Pith Number

pith:Q4D5V5CC

pith:2016:Q4D5V5CCCOGLHQJL4STRDF7EZ2

not attested not anchored not stored refs pending

The countable type properties in free paratopological groups

Chuan Liu, Fucai Lin, Kexiu Zhang

arxiv:1611.00202 v1 · 2016-11-01 · math.GR · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q4D5V5CCCOGLHQJL4STRDF7EZ2}

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	2026-05-18T01:00:41.272718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8707daf442138cb3c12be4a71197e4ce813856ca4a767655048ba71aa625fb7c

Aliases

arxiv: 1611.00202 · arxiv_version: 1611.00202v1 · doi: 10.48550/arxiv.1611.00202 · pith_short_12: Q4D5V5CCCOGL · pith_short_16: Q4D5V5CCCOGLHQJL · pith_short_8: Q4D5V5CC

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/Q4D5V5CCCOGLHQJL4STRDF7EZ2 \
  | 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: 8707daf442138cb3c12be4a71197e4ce813856ca4a767655048ba71aa625fb7c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7530cab64759e4fda669b0c9dc2a2057b314b907c0c43ff995063dc063e8d2ac",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-11-01T12:47:56Z",
    "title_canon_sha256": "084fa76d052c433a1958b337127a956baedcda28c349d3242938774f4d4c8e30"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.00202",
    "kind": "arxiv",
    "version": 1
  }
}