Pith Number

pith:TCLVOPLD

pith:2019:TCLVOPLDKGHAZ3ZRJBMPOOXUXZ

not attested not anchored not stored refs pending

Sharp Hardy-Leray inequality for three-dimensional solenoidal fields with axisymmetric swirl

Futoshi Takahashi, Naoki Hamamoto

arxiv:1904.01338 v1 · 2019-04-02 · 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{TCLVOPLDKGHAZ3ZRJBMPOOXUXZ}

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	2026-05-17T23:49:35.030939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9897573d63518e0cef314858f73af4be4e74f14f0349c5ae0c813bce62c173d6

Aliases

arxiv: 1904.01338 · arxiv_version: 1904.01338v1 · doi: 10.48550/arxiv.1904.01338 · pith_short_12: TCLVOPLDKGHA · pith_short_16: TCLVOPLDKGHAZ3ZR · pith_short_8: TCLVOPLD

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/TCLVOPLDKGHAZ3ZRJBMPOOXUXZ \
  | 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: 9897573d63518e0cef314858f73af4be4e74f14f0349c5ae0c813bce62c173d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "456fab1fa2c5e0a3b432e15f2a985fb2625a583a11ea646ac5be6ffe6b9fda88",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-04-02T11:20:01Z",
    "title_canon_sha256": "25c4749dd635d2d286b177aba7e908e64aac1c84c8b03ec1b942ac14a7e7fe76"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.01338",
    "kind": "arxiv",
    "version": 1
  }
}