Pith Number

pith:KPZZQZNK

pith:2009:KPZZQZNK2SX6XRFGQ7IXIMVRVZ

not attested not anchored not stored refs pending

The (1-E)-transform in combinatorial Hopf algebras

F. Hivert, J.-C. Novelli, J.-G. Luque, J.-Y. Thibon

arxiv:0912.0184 v2 · 2009-12-01 · 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{KPZZQZNK2SX6XRFGQ7IXIMVRVZ}

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	2026-05-18T03:34:03.781031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53f39865aad4afebc4a687d17432b1ae7a0d1ff61863dba2a177703f8108e1fe

Aliases

arxiv: 0912.0184 · arxiv_version: 0912.0184v2 · doi: 10.48550/arxiv.0912.0184 · pith_short_12: KPZZQZNK2SX6 · pith_short_16: KPZZQZNK2SX6XRFG · pith_short_8: KPZZQZNK

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/KPZZQZNK2SX6XRFGQ7IXIMVRVZ \
  | 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: 53f39865aad4afebc4a687d17432b1ae7a0d1ff61863dba2a177703f8108e1fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1bebf95f26e9629bb734f3f12402574233b4509ab0789ab51eaec8f27ec80d85",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-12-01T15:23:07Z",
    "title_canon_sha256": "cb413d8fcb8f8e682f038b351f8e8076b6cc8146faa2f905d09702bd23a0d7a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.0184",
    "kind": "arxiv",
    "version": 2
  }
}