Pith Number

pith:3BVUA5VB

pith:2018:3BVUA5VBD5SY6JIHGJ4N6RCORX

not attested not anchored not stored refs pending

Maximizing spectral radius and number of spanning trees in bipartite graphs

Ravindra Bapat

arxiv:1809.10342 v1 · 2018-09-27 · 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{3BVUA5VBD5SY6JIHGJ4N6RCORX}

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	2026-05-18T00:04:38.574180Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d86b4076a11f658f25073278df444e8dd281fe52399fb36e64dd3093fa26176a

Aliases

arxiv: 1809.10342 · arxiv_version: 1809.10342v1 · doi: 10.48550/arxiv.1809.10342 · pith_short_12: 3BVUA5VBD5SY · pith_short_16: 3BVUA5VBD5SY6JIH · pith_short_8: 3BVUA5VB

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/3BVUA5VBD5SY6JIHGJ4N6RCORX \
  | 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: d86b4076a11f658f25073278df444e8dd281fe52399fb36e64dd3093fa26176a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "297f0f9d390f066c594b83b7839b4b8d61fe82520e8097d2b4baf94b5aeb138d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-09-27T04:54:15Z",
    "title_canon_sha256": "98e43d61fec75e5f86e2e17c16623f94378db312faeaed89aa8ce7ac20be7ae8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.10342",
    "kind": "arxiv",
    "version": 1
  }
}