Pith Number

pith:LSXVOUNS

pith:2005:LSXVOUNS56OCZRZ7FA5W2V2L6Y

not attested not anchored not stored refs pending

Finite covers of groups by cosets or subgroups

Zhi-Wei Sun

arxiv:math/0501451 v4 · 2005-01-25 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LSXVOUNS56OCZRZ7FA5W2V2L6Y}

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	2026-07-04T14:50:10.191799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5caf5751b2ef9c2cc73f283b6d574bf60823fab2d073eb71901a6c0885ff6e22

Aliases

arxiv: math/0501451 · arxiv_version: math/0501451v4 · doi: 10.48550/arxiv.math/0501451 · pith_short_12: LSXVOUNS56OC · pith_short_16: LSXVOUNS56OCZRZ7 · pith_short_8: LSXVOUNS

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/LSXVOUNS56OCZRZ7FA5W2V2L6Y \
  | 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: 5caf5751b2ef9c2cc73f283b6d574bf60823fab2d073eb71901a6c0885ff6e22

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a7dfd73d8ec8d00dc68f9ffb47bcf4ceeb49751089fbff7326dfb8043a9d165",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2005-01-25T15:54:18Z",
    "title_canon_sha256": "4b184055050aed1f8636d07041070a024cbbd6e539a7dd111e83aae8899c4fa2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0501451",
    "kind": "arxiv",
    "version": 4
  }
}