Pith Number

pith:7RNJRU7T

pith:2018:7RNJRU7THVLU63M3M7FLZ2RD3S

not attested not anchored not stored refs pending

A noncommutative cycle index and new bases of quasi-symmetric functions and noncommutative symmetric functions

Frederic Toumazet, Jean-Christophe Novelli, Jean-Yves Thibon

arxiv:1804.01762 v2 · 2018-04-05 · 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{7RNJRU7THVLU63M3M7FLZ2RD3S}

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	2026-05-17T23:50:28.280185Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc5a98d3f33d574f6d9b67cabcea23dca0d9c4f2d8dfb3d7f902f7ddc1061069

Aliases

arxiv: 1804.01762 · arxiv_version: 1804.01762v2 · doi: 10.48550/arxiv.1804.01762 · pith_short_12: 7RNJRU7THVLU · pith_short_16: 7RNJRU7THVLU63M3 · pith_short_8: 7RNJRU7T

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/7RNJRU7THVLU63M3M7FLZ2RD3S \
  | 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: fc5a98d3f33d574f6d9b67cabcea23dca0d9c4f2d8dfb3d7f902f7ddc1061069

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d580762caa716c92a4841cbf8e8cf6f90c3035e8a334ae3dc0ad41ccc48e8d07",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-04-05T10:26:25Z",
    "title_canon_sha256": "58af71569c56cde4292970c1ad91ecadbe128c211f01c3dfa39b138cfb2c09ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1804.01762",
    "kind": "arxiv",
    "version": 2
  }
}