Pith Number

pith:DANMJWHT

pith:2007:DANMJWHTCUXBPJQBTDD4OO24QM

not attested not anchored not stored refs pending

Lieb-Thirring inequalities with improved constants

Ari Laptev, Jean Dolbeault (CEREMADE), Michael Loss

arxiv:0708.1165 v2 · 2007-08-08 · 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{DANMJWHTCUXBPJQBTDD4OO24QM}

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	2026-05-18T04:09:15.067132Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

181ac4d8f3152e17a60198c7c73b5c832dd744122924650e9326642a24ec59c8

Aliases

arxiv: 0708.1165 · arxiv_version: 0708.1165v2 · doi: 10.48550/arxiv.0708.1165 · pith_short_12: DANMJWHTCUXB · pith_short_16: DANMJWHTCUXBPJQB · pith_short_8: DANMJWHT

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/DANMJWHTCUXBPJQBTDD4OO24QM \
  | 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: 181ac4d8f3152e17a60198c7c73b5c832dd744122924650e9326642a24ec59c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f7ad7b429021ce6cdca2a1b9b233e1173ed37c42b908cd7d92bc60f54a8e12d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2007-08-08T20:14:18Z",
    "title_canon_sha256": "3e9b440b381d9ada587984a9fba30b19ee9dc2928639a61b495c13482c5a5403"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0708.1165",
    "kind": "arxiv",
    "version": 2
  }
}