Pith Number

pith:BFEY2E2I

pith:2015:BFEY2E2IIXIKPC5TCPBAIUTWAL

not attested not anchored not stored refs pending

Proof of a conjecture on `plateaux' phenomenon of graph Laplacian eigenvalues

Ebrahim Ghorbani

arxiv:1510.05117 v3 · 2015-10-17 · 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{BFEY2E2IIXIKPC5TCPBAIUTWAL}

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	2026-05-18T01:17:32.829626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09498d134845d0a78bb313c204527602c3e07579a64e1dd36ebe4361a5087b0c

Aliases

arxiv: 1510.05117 · arxiv_version: 1510.05117v3 · doi: 10.48550/arxiv.1510.05117 · pith_short_12: BFEY2E2IIXIK · pith_short_16: BFEY2E2IIXIKPC5T · pith_short_8: BFEY2E2I

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/BFEY2E2IIXIKPC5TCPBAIUTWAL \
  | 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: 09498d134845d0a78bb313c204527602c3e07579a64e1dd36ebe4361a5087b0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7124bed7777e610947fa3bacc48d87ec881e4711315fa92195a5a6acc81a6a04",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-10-17T11:32:24Z",
    "title_canon_sha256": "705dda62bfc28e9f0a0db87d8f8ee5fcf09093c6e31fd81e729f64b758dedffe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.05117",
    "kind": "arxiv",
    "version": 3
  }
}