Pith Number

pith:LRKPRN47

pith:2015:LRKPRN47CXOK42OKCIMV2RLR2S

not attested not anchored not stored refs pending

Graphs in the 3--sphere with maximum symmetry

Bruno Zimmermann, Chao Wang, Shicheng Wang, Yimu Zhang

arxiv:1510.00822 v2 · 2015-10-03 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LRKPRN47CXOK42OKCIMV2RLR2S}

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	2026-05-18T00:32:15.386358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c54f8b79f15dcae69ca12195d4571d4b1e0eae97e0158219ff963cb67d4721d

Aliases

arxiv: 1510.00822 · arxiv_version: 1510.00822v2 · doi: 10.48550/arxiv.1510.00822 · pith_short_12: LRKPRN47CXOK · pith_short_16: LRKPRN47CXOK42OK · pith_short_8: LRKPRN47

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/LRKPRN47CXOK42OKCIMV2RLR2S \
  | 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: 5c54f8b79f15dcae69ca12195d4571d4b1e0eae97e0158219ff963cb67d4721d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdeca9a029f549819cce971b04b81f272c0e9c528a2d1fe1399fc29f7cb730ba",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-10-03T13:47:44Z",
    "title_canon_sha256": "f98cc1308b510675a23b36c0e14ca4dad87c33d5d8e3cd2868f613fa21bb622d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.00822",
    "kind": "arxiv",
    "version": 2
  }
}