Pith Number

pith:MHPMR3CI

pith:2019:MHPMR3CISDLO6O4FVISBFJOH3E

not attested not anchored not stored refs pending

Split Hopf algebras, quasi-shuffle algebras, and the cohomology of Omega Sigma X

Nicholas J. Kuhn

arxiv:1907.04411 v1 · 2019-07-09 · math.RA · math.AT · 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{MHPMR3CISDLO6O4FVISBFJOH3E}

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	2026-05-17T23:41:01.828938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61dec8ec4890d6ef3b85aa2412a5c7d9229e94b2ebe69ded90e7d83b06ff0140

Aliases

arxiv: 1907.04411 · arxiv_version: 1907.04411v1 · doi: 10.48550/arxiv.1907.04411 · pith_short_12: MHPMR3CISDLO · pith_short_16: MHPMR3CISDLO6O4F · pith_short_8: MHPMR3CI

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/MHPMR3CISDLO6O4FVISBFJOH3E \
  | 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: 61dec8ec4890d6ef3b85aa2412a5c7d9229e94b2ebe69ded90e7d83b06ff0140

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70b521a00794b0629d2231d5bdd759d4020843c1c3dc7c3c021eee82d698ee5d",
    "cross_cats_sorted": [
      "math.AT",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2019-07-09T20:57:09Z",
    "title_canon_sha256": "ad9e0b04fb033a44970a8c14a81bc93f5c138cf40786d7344c1c42cd01ba7824"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.04411",
    "kind": "arxiv",
    "version": 1
  }
}