Pith Number

pith:PGLIQWZ6

pith:2013:PGLIQWZ6U43IPE3KQQEFSGYDRM

not attested not anchored not stored refs pending

$k$-Schur functions and affine Schubert calculus

Anne Schilling, Jennifer Morse, Luc Lapointe, Mark Shimozono, Mike Zabrocki, Thomas Lam

arxiv:1301.3569 v2 · 2013-01-16 · 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{PGLIQWZ6U43IPE3KQQEFSGYDRM}

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	2026-05-18T00:49:52.931895Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7996885b3ea73687936a8408591b038b29064eeef686c1a5d18841c59d893153

Aliases

arxiv: 1301.3569 · arxiv_version: 1301.3569v2 · doi: 10.48550/arxiv.1301.3569 · pith_short_12: PGLIQWZ6U43I · pith_short_16: PGLIQWZ6U43IPE3K · pith_short_8: PGLIQWZ6

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/PGLIQWZ6U43IPE3KQQEFSGYDRM \
  | 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: 7996885b3ea73687936a8408591b038b29064eeef686c1a5d18841c59d893153

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5eeef278f2d8ee34bf041e104fb8e8f50f08a07998d939cf7cfd3b7f729d2d3c",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-01-16T03:23:37Z",
    "title_canon_sha256": "c66580b3a690a2fde993aaaf0d45632b8657afa40b488fb1e1b02928eeea0c81"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.3569",
    "kind": "arxiv",
    "version": 2
  }
}