Pith Number

pith:5XMPWAXI

pith:2025:5XMPWAXIT7OFXM3CD7BLXWQZ37

not attested not anchored not stored refs pending

Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration

Adrien Busnot Laurent, Yunhe Sheng, Yunnan Li

arxiv:2512.21971 v1 · 2025-12-26 · math.RA · cs.NA · math.CO · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5XMPWAXIT7OFXM3CD7BLXWQZ37}

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.

Cited by

3 papers in Pith

Post-processed frozen-flow methods for the long time sampling of ergodic dynamics on Riemannian manifolds

Aromatic and clumped multi-indices: algebraic structure and Hopf embeddings

The free tracial post-Lie-Rinehart algebra of planar aromatic trees for the design of divergence-free Lie-group methods

Receipt and verification

First computed	2026-08-10T01:14:03.275303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

edd8fb02e89fdc5bb3621fc2bbda19dfcf9c530bf393f6811dbdf9693dce6998

Aliases

arxiv: 2512.21971 · arxiv_version: 2512.21971v1 · doi: 10.48550/arxiv.2512.21971 · pith_short_12: 5XMPWAXIT7OF · pith_short_16: 5XMPWAXIT7OFXM3C · pith_short_8: 5XMPWAXI

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/5XMPWAXIT7OFXM3CD7BLXWQZ37 \
  | 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: edd8fb02e89fdc5bb3621fc2bbda19dfcf9c530bf393f6811dbdf9693dce6998

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c750d289d214b9427376346ef72143a9245fba15ba42a3abe3ec02b9d981943",
    "cross_cats_sorted": [
      "cs.NA",
      "math.CO",
      "math.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2025-12-26T10:34:24Z",
    "title_canon_sha256": "dfbfeb87939539643d306976d34d4899667b8415b54999ad9bb0bd35cdb2fd75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.21971",
    "kind": "arxiv",
    "version": 1
  }
}