Pith Number

pith:LI5TA75X

pith:2016:LI5TA75XEAY2UJIPDL6XRCKF5G

not attested not anchored not stored refs pending

The $k$-spaces property of free Abelian topological groups over non-metrizable La\v{s}nev spaces

Chuan Liu, Fucai Lin

arxiv:1604.04969 v1 · 2016-04-18 · 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{LI5TA75XEAY2UJIPDL6XRCKF5G}

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	2026-05-18T01:16:56.175533Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a3b307fb72031aa250f1afd788945e9af1f3d09a65bf2d994dd816878a9a327

Aliases

arxiv: 1604.04969 · arxiv_version: 1604.04969v1 · doi: 10.48550/arxiv.1604.04969 · pith_short_12: LI5TA75XEAY2 · pith_short_16: LI5TA75XEAY2UJIP · pith_short_8: LI5TA75X

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/LI5TA75XEAY2UJIPDL6XRCKF5G \
  | 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: 5a3b307fb72031aa250f1afd788945e9af1f3d09a65bf2d994dd816878a9a327

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dfd3fc17652bd311ce579f7b415c43b83a56314a6b9f2640f027132f7561e3f3",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2016-04-18T03:12:22Z",
    "title_canon_sha256": "d744a9270b34880ca1fad1c56ec43a795dc2c1773abeeca57e57e5d3c7db7571"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.04969",
    "kind": "arxiv",
    "version": 1
  }
}