Pith Number

pith:YOTO2TFR

pith:2009:YOTO2TFR4Z5TPDWAT5R2LX33FR

not attested not anchored not stored refs pending

Affine Schubert classes, Schur positivity, and combinatorial Hopf algebras

Thomas Lam

arxiv:0906.0385 v1 · 2009-06-01 · math.AG · 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{YOTO2TFR4Z5TPDWAT5R2LX33FR}

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	2026-05-18T02:58:03.134685Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3a6ed4cb1e67b378ec09f63a5df7b2c575627b0b4fa8eb0b3d403624a71ec81

Aliases

arxiv: 0906.0385 · arxiv_version: 0906.0385v1 · doi: 10.48550/arxiv.0906.0385 · pith_short_12: YOTO2TFR4Z5T · pith_short_16: YOTO2TFR4Z5TPDWA · pith_short_8: YOTO2TFR

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/YOTO2TFR4Z5TPDWAT5R2LX33FR \
  | 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: c3a6ed4cb1e67b378ec09f63a5df7b2c575627b0b4fa8eb0b3d403624a71ec81

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20236f9f62f522f93230da7d34a30fdefa64bb11c6c09af9bb07c0be8ed3109f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2009-06-01T21:49:26Z",
    "title_canon_sha256": "c9088a9f623d6f8ed94397ebfcdfef2bc82762521f078fa0a98962afc7b941d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.0385",
    "kind": "arxiv",
    "version": 1
  }
}