Pith Number

pith:QULP262M

pith:2014:QULP262MO5FBCV24YOKCJAWAAE

not attested not anchored not stored refs pending

Monotonicity properties of certain Laplacian eigenvectors associated with trees

Ravindra B. Bapat

arxiv:1411.0210 v1 · 2014-11-02 · 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{QULP262MO5FBCV24YOKCJAWAAE}

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	2026-05-18T02:38:52.266456Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8516fd7b4c774a11575cc3942482c0013c50878cb1a24de9e407eff16e5514a8

Aliases

arxiv: 1411.0210 · arxiv_version: 1411.0210v1 · doi: 10.48550/arxiv.1411.0210 · pith_short_12: QULP262MO5FB · pith_short_16: QULP262MO5FBCV24 · pith_short_8: QULP262M

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/QULP262MO5FBCV24YOKCJAWAAE \
  | 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: 8516fd7b4c774a11575cc3942482c0013c50878cb1a24de9e407eff16e5514a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4a0ea87d5c4b460e28e3036fa1e4b729b36fde4b46b754ed6118056c9c7992a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-11-02T06:41:07Z",
    "title_canon_sha256": "f916005e61cf7bbe0541627c10fa6553a9ec0b81c83598528a70fc006ac37537"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.0210",
    "kind": "arxiv",
    "version": 1
  }
}