Pith Number

pith:DBZMOCRF

pith:2012:DBZMOCRFSWRO6Q5YDKG3SLKVE4

not attested not anchored not stored refs pending

Combinatorial expansions for families of non-commutative k-Schur functions

Chris Berg, Franco Saliola, Luis Serrano

arxiv:1208.4857 v1 · 2012-08-23 · 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{DBZMOCRFSWRO6Q5YDKG3SLKVE4}

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	2026-05-18T03:47:52.370784Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1872c70a2595a2ef43b81a8db92d5527138ce7ba3fa4fd223ebc279e722269df

Aliases

arxiv: 1208.4857 · arxiv_version: 1208.4857v1 · doi: 10.48550/arxiv.1208.4857 · pith_short_12: DBZMOCRFSWRO · pith_short_16: DBZMOCRFSWRO6Q5Y · pith_short_8: DBZMOCRF

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/DBZMOCRFSWRO6Q5YDKG3SLKVE4 \
  | 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: 1872c70a2595a2ef43b81a8db92d5527138ce7ba3fa4fd223ebc279e722269df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42cbd38ac7a42edcd68c0d4fda7b420c6c0c8e04b4dd68642e33c7245da40cb4",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-08-23T20:05:44Z",
    "title_canon_sha256": "91fe047c78f336d3f70c9cbc95695bf479d13a3a7ced40c7fe5b952eb2fbb11e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.4857",
    "kind": "arxiv",
    "version": 1
  }
}