Pith Number

pith:NL4TXACO

pith:2024:NL4TXACOTPQBNV75QM7MNYHER5

not attested not anchored not stored refs pending

A Linear Lower Bound for the Square Energy of Graphs

Bojan Mohar, Hitesh Kumar, Saieed Akbari, Shivaramakrishna Pragada

arxiv:2409.18220 v1 · 2024-09-26 · 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{NL4TXACOTPQBNV75QM7MNYHER5}

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

1 paper in Pith

Refinement of a conjecture on positive square energy of graphs

Receipt and verification

First computed	2026-07-05T09:12:32.859834Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6af93b804e9be016d7fd833ec6e0e48f635169d9bd4c05e913b0fef21fa1b69a

Aliases

arxiv: 2409.18220 · arxiv_version: 2409.18220v1 · doi: 10.48550/arxiv.2409.18220 · pith_short_12: NL4TXACOTPQB · pith_short_16: NL4TXACOTPQBNV75 · pith_short_8: NL4TXACO

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/NL4TXACOTPQBNV75QM7MNYHER5 \
  | 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: 6af93b804e9be016d7fd833ec6e0e48f635169d9bd4c05e913b0fef21fa1b69a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69c1feb2c54360773c43da37a42f6b89ef1fac3566406b78b9ba3a576d71c6c2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-09-26T18:58:48Z",
    "title_canon_sha256": "2cfc78746d99ea2753a45edbcf0f678c1c40825d822b24817aa653ba4b52e061"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.18220",
    "kind": "arxiv",
    "version": 1
  }
}