Pith Number

pith:3UG3BBED

pith:2021:3UG3BBEDN4GHR7F2RT5YMTWLSZ

not attested not anchored not stored refs pending

On the spectral radius of unicyclic and bicyclic graphs with a fixed diameter

F.F. Wang, H.Y. Shan, Y.Y. Zhai

arxiv:2106.09238 v1 · 2021-06-17 · 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{3UG3BBEDN4GHR7F2RT5YMTWLSZ}

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	2026-07-05T02:50:13.994077Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd0db084836f0c78fcba8cfb864ecb965fcb5d7d8a720579274fa8c02171f300

Aliases

arxiv: 2106.09238 · arxiv_version: 2106.09238v1 · doi: 10.48550/arxiv.2106.09238 · pith_short_12: 3UG3BBEDN4GH · pith_short_16: 3UG3BBEDN4GHR7F2 · pith_short_8: 3UG3BBED

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/3UG3BBEDN4GHR7F2RT5YMTWLSZ \
  | 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: dd0db084836f0c78fcba8cfb864ecb965fcb5d7d8a720579274fa8c02171f300

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca07091f2f3de71e9af35d12211cf166b17d01bdcde0835747cc3d7c9c48edc6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-06-17T04:11:27Z",
    "title_canon_sha256": "7e72e720e57a02397311f733a0e52f747f94cfe2887d8b9947ede2c000970708"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.09238",
    "kind": "arxiv",
    "version": 1
  }
}