Pith Number

pith:3FZHYKDN

pith:2020:3FZHYKDNRAIJWU4YDCK5ZH7XVZ

not attested not anchored not stored refs pending

On graphs with some normalized Laplacian eigenvalue of extremal multiplicity

Fenglei Tian, Junqing Cai, Xuntuan Su, Zuosong Liang

arxiv:2007.11844 v1 · 2020-07-23 · 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{3FZHYKDNRAIJWU4YDCK5ZH7XVZ}

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	2026-07-05T01:21:40.989472Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9727c286d88109b53981895dc9ff7ae68e440dd26385114af9fbf28ad91dd6f

Aliases

arxiv: 2007.11844 · arxiv_version: 2007.11844v1 · doi: 10.48550/arxiv.2007.11844 · pith_short_12: 3FZHYKDNRAIJ · pith_short_16: 3FZHYKDNRAIJWU4Y · pith_short_8: 3FZHYKDN

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/3FZHYKDNRAIJWU4YDCK5ZH7XVZ \
  | 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: d9727c286d88109b53981895dc9ff7ae68e440dd26385114af9fbf28ad91dd6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce2e8a84161381449a85edb4e522d2d47cd2d173683cca80f5ad22cd85e1f586",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2020-07-23T08:16:16Z",
    "title_canon_sha256": "0fee4397d11436a7132161a09f7dac630a9f901a5d974777d1aa823563cbcc97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2007.11844",
    "kind": "arxiv",
    "version": 1
  }
}