Pith Number

pith:GDE5I7FW

pith:2015:GDE5I7FW6KHECON7YL3JEG6J7Q

not attested not anchored not stored refs pending

The Caffarelli-Kohn-Nirenberg Inequality for Submanifolds in Riemannian Manifolds

Feliciano Vit\'orio, Heudson Mirandola, M\'arcio Batista

arxiv:1509.03857 v1 · 2015-09-13 · math.DG · 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{GDE5I7FW6KHECON7YL3JEG6J7Q}

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	2026-05-18T01:33:14.281098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30c9d47cb6f28e4139bfc2f6921bc9fc3ba312e7613bc092403275dcd1a82730

Aliases

arxiv: 1509.03857 · arxiv_version: 1509.03857v1 · doi: 10.48550/arxiv.1509.03857 · pith_short_12: GDE5I7FW6KHE · pith_short_16: GDE5I7FW6KHECON7 · pith_short_8: GDE5I7FW

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/GDE5I7FW6KHECON7YL3JEG6J7Q \
  | 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: 30c9d47cb6f28e4139bfc2f6921bc9fc3ba312e7613bc092403275dcd1a82730

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38f88ce7a094578eb7cbf136d606017b2f73362b9fc7134056c2c711db2f4da4",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-09-13T15:06:03Z",
    "title_canon_sha256": "4eed161efcc1991be80932b57388159a2eabfb991fbf58e30bb896d2780c97b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.03857",
    "kind": "arxiv",
    "version": 1
  }
}