Pith Number

pith:UENBTMJ6

pith:2024:UENBTMJ662IKU2B7UV27O5X4Q4

not attested not anchored not stored refs pending

Exploring Graphs with Distinct $M$-Eigenvalues: Product Operation, Wronskian Vertices, and Controllability

Haiying Shan, Xiaoqi Liu

arxiv:2412.18759 v1 · 2024-12-25 · 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{UENBTMJ662IKU2B7UV27O5X4Q4}

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	2026-07-05T09:54:10.265032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a11a19b13ef690aa683fa575f776fc87292303f75142fbd0b029800ed1239ede

Aliases

arxiv: 2412.18759 · arxiv_version: 2412.18759v1 · doi: 10.48550/arxiv.2412.18759 · pith_short_12: UENBTMJ662IK · pith_short_16: UENBTMJ662IKU2B7 · pith_short_8: UENBTMJ6

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/UENBTMJ662IKU2B7UV27O5X4Q4 \
  | 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: a11a19b13ef690aa683fa575f776fc87292303f75142fbd0b029800ed1239ede

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96a37d5757e39e0c51de2d2a96ca1c012e57348d2a42823402c113f13f9ef69e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-12-25T03:10:00Z",
    "title_canon_sha256": "1b629c7b7800e565901a57a030ae435df3a8058ba8951eedd720913f88f5c71a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.18759",
    "kind": "arxiv",
    "version": 1
  }
}