Pith Number

pith:4YNTMCQE

pith:2016:4YNTMCQEJUNNQ2363RRPWD64T7

not attested not anchored not stored refs pending

Concentration-compactness principle for nonlocal scalar field equations with critical growth

Diego Ferraz, Jo\~ao Marcos do \'O

arxiv:1609.06501 v3 · 2016-09-21 · 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{4YNTMCQEJUNNQ2363RRPWD64T7}

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	2026-05-18T00:53:50.631538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e61b360a044d1ad86b7edc62fb0fdc9ff06c5159235b090071ec1a2659b3fb99

Aliases

arxiv: 1609.06501 · arxiv_version: 1609.06501v3 · doi: 10.48550/arxiv.1609.06501 · pith_short_12: 4YNTMCQEJUNN · pith_short_16: 4YNTMCQEJUNNQ236 · pith_short_8: 4YNTMCQE

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/4YNTMCQEJUNNQ2363RRPWD64T7 \
  | 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: e61b360a044d1ad86b7edc62fb0fdc9ff06c5159235b090071ec1a2659b3fb99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26edcdee725a4968025bd7369c8067a07d4147bec3ebe1184f9995c8c74f94d5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-21T11:23:57Z",
    "title_canon_sha256": "ac71904c3d4d1a4ec94510814e47b95cd7b9bfab7ee27625115e9c2d25190179"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06501",
    "kind": "arxiv",
    "version": 3
  }
}