Pith Number

pith:PJAQKERB

pith:2017:PJAQKERB2EQIVZAZ3MZEXLPYD3

not attested not anchored not stored refs pending

Sharp Caffarelli-Kohn-Nirenberg inequalities on Riemannian manifolds: the influence of curvature

Van Hoang Nguyen

arxiv:1709.06120 v1 · 2017-09-18 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PJAQKERB2EQIVZAZ3MZEXLPYD3}

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	2026-05-18T00:34:54.364410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a41051221d1208ae419db324badf81eeeeacd7349b5920c4fb6c004e15d84d9

Aliases

arxiv: 1709.06120 · arxiv_version: 1709.06120v1 · doi: 10.48550/arxiv.1709.06120 · pith_short_12: PJAQKERB2EQI · pith_short_16: PJAQKERB2EQIVZAZ · pith_short_8: PJAQKERB

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/PJAQKERB2EQIVZAZ3MZEXLPYD3 \
  | 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: 7a41051221d1208ae419db324badf81eeeeacd7349b5920c4fb6c004e15d84d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9862e9780c6ae396b04bee45c427304f192ad38e7e010d5cd5ed2b8b05ff0a5e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2017-09-18T18:47:01Z",
    "title_canon_sha256": "252f461d83cc3980e783f32ac53984aacd63e9e0241a3a5291f4245d67adc959"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.06120",
    "kind": "arxiv",
    "version": 1
  }
}