Pith Number

pith:TPXDZYZM

pith:2011:TPXDZYZMXVLBS4JQBGGSOGLEXG

not attested not anchored not stored refs pending

Nonpositive Eigenvalues of the Adjacency Matrix and Lower Bounds for Laplacian Eigenvalues

Charles R. Johnson, Lee Kennedy-Shaffer, Miriam Farber, Zachary B. Charles

arxiv:1108.4810 v3 · 2011-08-24 · 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{TPXDZYZMXVLBS4JQBGGSOGLEXG}

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	2026-05-18T03:54:49.421225Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9bee3ce32cbd56197130098d271964b98dab418348244522e5c931935a2c3e68

Aliases

arxiv: 1108.4810 · arxiv_version: 1108.4810v3 · doi: 10.48550/arxiv.1108.4810 · pith_short_12: TPXDZYZMXVLB · pith_short_16: TPXDZYZMXVLBS4JQ · pith_short_8: TPXDZYZM

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/TPXDZYZMXVLBS4JQBGGSOGLEXG \
  | 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: 9bee3ce32cbd56197130098d271964b98dab418348244522e5c931935a2c3e68

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43a74a08bc6681f6665f6ef634c7466dbd57692eaf2b7a1e303c1e89d834e246",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-08-24T11:06:55Z",
    "title_canon_sha256": "398e93f771c9f9350027be805702d7d2a719c0af83472738fdcf589c92e69c65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4810",
    "kind": "arxiv",
    "version": 3
  }
}