Pith Number

pith:TKUL2NC7

pith:2010:TKUL2NC7CSEZJHR3AOR6TUSLY4

not attested not anchored not stored refs pending

Sharp spectral estimates in domains of infinite volume

Leander Geisinger, Timo Weidl

arxiv:1012.5972 v1 · 2010-12-29 · math.SP · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TKUL2NC7CSEZJHR3AOR6TUSLY4}

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	2026-05-18T02:04:16.807521Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9aa8bd345f1489949e3b03a3e9d24bc73eef19848809f6f08a391f459b3e0c76

Aliases

arxiv: 1012.5972 · arxiv_version: 1012.5972v1 · doi: 10.48550/arxiv.1012.5972 · pith_short_12: TKUL2NC7CSEZ · pith_short_16: TKUL2NC7CSEZJHR3 · pith_short_8: TKUL2NC7

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/TKUL2NC7CSEZJHR3AOR6TUSLY4 \
  | 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: 9aa8bd345f1489949e3b03a3e9d24bc73eef19848809f6f08a391f459b3e0c76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "269058cc53ed0ef94bcf731a22dd115fc2a335e2c3079a183218652efbd495cf",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2010-12-29T16:30:05Z",
    "title_canon_sha256": "4c0ddeac8b5ca346fddef208b2b372f99caeecd555b4331c20ba83d9ff0bd7e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.5972",
    "kind": "arxiv",
    "version": 1
  }
}