Pith Number

pith:QSW2HJ4S

pith:2013:QSW2HJ4SSAWXQPPFQLLINWCC4P

not attested not anchored not stored refs pending

The obstruction to the existence of a loopless star product

Thomas Willwacher

arxiv:1309.7921 v2 · 2013-09-30 · 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{QSW2HJ4SSAWXQPPFQLLINWCC4P}

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	2026-05-18T02:26:45.626903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84ada3a792902d783de582d686d842e3cd0d106a9aa2b380cf1e2064b47c082c

Aliases

arxiv: 1309.7921 · arxiv_version: 1309.7921v2 · doi: 10.48550/arxiv.1309.7921 · pith_short_12: QSW2HJ4SSAWX · pith_short_16: QSW2HJ4SSAWXQPPF · pith_short_8: QSW2HJ4S

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/QSW2HJ4SSAWXQPPFQLLINWCC4P \
  | 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: 84ada3a792902d783de582d686d842e3cd0d106a9aa2b380cf1e2064b47c082c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d2ca8d03db78bf77d827b9968ef34aff9baa486f07d2c0305e6f28104eb496a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2013-09-30T17:05:10Z",
    "title_canon_sha256": "0805b0a3457f064924ebb7541cf36ddc4fc35f4564ddfe9be566ce832417526d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.7921",
    "kind": "arxiv",
    "version": 2
  }
}