Pith Number

pith:GVFLIPGL

pith:2015:GVFLIPGLYFI3LNTF4QG3TQY65G

not attested not anchored not stored refs pending

Explicit constructions of loops with commuting inner mappings

Ale\v{s} Dr\'apal, Petr Vojt\v{e}chovsk\'y

arxiv:1509.05706 v1 · 2015-09-18 · 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{GVFLIPGLYFI3LNTF4QG3TQY65G}

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	2026-05-18T01:32:42.558642Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

354ab43ccbc151b5b665e40db9c31ee9b957709999ba687c92a3bc15df950723

Aliases

arxiv: 1509.05706 · arxiv_version: 1509.05706v1 · doi: 10.48550/arxiv.1509.05706 · pith_short_12: GVFLIPGLYFI3 · pith_short_16: GVFLIPGLYFI3LNTF · pith_short_8: GVFLIPGL

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/GVFLIPGLYFI3LNTF4QG3TQY65G \
  | 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: 354ab43ccbc151b5b665e40db9c31ee9b957709999ba687c92a3bc15df950723

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1de8b3332627dd15713b313b4ed25f40fd99cb36d48890356594f16acba0f1f6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-18T17:05:45Z",
    "title_canon_sha256": "98224893812cdfcedb73078a1584fe879aa571ce7d55dc9df2912fe84034bec0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05706",
    "kind": "arxiv",
    "version": 1
  }
}