e6876483d7bdaeb6024f81b0cfe07da9490786c2a7428c4582"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.00045",
    "kind": "arxiv",
    "version": 2
  }
}