Pith Number

pith:KIK6VKVC

pith:2004:KIK6VKVCBL6HLFSUQOD5Y4EXKC

not attested not anchored not stored refs pending

Canonical characters on quasi-symmetric functions and bivariate Catalan numbers

Marcelo Aguiar, Samuel K. Hsiao

arxiv:math/0408053 v1 · 2004-08-04 · math.CO · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KIK6VKVCBL6HLFSUQOD5Y4EXKC}

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	2026-05-18T01:05:26.140499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5215eaaaa20afc7596548387dc709750b902bc39e76643fa025b9629bac96669

Aliases

arxiv: math/0408053 · arxiv_version: math/0408053v1 · doi: 10.48550/arxiv.math/0408053 · pith_short_12: KIK6VKVCBL6H · pith_short_16: KIK6VKVCBL6HLFSU · pith_short_8: KIK6VKVC

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/KIK6VKVCBL6HLFSUQOD5Y4EXKC \
  | 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: 5215eaaaa20afc7596548387dc709750b902bc39e76643fa025b9629bac96669

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03629767b63b5e334ff34a4906b6ccecfece5c1dbf5e97a7d50dd0d3fa6e594f",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2004-08-04T16:54:09Z",
    "title_canon_sha256": "816ad83f94de29af2465292cd5cdeab39f49582d298902030cf8b680976b2e2d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0408053",
    "kind": "arxiv",
    "version": 1
  }
}