Pith Number

pith:F6F57QZQ

pith:2015:F6F57QZQJQKCQRMFSFDOFQMZS3

not attested not anchored not stored refs pending

Embeddability and universal theory of partially commutative groups

Montserrat Casals-Ruiz

arxiv:1506.03261 v1 · 2015-06-10 · 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{F6F57QZQJQKCQRMFSFDOFQMZS3}

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	2026-05-18T01:55:31.117997Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f8bdfc3304c142845859146e2c19996cbfbbed7089d52e9858bb503abe06406

Aliases

arxiv: 1506.03261 · arxiv_version: 1506.03261v1 · doi: 10.48550/arxiv.1506.03261 · pith_short_12: F6F57QZQJQKC · pith_short_16: F6F57QZQJQKCQRMF · pith_short_8: F6F57QZQ

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/F6F57QZQJQKCQRMFSFDOFQMZS3 \
  | 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: 2f8bdfc3304c142845859146e2c19996cbfbbed7089d52e9858bb503abe06406

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d37b447550f7f86c09d3416c202384ab3dc45bdc3123207185326651fb90e40",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-06-10T11:37:44Z",
    "title_canon_sha256": "57fd68d624fee3b3e1b8e33832698059fa49d62461092b5ee977076d6e637f1b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.03261",
    "kind": "arxiv",
    "version": 1
  }
}