Pith Number

pith:CHCLSCWC

pith:2009:CHCLSCWCFXR7CZ2CXPBVMJZL5S

not attested not anchored not stored refs pending

Twisted dendriform algebras and the pre-Lie Magnus expansion

Dominique Manchon, Kurusch Ebrahimi-Fard

arxiv:0910.2166 v3 · 2009-10-12 · 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{CHCLSCWCFXR7CZ2CXPBVMJZL5S}

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	2026-05-18T04:22:01.137373Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11c4b90ac22de3f16742bbc356272becb8dde7d583f7531c2feecf2b0478ec0b

Aliases

arxiv: 0910.2166 · arxiv_version: 0910.2166v3 · doi: 10.48550/arxiv.0910.2166 · pith_short_12: CHCLSCWCFXR7 · pith_short_16: CHCLSCWCFXR7CZ2C · pith_short_8: CHCLSCWC

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/CHCLSCWCFXR7CZ2CXPBVMJZL5S \
  | 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: 11c4b90ac22de3f16742bbc356272becb8dde7d583f7531c2feecf2b0478ec0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "637c85f5cead4ed4cac2c0edc977dbf6281a1567fb4b70b7551e0d9f8918251e",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-10-12T14:17:41Z",
    "title_canon_sha256": "f85ae5a1c578734d3f60cfd412bd04a1e143d84f77bda85567fbaac3ea86d557"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.2166",
    "kind": "arxiv",
    "version": 3
  }
}