Pith Number

pith:Q2J4RMRL

pith:2011:Q2J4RMRLRH6R36RCJBYMXYK2AN

not attested not anchored not stored refs pending

On the extremal energy of integral weighted trees

Chang-Qing Xu, Guang-Hui Xu, Jia-Yu Shao, Richard A. Brualdi, Shi-Cai Gong

arxiv:1106.5940 v1 · 2011-06-29 · 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{Q2J4RMRLRH6R36RCJBYMXYK2AN}

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	2026-05-18T04:19:04.853168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8693c8b22b89fd1dfa224870cbe15a0379f2fa5faec178e1aeb70761c928a9e8

Aliases

arxiv: 1106.5940 · arxiv_version: 1106.5940v1 · doi: 10.48550/arxiv.1106.5940 · pith_short_12: Q2J4RMRLRH6R · pith_short_16: Q2J4RMRLRH6R36RC · pith_short_8: Q2J4RMRL

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/Q2J4RMRLRH6R36RCJBYMXYK2AN \
  | 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: 8693c8b22b89fd1dfa224870cbe15a0379f2fa5faec178e1aeb70761c928a9e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd151f1c3b3aa4f4a18851df549aa528156259e2993d76e879f7dd2f3b98ee0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-06-29T14:06:16Z",
    "title_canon_sha256": "20e5238536805ec393ed9c8d16887c188c5c711c993452ccd476d74e3c0594b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.5940",
    "kind": "arxiv",
    "version": 1
  }
}