Pith Number

pith:7AKIX47O

pith:2023:7AKIX47OJGU4OWY7LN5RHT6MLG

not attested not anchored not stored refs pending

Associativity certificates for Kontsevich's star-product $\star$ mod $\bar{o}(\hbar^k)$: $k\leqslant 6$ unlike $k\geqslant7$

Arthemy V. Kiselev, Ricardo Buring

arxiv:2309.16664 v2 · 2023-09-28 · math.QA · math-ph · math.CO · math.MP · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7AKIX47OJGU4OWY7LN5RHT6MLG}

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	2026-07-05T07:33:20.068786Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8148bf3ee49a9c75b1f5b7b13cfcc599900641b4e42d19c219bf9aa9c289069

Aliases

arxiv: 2309.16664 · arxiv_version: 2309.16664v2 · doi: 10.48550/arxiv.2309.16664 · pith_short_12: 7AKIX47OJGU4 · pith_short_16: 7AKIX47OJGU4OWY7 · pith_short_8: 7AKIX47O

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/7AKIX47OJGU4OWY7LN5RHT6MLG \
  | 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: f8148bf3ee49a9c75b1f5b7b13cfcc599900641b4e42d19c219bf9aa9c289069

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84461e8942cdd7da9a4247834adede033b7fbea2977f84993646544edbd2bbc4",
    "cross_cats_sorted": [
      "math-ph",
      "math.CO",
      "math.MP",
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2023-09-28T17:58:37Z",
    "title_canon_sha256": "4303273753d2fd73392aecb9c71bc39d9e660571d985ec2a2ec1e0605327e6cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2309.16664",
    "kind": "arxiv",
    "version": 2
  }
}