Pith Number

pith:HR6OJTL2

pith:2010:HR6OJTL2ARTOSHUGYT45G4DLDR

not attested not anchored not stored refs pending

$L^p$-$L^q$ estimates for Electromagnetic Helmholtz equation

Andoni Garcia

arxiv:1011.0915 v1 · 2010-11-03 · 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{HR6OJTL2ARTOSHUGYT45G4DLDR}

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	2026-05-18T04:37:12.114939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c7ce4cd7a0466e91e86c4f9d3706b1c59d9d5486bea77d8f47fe86aaf5a821d

Aliases

arxiv: 1011.0915 · arxiv_version: 1011.0915v1 · doi: 10.48550/arxiv.1011.0915 · pith_short_12: HR6OJTL2ARTO · pith_short_16: HR6OJTL2ARTOSHUG · pith_short_8: HR6OJTL2

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/HR6OJTL2ARTOSHUGYT45G4DLDR \
  | 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: 3c7ce4cd7a0466e91e86c4f9d3706b1c59d9d5486bea77d8f47fe86aaf5a821d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c396a12879c0c0ebb7367dd784845a651ab8e17a5210f8426b98b2fb7fbecbf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-11-03T15:23:16Z",
    "title_canon_sha256": "9ff9ec423243f82a8d439d052db1d693bcf12eafd6ef0cedbbf9593ba0c36ef4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.0915",
    "kind": "arxiv",
    "version": 1
  }
}