Pith Number

pith:SVHJOAME

pith:2015:SVHJOAME5IMOKUUGNCG2WYQF3Q

not attested not anchored not stored refs pending

Some energy inequalities involving fractional GJMS operators

Jeffrey S. Case

arxiv:1509.08347 v2 · 2015-09-28 · 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{SVHJOAME5IMOKUUGNCG2WYQF3Q}

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	2026-05-18T00:49:19.388779Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

954e970184ea18e55286688dab6205dc11f308a2f137fb3909ad896a07c60f5c

Aliases

arxiv: 1509.08347 · arxiv_version: 1509.08347v2 · doi: 10.48550/arxiv.1509.08347 · pith_short_12: SVHJOAME5IMO · pith_short_16: SVHJOAME5IMOKUUG · pith_short_8: SVHJOAME

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/SVHJOAME5IMOKUUGNCG2WYQF3Q \
  | 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: 954e970184ea18e55286688dab6205dc11f308a2f137fb3909ad896a07c60f5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "00c2af0a3fdd08c2b24610d49b1c5c21ee3659cde8e1fb673863c7c3bbaac3c5",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2015-09-28T15:06:25Z",
    "title_canon_sha256": "5bf123ccb31723a642604bba490750be91b6055b6211606e69abb27786208572"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08347",
    "kind": "arxiv",
    "version": 2
  }
}