Pith Number

pith:EQTV6KRD

pith:2013:EQTV6KRD7GEWVHLQCPO2BGPEIJ

not attested not anchored not stored refs pending

Concentrating Bound States for Kirchhoff type problems in ${\R^3}$ involving critical Sobolev exponents

Gongbao LI, Shuangjie Peng, Yi He

arxiv:1306.0122 v1 · 2013-06-01 · 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{EQTV6KRD7GEWVHLQCPO2BGPEIJ}

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	2026-05-18T03:21:56.082514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

24275f2a23f9896a9d7013dda099e442659388c22e9d7782df240a7d9cdc9a8d

Aliases

arxiv: 1306.0122 · arxiv_version: 1306.0122v1 · doi: 10.48550/arxiv.1306.0122 · pith_short_12: EQTV6KRD7GEW · pith_short_16: EQTV6KRD7GEWVHLQ · pith_short_8: EQTV6KRD

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/EQTV6KRD7GEWVHLQCPO2BGPEIJ \
  | 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: 24275f2a23f9896a9d7013dda099e442659388c22e9d7782df240a7d9cdc9a8d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c82ffd270e3bb4b69fca4a4bf7445cf58f5ee047061c294017c48e4e9e8d067",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-06-01T15:24:59Z",
    "title_canon_sha256": "df1ed466dc992e307545d56ad8cc70fb0476b22d99d726db1fba1d90005905ce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.0122",
    "kind": "arxiv",
    "version": 1
  }
}