Pith Number

pith:QJSQW5NK

pith:1999:QJSQW5NKK5QGXWFKO5XLIDWJNT

not attested not anchored not stored refs pending

Shifted Quasi-Symmetric Functions and the Hopf algebra of peak functions

(2) University of Wisconsin-Madison), Frank Sottile (2), Nantel Bergeron (1), Stefan Mykytiuk (1), Stephanie van Willigenburg(1) ((1) York University, Toronto

arxiv:math/9904105 v1 · 1999-04-20 · math.CO · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QJSQW5NKK5QGXWFKO5XLIDWJNT}

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	2026-05-18T01:00:03.358387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82650b75aa57606bd8aa776eb40ec96cc9f2bc150bed72e82e9f32885f17ca0a

Aliases

arxiv: math/9904105 · arxiv_version: math/9904105v1 · doi: 10.48550/arxiv.math/9904105 · pith_short_12: QJSQW5NKK5QG · pith_short_16: QJSQW5NKK5QGXWFK · pith_short_8: QJSQW5NK

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/QJSQW5NKK5QGXWFKO5XLIDWJNT \
  | 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: 82650b75aa57606bd8aa776eb40ec96cc9f2bc150bed72e82e9f32885f17ca0a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7414b063cabb1b9931f013f584f6bb0022f050a871c8dc108caaff784ee36862",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1999-04-20T22:06:32Z",
    "title_canon_sha256": "681a0bb6c3aafba1d109342ec3c4b19da06dae33637f0c650fe376edf1da62b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9904105",
    "kind": "arxiv",
    "version": 1
  }
}