Pith Number

pith:36URGN73

pith:2013:36URGN73NTZ45DORARFV4N3PTE

not attested not anchored not stored refs pending

Sobolev norm estimates for a class of bilinear multipliers

Fr\'ed\'eric Bernicot, Vjekoslav Kova\v{c}

arxiv:1307.7910 v1 · 2013-07-30 · 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{36URGN73NTZ45DORARFV4N3PTE}

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	2026-05-18T03:02:46.836045Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dfa91337fb6cf3ce8dd1044b5e376f9907185bda1aea6c59552282bfc46678e5

Aliases

arxiv: 1307.7910 · arxiv_version: 1307.7910v1 · doi: 10.48550/arxiv.1307.7910 · pith_short_12: 36URGN73NTZ4 · pith_short_16: 36URGN73NTZ45DOR · pith_short_8: 36URGN73

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/36URGN73NTZ45DORARFV4N3PTE \
  | 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: dfa91337fb6cf3ce8dd1044b5e376f9907185bda1aea6c59552282bfc46678e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2e963879843292c9bedf69637f934c7eaf409e60affa9d4e9bc0951a0d69b73",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-07-30T11:16:16Z",
    "title_canon_sha256": "936f1e1b04b83845ee9d4e30a67558b16607be40f391e024570027cd36526c8f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.7910",
    "kind": "arxiv",
    "version": 1
  }
}