Pith Number

pith:N3M3MYEA

pith:2015:N3M3MYEAK23D6XFPVMIEMYQ6KO

not attested not anchored not stored refs pending

On compact bicrossed products

Issan Patri, Kunal Mukherjee, Pierre Fima

arxiv:1504.00092 v3 · 2015-04-01 · math.OA · 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{N3M3MYEAK23D6XFPVMIEMYQ6KO}

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	2026-05-18T00:20:32.644126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ed9b6608056b63f5cafab1046621e53ae32c9ea7e1857bf1d2bab33ee104906

Aliases

arxiv: 1504.00092 · arxiv_version: 1504.00092v3 · doi: 10.48550/arxiv.1504.00092 · pith_short_12: N3M3MYEAK23D · pith_short_16: N3M3MYEAK23D6XFP · pith_short_8: N3M3MYEA

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/N3M3MYEAK23D6XFPVMIEMYQ6KO \
  | 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: 6ed9b6608056b63f5cafab1046621e53ae32c9ea7e1857bf1d2bab33ee104906

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c58615c328ff74634a8956ca608cc1e3b4aa42fceaac4bb300bff4abe3e6ddc",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2015-04-01T03:02:12Z",
    "title_canon_sha256": "bd4e59eeededd35ca38d47a8e8d38406e08e6663fbcae86f8fadb3a89f1e9942"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.00092",
    "kind": "arxiv",
    "version": 3
  }
}