Pith Number

pith:XCMLNUAP

pith:2012:XCMLNUAP23TRR7ACO5TJCEKQEV

not attested not anchored not stored refs pending

Sharp L^p bounds on spectral clusters for Lipschitz metrics

Daniel Tataru, Hart Smith, Herbert Koch

arxiv:1207.2417 v1 · 2012-07-10 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XCMLNUAP23TRR7ACO5TJCEKQEV}

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	2026-05-18T03:51:24.196360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b898b6d00fd6e718fc027766911150254caa8242fbbf22dc9a36377a8440fbae

Aliases

arxiv: 1207.2417 · arxiv_version: 1207.2417v1 · doi: 10.48550/arxiv.1207.2417 · pith_short_12: XCMLNUAP23TR · pith_short_16: XCMLNUAP23TRR7AC · pith_short_8: XCMLNUAP

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/XCMLNUAP23TRR7ACO5TJCEKQEV \
  | 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: b898b6d00fd6e718fc027766911150254caa8242fbbf22dc9a36377a8440fbae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a50bd99019285703f856fcbf2ef7e2e6bce8552f74165469daf908bf9c747d83",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-07-10T17:22:01Z",
    "title_canon_sha256": "523e12ff78c32cae3daca002dab44f7ff5a241af330c476a0b6a81deec146c15"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.2417",
    "kind": "arxiv",
    "version": 1
  }
}