Pith Number

pith:2XWWDI37

pith:2010:2XWWDI37AF6RX2KFQFYHNNM5ZW

not attested not anchored not stored refs pending

An Asymptotic Faber-Krahn Inequality for the Combinatorial Laplacian on Z^2

Yakov Shlapentokh-Rothman

arxiv:1008.4092 v1 · 2010-08-24 · math.SP · 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{2XWWDI37AF6RX2KFQFYHNNM5ZW}

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	2026-05-18T04:41:54.167601Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5ed61a37f017d1be945817076b59dcd91b74ca2a0cf2573cf80eae9d19ce058

Aliases

arxiv: 1008.4092 · arxiv_version: 1008.4092v1 · doi: 10.48550/arxiv.1008.4092 · pith_short_12: 2XWWDI37AF6R · pith_short_16: 2XWWDI37AF6RX2KF · pith_short_8: 2XWWDI37

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/2XWWDI37AF6RX2KFQFYHNNM5ZW \
  | 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: d5ed61a37f017d1be945817076b59dcd91b74ca2a0cf2573cf80eae9d19ce058

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "56bd1044c96be03e5b32ac7e493c98b036abd197a21a193a611ce5f4e01cd248",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-08-24T17:29:16Z",
    "title_canon_sha256": "bf2f646eb5600ae18a7a049a1c05bdc0075dda7d59cfc1269550eea9050f1586"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.4092",
    "kind": "arxiv",
    "version": 1
  }
}