Pith Number

pith:SOPAEXZG

pith:2014:SOPAEXZGR5OVXP3XLXN4C2CL6V

not attested not anchored not stored refs pending

On finite groups all of whose cubic Cayley graphs are integral

Kaishun Wang, Xuanlong Ma

arxiv:1409.4939 v4 · 2014-09-17 · 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{SOPAEXZGR5OVXP3XLXN4C2CL6V}

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	2026-05-18T01:46:14.056620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

939e025f268f5d5bbf775ddbc1684bf55587c0bac8fc0b62fb678833867f517b

Aliases

arxiv: 1409.4939 · arxiv_version: 1409.4939v4 · doi: 10.48550/arxiv.1409.4939 · pith_short_12: SOPAEXZGR5OV · pith_short_16: SOPAEXZGR5OVXP3X · pith_short_8: SOPAEXZG

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/SOPAEXZGR5OVXP3XLXN4C2CL6V \
  | 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: 939e025f268f5d5bbf775ddbc1684bf55587c0bac8fc0b62fb678833867f517b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "252927961b03382c66b59325a798278697f48b1b1c6d5c4abd05a21e1f482e8f",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2014-09-17T10:41:15Z",
    "title_canon_sha256": "39b0636f20c06dacee0932ea7146965469bafeb3b8f75d94534a47a7e475fdec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.4939",
    "kind": "arxiv",
    "version": 4
  }
}