Pith Number

pith:XL2ADR2Q

pith:2013:XL2ADR2QC4WXCIRHQGHS2DYF6K

not attested not anchored not stored refs pending

On $L^p$ resolvent estimates for elliptic operators on compact manifolds

Gunther Uhlmann, Katsiaryna Krupchyk

arxiv:1304.0048 v1 · 2013-03-30 · math.AP · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XL2ADR2QC4WXCIRHQGHS2DYF6K}

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	2026-05-18T03:29:26.216414Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

baf401c750172d712227818f2d0f05f2960b4b4e88b52011e55897d638d24afb

Aliases

arxiv: 1304.0048 · arxiv_version: 1304.0048v1 · doi: 10.48550/arxiv.1304.0048 · pith_short_12: XL2ADR2QC4WX · pith_short_16: XL2ADR2QC4WXCIRH · pith_short_8: XL2ADR2Q

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/XL2ADR2QC4WXCIRHQGHS2DYF6K \
  | 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: baf401c750172d712227818f2d0f05f2960b4b4e88b52011e55897d638d24afb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4cc11598bc91407606cd185f1146bafdba6256857f0e1938b6c2696a5b838a4",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-03-30T00:00:19Z",
    "title_canon_sha256": "eb10fece26fba064074b8904fe4ca3d3b363196f53794dbc11be61d7094c4ff4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.0048",
    "kind": "arxiv",
    "version": 1
  }
}