Pith Number

pith:KTEEWGVR

pith:2011:KTEEWGVRWM2VJ43ADFR27FNOWQ

not attested not anchored not stored refs pending

Liouville-type theorems and bounds of solutions for Hardy-H\'enon elliptic systems

Quoc Hung Phan

arxiv:1108.1312 v1 · 2011-08-05 · 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{KTEEWGVRWM2VJ43ADFR27FNOWQ}

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	2026-05-18T00:04:05.533176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54c84b1ab1b33554f3601963af95aeb4392e5dd61a425dbfe66c9dc579101a2d

Aliases

arxiv: 1108.1312 · arxiv_version: 1108.1312v1 · doi: 10.48550/arxiv.1108.1312 · pith_short_12: KTEEWGVRWM2V · pith_short_16: KTEEWGVRWM2VJ43A · pith_short_8: KTEEWGVR

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/KTEEWGVRWM2VJ43ADFR27FNOWQ \
  | 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: 54c84b1ab1b33554f3601963af95aeb4392e5dd61a425dbfe66c9dc579101a2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "181053e030699ca1a2e7af4ddea69fff39bf97567282f7f4bcca7c29143b999a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-08-05T12:10:20Z",
    "title_canon_sha256": "9ba20a18b9ac2d9d3f9ade23da8b18bdf76629c152429cc5c541efbc3a578d4b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.1312",
    "kind": "arxiv",
    "version": 1
  }
}