Pith Number

pith:JDE4NRK3

pith:2015:JDE4NRK35VC3DKASLVHDLORCJV

not attested not anchored not stored refs pending

Cacti with maximum Kirchhoff index

Wen-Rui Wang, Xiang-Feng Pan

arxiv:1511.03080 v1 · 2015-11-10 · 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{JDE4NRK35VC3DKASLVHDLORCJV}

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	2026-05-18T01:27:17.062038Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48c9c6c55bed45b1a8125d4e35ba224d56a3ffafd8e115b79deff11dc406384f

Aliases

arxiv: 1511.03080 · arxiv_version: 1511.03080v1 · doi: 10.48550/arxiv.1511.03080 · pith_short_12: JDE4NRK35VC3 · pith_short_16: JDE4NRK35VC3DKAS · pith_short_8: JDE4NRK3

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/JDE4NRK35VC3DKASLVHDLORCJV \
  | 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: 48c9c6c55bed45b1a8125d4e35ba224d56a3ffafd8e115b79deff11dc406384f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "60b443ae7631d4d1c6670ca9f12ddce05fa393634fe568f418f20eb3653bbef7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-11-10T12:18:05Z",
    "title_canon_sha256": "31b72a84d853922d21e440a8483847663bd404b7a0a7aef6eda191fffa77b9a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.03080",
    "kind": "arxiv",
    "version": 1
  }
}