Pith Number

pith:BERNG6ZK

pith:2010:BERNG6ZK47AP7IZ43BXCOAWUFI

not attested not anchored not stored refs pending

Hopf algebras and homotopy invariants

Jelena Grbic, Victor Buchstaber

arxiv:1011.2549 v3 · 2010-11-11 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BERNG6ZK47AP7IZ43BXCOAWUFI}

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	2026-05-18T03:40:14.622607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0922d37b2ae7c0ffa33cd86e2702d42a168e264394469c882802e49def1b82cf

Aliases

arxiv: 1011.2549 · arxiv_version: 1011.2549v3 · doi: 10.48550/arxiv.1011.2549 · pith_short_12: BERNG6ZK47AP · pith_short_16: BERNG6ZK47AP7IZ4 · pith_short_8: BERNG6ZK

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/BERNG6ZK47AP7IZ43BXCOAWUFI \
  | 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: 0922d37b2ae7c0ffa33cd86e2702d42a168e264394469c882802e49def1b82cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6db3b7e8fb43bf5ddd1ea733b95100bc0f861a12cae9d400371aa86c4089064c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2010-11-11T03:21:21Z",
    "title_canon_sha256": "29b107b21b9648bf00f8ddf5bddad5bd160db148fe9c247eb54d4c58798141bc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2549",
    "kind": "arxiv",
    "version": 3
  }
}