Pith Number

pith:R5CQAQF5

pith:2011:R5CQAQF52VUWN3NHSOQZUR2HXO

not attested not anchored not stored refs pending

Some bounds on commutativity degree

M. K. Yadav, R. K. Nath

arxiv:1108.3202 v1 · 2011-08-16 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R5CQAQF52VUWN3NHSOQZUR2HXO}

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	2026-05-18T04:15:27.773147Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f450040bdd56966eda793a19a4747bb9897bc085d5463ec36a5b1dbb939b7ea

Aliases

arxiv: 1108.3202 · arxiv_version: 1108.3202v1 · doi: 10.48550/arxiv.1108.3202 · pith_short_12: R5CQAQF52VUW · pith_short_16: R5CQAQF52VUWN3NH · pith_short_8: R5CQAQF5

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/R5CQAQF52VUWN3NHSOQZUR2HXO \
  | 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: 8f450040bdd56966eda793a19a4747bb9897bc085d5463ec36a5b1dbb939b7ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed325c27e3f5f9e6bc7fd587451ccc357b82f7ed83fb1fcd1c40d9dbc160d4bc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-08-16T10:41:34Z",
    "title_canon_sha256": "cac73bb2786d927e1e80c4bd9856f5a6f9a5c8ab5d8ca5445fd5a7af8fc08c5f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.3202",
    "kind": "arxiv",
    "version": 1
  }
}