Pith Number

pith:2QQ5SJ3M

pith:2015:2QQ5SJ3MHBPH3FQY6ON6VXEMYL

not attested not anchored not stored refs pending

Commutativity preserving extensions of groups

Primoz Moravec, Urban Jezernik

arxiv:1510.01536 v1 · 2015-10-06 · 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{2QQ5SJ3MHBPH3FQY6ON6VXEMYL}

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	2026-05-18T01:30:56.697988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d421d9276c385e7d9618f39beadc8cc2e6b641a7453a99719f8fef867540b67a

Aliases

arxiv: 1510.01536 · arxiv_version: 1510.01536v1 · doi: 10.48550/arxiv.1510.01536 · pith_short_12: 2QQ5SJ3MHBPH · pith_short_16: 2QQ5SJ3MHBPH3FQY · pith_short_8: 2QQ5SJ3M

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/2QQ5SJ3MHBPH3FQY6ON6VXEMYL \
  | 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: d421d9276c385e7d9618f39beadc8cc2e6b641a7453a99719f8fef867540b67a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13557deb0f93493080995e18e9b28a2a5a500ca82fb66fba8712ebe62c94fd67",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-10-06T11:45:43Z",
    "title_canon_sha256": "883eb91f0f1454cf5b7354b44a33c550835388197b6c64c2dd04e6bb0dccecca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01536",
    "kind": "arxiv",
    "version": 1
  }
}