Pith Number

pith:LEQRSJGJ

pith:2013:LEQRSJGJUGXYGMVG6N5YKKDGLY

not attested not anchored not stored refs pending

Dual bases for non commutative symmetric and quasi-symmetric functions via monoidal factorization

Christophe Tollu (LIPN), G\'erard Henry Edmond Duchamp (LIPN), Ladji Kane (LIPN), Vincel Hoang Ngoc Minh (LIPN)

arxiv:1305.4447 v1 · 2013-05-20 · math.CO · cs.SC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LEQRSJGJUGXYGMVG6N5YKKDGLY}

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	2026-05-18T03:25:23.668136Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59211924c9a1af8332a6f37b8528665e00abbb533d7303edf25ed53f4fcdcd4d

Aliases

arxiv: 1305.4447 · arxiv_version: 1305.4447v1 · doi: 10.48550/arxiv.1305.4447 · pith_short_12: LEQRSJGJUGXY · pith_short_16: LEQRSJGJUGXYGMVG · pith_short_8: LEQRSJGJ

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/LEQRSJGJUGXYGMVG6N5YKKDGLY \
  | 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: 59211924c9a1af8332a6f37b8528665e00abbb533d7303edf25ed53f4fcdcd4d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60733b8cea1b79bc307c946625654cae59ba071fc1ebfed45555f5a7d72f5017",
    "cross_cats_sorted": [
      "cs.SC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-05-20T06:36:08Z",
    "title_canon_sha256": "a0d7f653319c4965bfd671f4cafcffd1d5cc7010070d03bdf82aff165decfe1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4447",
    "kind": "arxiv",
    "version": 1
  }
}