Pith Number

pith:6TVQVBZ4

pith:2015:6TVQVBZ4ISPNBKKTGGCAMXYAUV

not attested not anchored not stored refs pending

Existence of positive solution for a nonlinear elliptic equation with saddle-like potential and nonlinearity with exponential critical growth in $\mathbb{R}^{2}$

Claudianor O. Alves

arxiv:1506.04947 v1 · 2015-06-16 · 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{6TVQVBZ4ISPNBKKTGGCAMXYAUV}

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	2026-05-18T01:48:05.414205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4eb0a873c449ed0a9533184065f00a5765681dff181c9086525aaafdbff67ff

Aliases

arxiv: 1506.04947 · arxiv_version: 1506.04947v1 · doi: 10.48550/arxiv.1506.04947 · pith_short_12: 6TVQVBZ4ISPN · pith_short_16: 6TVQVBZ4ISPNBKKT · pith_short_8: 6TVQVBZ4

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/6TVQVBZ4ISPNBKKTGGCAMXYAUV \
  | 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: f4eb0a873c449ed0a9533184065f00a5765681dff181c9086525aaafdbff67ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0a742455fb75f4cc05f015ed6408dd23b960ced9979c3f81be8620f0040e723",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-06-16T12:47:09Z",
    "title_canon_sha256": "cbcecc26e901582d8081fcf7c1411df0665b77028c8eb091a5a9c83f7716dfd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.04947",
    "kind": "arxiv",
    "version": 1
  }
}