Pith Number

pith:7FHOWZQZ

pith:2015:7FHOWZQZWEQ6WIVLIZIW32BC42

not attested not anchored not stored refs pending

Borderline variational problems involving fractional Laplacians and critical singularities

Nassif Ghoussoub, Shaya Shakerian

arxiv:1503.08193 v2 · 2015-03-27 · 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{7FHOWZQZWEQ6WIVLIZIW32BC42}

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	2026-05-18T02:09:54.047664Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f94eeb6619b121eb22ab46516de822e687e0305f261ddcc61cfff8139f929019

Aliases

arxiv: 1503.08193 · arxiv_version: 1503.08193v2 · doi: 10.48550/arxiv.1503.08193 · pith_short_12: 7FHOWZQZWEQ6 · pith_short_16: 7FHOWZQZWEQ6WIVL · pith_short_8: 7FHOWZQZ

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/7FHOWZQZWEQ6WIVLIZIW32BC42 \
  | 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: f94eeb6619b121eb22ab46516de822e687e0305f261ddcc61cfff8139f929019

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce31b81a73ccb16ac1eb2219adbbfe19128a3c7abc9a4875d9786383e72ed847",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-27T19:32:42Z",
    "title_canon_sha256": "3232b5aa39455e63909d69e8e0dc6af9fcd447638e66422955f097e34fc638aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.08193",
    "kind": "arxiv",
    "version": 2
  }
}