Pith Number

pith:XO2LAWBE

pith:2016:XO2LAWBEAU35ZDSKTTRZ3VISSI

not attested not anchored not stored refs pending

The $k_{R}$-property of free Abelian topological groups and products of sequential fans

Chuan Liu, Fucai Lin, Shou Lin

arxiv:1610.02522 v6 · 2016-10-08 · math.GN · math.FA · 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{XO2LAWBEAU35ZDSKTTRZ3VISSI}

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	2026-05-18T00:29:39.506536Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbb4b058240537dc8e4a9ce39dd5129223985834de57e89f3e82292be2de4c96

Aliases

arxiv: 1610.02522 · arxiv_version: 1610.02522v6 · doi: 10.48550/arxiv.1610.02522 · pith_short_12: XO2LAWBEAU35 · pith_short_16: XO2LAWBEAU35ZDSK · pith_short_8: XO2LAWBE

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/XO2LAWBEAU35ZDSKTTRZ3VISSI \
  | 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: bbb4b058240537dc8e4a9ce39dd5129223985834de57e89f3e82292be2de4c96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "649239f8913782915a7dfcd1e03197b70aea1b9b39fd7b9605527a848b64a4ce",
    "cross_cats_sorted": [
      "math.FA",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GN",
    "submitted_at": "2016-10-08T12:57:48Z",
    "title_canon_sha256": "a9526f10480298c665f4894c51affa75f940384cf60ea279b996800901d5bdd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.02522",
    "kind": "arxiv",
    "version": 6
  }
}