Pith Number

pith:2QP3CJ3V

pith:2015:2QP3CJ3VAWGQEPF755SNO7YACI

not attested not anchored not stored refs pending

Two Weak Forms of Countability Axioms in Free Topological Groups

Chuan Liu, Fucai Lin, Jiling Cao

arxiv:1507.04087 v2 · 2015-07-15 · 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{2QP3CJ3VAWGQEPF755SNO7YACI}

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	2026-05-18T01:17:00.619641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d41fb12775058d023cbfef64d77f00120b00f06e8e658db40eea821df3f40131

Aliases

arxiv: 1507.04087 · arxiv_version: 1507.04087v2 · doi: 10.48550/arxiv.1507.04087 · pith_short_12: 2QP3CJ3VAWGQ · pith_short_16: 2QP3CJ3VAWGQEPF7 · pith_short_8: 2QP3CJ3V

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/2QP3CJ3VAWGQEPF755SNO7YACI \
  | 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: d41fb12775058d023cbfef64d77f00120b00f06e8e658db40eea821df3f40131

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a00583f2e3600bb651ec286bf0d8e8d5bf2d82c505bcbc041677245816040130",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-07-15T05:25:26Z",
    "title_canon_sha256": "07655711c28ca4991f08338c2c64928b98df29d2cee7cc0b98276cc84bcae35d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.04087",
    "kind": "arxiv",
    "version": 2
  }
}