Pith Number

pith:NJL444EV

pith:2011:NJL444EVUQCOINEST5CL2U6C5U

not attested not anchored not stored refs pending

Disconnected Julia sets and gaps in the spectrum of Laplacians on symmetric finitely ramified fractals

Alexander Teplyaev, Benjamin Steinhurst, Denglin Zhou, Katheryn Hare

arxiv:1105.1747 v2 · 2011-05-09 · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NJL444EVUQCOINEST5CL2U6C5U}

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	2026-05-18T00:12:11.867909Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a57ce7095a404e434929f44bd53c2ed327503a3adac789d4dc9e9dd23c2bb82

Aliases

arxiv: 1105.1747 · arxiv_version: 1105.1747v2 · doi: 10.48550/arxiv.1105.1747 · pith_short_12: NJL444EVUQCO · pith_short_16: NJL444EVUQCOINES · pith_short_8: NJL444EV

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/NJL444EVUQCOINEST5CL2U6C5U \
  | 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: 6a57ce7095a404e434929f44bd53c2ed327503a3adac789d4dc9e9dd23c2bb82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d9065980c73a2b23cf1fad7b4597c117e3dfc372cfb71205c51f9e97414898c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-05-09T18:11:16Z",
    "title_canon_sha256": "2c1b8d75e50f83579703bc92c619deb9aa910238c6b839a81406f22858189c8b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.1747",
    "kind": "arxiv",
    "version": 2
  }
}