Pith Number

pith:NJ364F3W

pith:2021:NJ364F3WA2CKR4L3FIHSYTYGFE

not attested not anchored not stored refs pending

Optimizers for the finite-rank Lieb-Thirring inequality

David Gontier, Mathieu Lewin, Rupert L. Frank

arxiv:2109.05984 v2 · 2021-09-13 · math.AP · math-ph · math.MP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NJ364F3WA2CKR4L3FIHSYTYGFE}

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	2026-07-05T06:09:03.548499Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a77ee17760684a8f17b2a0f2c4f06290d4e366a0b2e1ce9f3c69679f4bc0caa

Aliases

arxiv: 2109.05984 · arxiv_version: 2109.05984v2 · doi: 10.48550/arxiv.2109.05984 · pith_short_12: NJ364F3WA2CK · pith_short_16: NJ364F3WA2CKR4L3 · pith_short_8: NJ364F3W

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/NJ364F3WA2CKR4L3FIHSYTYGFE \
  | 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: 6a77ee17760684a8f17b2a0f2c4f06290d4e366a0b2e1ce9f3c69679f4bc0caa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a20d919d1804425fe7682b7e792357a210181af882fa912c4d5a70148a923983",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-09-13T14:00:39Z",
    "title_canon_sha256": "9a0bd8da5657a70cf7406098d8df28a6fc8de6862bbde514841e699b4eade8cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2109.05984",
    "kind": "arxiv",
    "version": 2
  }
}