Pith Number

pith:3YZ4KKRQ

pith:2013:3YZ4KKRQXUSVTUBBFVVDICX3WY

not attested not anchored not stored refs pending

On paratopological groups

Chuan Liu, Fucai Lin

arxiv:1302.4190 v1 · 2013-02-18 · math.GN · 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{3YZ4KKRQXUSVTUBBFVVDICX3WY}

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	2026-05-18T03:33:23.828297Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de33c52a30bd2559d0212d6a340afbb63ec9ad75069fc627c23401f82ac054e0

Aliases

arxiv: 1302.4190 · arxiv_version: 1302.4190v1 · doi: 10.48550/arxiv.1302.4190 · pith_short_12: 3YZ4KKRQXUSV · pith_short_16: 3YZ4KKRQXUSVTUBB · pith_short_8: 3YZ4KKRQ

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/3YZ4KKRQXUSVTUBBFVVDICX3WY \
  | 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: de33c52a30bd2559d0212d6a340afbb63ec9ad75069fc627c23401f82ac054e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "11952ebb5a153b123bb8b1b52281c8be98dd582a5c40fc34e7db14838b9f2492",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2013-02-18T09:12:21Z",
    "title_canon_sha256": "85458ea06569b1b6721614aa2a12fd58d65793e742a49a14eb2bcf1a8aa8c7ae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4190",
    "kind": "arxiv",
    "version": 1
  }
}