Pith Number

pith:LW77ZUSP

pith:2019:LW77ZUSPZ4BNPHUDA7X4WTRWAL

not attested not anchored not stored refs pending

Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups

Enric Ventura, Mallika Roy

arxiv:1906.02144 v1 · 2019-06-05 · 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{LW77ZUSPZ4BNPHUDA7X4WTRWAL}

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	2026-05-17T23:44:05.157799Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5dbffcd24fcf02d79e8307efcb4e3602d3e9e9f9981488ebfd85a150fd0b4e20

Aliases

arxiv: 1906.02144 · arxiv_version: 1906.02144v1 · doi: 10.48550/arxiv.1906.02144 · pith_short_12: LW77ZUSPZ4BN · pith_short_16: LW77ZUSPZ4BNPHUD · pith_short_8: LW77ZUSP

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/LW77ZUSPZ4BNPHUDA7X4WTRWAL \
  | 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: 5dbffcd24fcf02d79e8307efcb4e3602d3e9e9f9981488ebfd85a150fd0b4e20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bf62d8cb009c4aaa08be25f81fa594f4c2c7d2f002b16990ce03c370186fe6a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-06-05T17:03:32Z",
    "title_canon_sha256": "264e3367bdf078b991ea23a539440ddb2c83f782bc96621996cd3d47b13f5c93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.02144",
    "kind": "arxiv",
    "version": 1
  }
}