Pith Number

pith:HUIIPFCI

pith:2014:HUIIPFCI5APQJQNGHS5HJED4V2

not attested not anchored not stored refs pending

Standing waves for a class of Schr\"odinger-Poisson equations in ${\mathbb{R}^3}$ involving critical Sobolev exponents

Gongbao LI, Yi He

arxiv:1412.4057 v1 · 2014-12-06 · 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{HUIIPFCI5APQJQNGHS5HJED4V2}

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	2026-05-18T02:31:28.006668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d10879448e81f04c1a63cba74907cae87b522dc0e68103cda389c5a7e639c5a

Aliases

arxiv: 1412.4057 · arxiv_version: 1412.4057v1 · doi: 10.48550/arxiv.1412.4057 · pith_short_12: HUIIPFCI5APQ · pith_short_16: HUIIPFCI5APQJQNG · pith_short_8: HUIIPFCI

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/HUIIPFCI5APQJQNGHS5HJED4V2 \
  | 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: 3d10879448e81f04c1a63cba74907cae87b522dc0e68103cda389c5a7e639c5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4f65b26ea91aad5720b88c09664398c18a12d6ec5f2026ffa71338f4974b7d0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-12-06T08:30:30Z",
    "title_canon_sha256": "9db5d9733f1bf6d7890464e6abf9a5eada8594c9cb32c163546feeb58b92de1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.4057",
    "kind": "arxiv",
    "version": 1
  }
}