Pith Number

pith:WLNOLDTH

pith:2016:WLNOLDTHNN5T7VQ4TLSXF37U6P

not attested not anchored not stored refs pending

Spectral threshold dominance, Brouwer's conjecture and maximality of Laplacian energy

Christoph Helmberg, Vilmar Trevisan

arxiv:1604.07867 v1 · 2016-04-26 · 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{WLNOLDTHNN5T7VQ4TLSXF37U6P}

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	2026-05-18T00:47:21.008066Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2dae58e676b7b3fd61c9ae572eff4f3e2adf6d2ec3d96992213adb6f0fbabed

Aliases

arxiv: 1604.07867 · arxiv_version: 1604.07867v1 · doi: 10.48550/arxiv.1604.07867 · pith_short_12: WLNOLDTHNN5T · pith_short_16: WLNOLDTHNN5T7VQ4 · pith_short_8: WLNOLDTH

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/WLNOLDTHNN5T7VQ4TLSXF37U6P \
  | 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: b2dae58e676b7b3fd61c9ae572eff4f3e2adf6d2ec3d96992213adb6f0fbabed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8e73b99bd60beccd19126220d4e6886060b34e207b4f4334cc4454f80801952",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-04-26T21:43:33Z",
    "title_canon_sha256": "edf68f5dd1e79d57544f33af0c6262239c0634ef18ba22fc01eb4c960fe1fb51"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.07867",
    "kind": "arxiv",
    "version": 1
  }
}