Pith Number

pith:D3KHGVOR

pith:2024:D3KHGVORCJZHDOGMH2WGCZ5DRC

not attested not anchored not stored refs pending

Extremal values for the square energies of graphs

Shengtong Zhang

arxiv:2409.15504 v2 · 2024-09-23 · math.CO · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D3KHGVORCJZHDOGMH2WGCZ5DRC}

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.

Cited by

6 papers in Pith

Path-Minimality of $p$-Energy for Connected Graphs

Path-Minimality for Positive $p$-Energies, Laplacian-Type Spectra, and Line Graphs

Path-Minimality of $p$-Energy for Connected Graphs

A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs

Path-Minimality of $p$-Energy for Connected Graphs

Receipt and verification

First computed	2026-07-05T09:11:48.562680Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1ed47355d1127271b8cc3eac6167a3888cd7259ce9e20bc13ab667e48b171c1d

Aliases

arxiv: 2409.15504 · arxiv_version: 2409.15504v2 · doi: 10.48550/arxiv.2409.15504 · pith_short_12: D3KHGVORCJZH · pith_short_16: D3KHGVORCJZHDOGM · pith_short_8: D3KHGVOR

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/D3KHGVORCJZHDOGMH2WGCZ5DRC \
  | 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: 1ed47355d1127271b8cc3eac6167a3888cd7259ce9e20bc13ab667e48b171c1d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea6921b72b7927c104ae2b0a4094d1270a4798f90aa9805091c15a3f8a771a0f",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-09-23T19:48:53Z",
    "title_canon_sha256": "b06123691d66950310c17c8db4efd2885635a3d995c85948e91f1cf6e3383bb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.15504",
    "kind": "arxiv",
    "version": 2
  }
}