Pith Number

pith:HRTY4FRX

pith:2012:HRTY4FRXJROORWWVZWF5IJ2V25

not attested not anchored not stored refs pending

Quasi-symmetric and non-commutative affine Schur functions

Chris Berg, Luis Serrano

arxiv:1205.2331 v1 · 2012-05-10 · 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{HRTY4FRXJROORWWVZWF5IJ2V25}

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	2026-05-18T03:55:56.607675Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c678e16374c5ce8dad5cd8bd42755d7773c083f0522c8d4c6328faad2a8782c

Aliases

arxiv: 1205.2331 · arxiv_version: 1205.2331v1 · doi: 10.48550/arxiv.1205.2331 · pith_short_12: HRTY4FRXJROO · pith_short_16: HRTY4FRXJROORWWV · pith_short_8: HRTY4FRX

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/HRTY4FRXJROORWWVZWF5IJ2V25 \
  | 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: 3c678e16374c5ce8dad5cd8bd42755d7773c083f0522c8d4c6328faad2a8782c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e19294a0654fbdda0d645e41d0a2f4ea3d89911aa02e6afe47e5cd83a5c4ff7e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-05-10T18:20:51Z",
    "title_canon_sha256": "e392bedd7bdc4cc243d90470b733657b39897471702d3978a8871ef2019f900c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.2331",
    "kind": "arxiv",
    "version": 1
  }
}