Pith Number

pith:QWSJLKJ7

pith:2012:QWSJLKJ7B4XBOD3FKO24BQQ6AQ

not attested not anchored not stored refs pending

Schubert Polynomials and $k$-Schur functions

Carolina Benedetti, Nantel Bergeron

arxiv:1209.4956 v1 · 2012-09-22 · math.CO · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QWSJLKJ7B4XBOD3FKO24BQQ6AQ}

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	2026-05-18T01:00:10.644607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

85a495a93f0f2e170f6553b5c0c21e041e431979c851423573088a205056c7e6

Aliases

arxiv: 1209.4956 · arxiv_version: 1209.4956v1 · doi: 10.48550/arxiv.1209.4956 · pith_short_12: QWSJLKJ7B4XB · pith_short_16: QWSJLKJ7B4XBOD3F · pith_short_8: QWSJLKJ7

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/QWSJLKJ7B4XBOD3FKO24BQQ6AQ \
  | 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: 85a495a93f0f2e170f6553b5c0c21e041e431979c851423573088a205056c7e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "19a3b290350908c9b85e2a1a8fa4947f3243264dddd747d1de4fb7bf336589cc",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-22T03:04:10Z",
    "title_canon_sha256": "283173b39c4d7c4c08326b6f372f71529cd75d41f3b1af90e847d98c6a2005b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4956",
    "kind": "arxiv",
    "version": 1
  }
}