Pith Number

pith:65U2KONJ

pith:2011:65U2KONJTDRQL4P3KZJRRZ6QTS

not attested not anchored not stored refs pending

A priori estimates for the Helmholtz equation with electromagnetic potentials in exterior domains

Alberto Ruiz, Juan Antonio Barcel\'o, Luca Fanelli, Maricruz Vilela

arxiv:1105.2953 v1 · 2011-05-15 · math.AP · 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{65U2KONJTDRQL4P3KZJRRZ6QTS}

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	2026-05-18T04:22:01.699262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f769a539a998e305f1fb565318e7d09c9a6f7fa4c33fd68f4fcc2de6e9475419

Aliases

arxiv: 1105.2953 · arxiv_version: 1105.2953v1 · doi: 10.48550/arxiv.1105.2953 · pith_short_12: 65U2KONJTDRQ · pith_short_16: 65U2KONJTDRQL4P3 · pith_short_8: 65U2KONJ

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/65U2KONJTDRQL4P3KZJRRZ6QTS \
  | 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: f769a539a998e305f1fb565318e7d09c9a6f7fa4c33fd68f4fcc2de6e9475419

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f032e9de19a03a76831f2d42769aa1d33aa98a0551fe86cf7876bd6b09b0d68",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-05-15T16:26:43Z",
    "title_canon_sha256": "a776cd1c0646a2d860d150063fabe226eb7eeb6bedea3d5d7023452227e13ed4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2953",
    "kind": "arxiv",
    "version": 1
  }
}