Pith Number

pith:MLCUZFAX

pith:2016:MLCUZFAXQKSH6VMOZBJPIAKIGI

not attested not anchored not stored refs pending

On the existence of weak solutions of semilinear elliptic equations and systems with Hardy potentials

Konstantinos T. Gkikas, Phuoc-Tai Nguyen

arxiv:1609.06671 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{MLCUZFAXQKSH6VMOZBJPIAKIGI}

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	2026-05-18T00:10:52.380684Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62c54c941782a47f558ec852f401483222345fda9c8cdeca508cd0a0d8a224ee

Aliases

arxiv: 1609.06671 · arxiv_version: 1609.06671v3 · doi: 10.48550/arxiv.1609.06671 · pith_short_12: MLCUZFAXQKSH · pith_short_16: MLCUZFAXQKSH6VMO · pith_short_8: MLCUZFAX

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/MLCUZFAXQKSH6VMOZBJPIAKIGI \
  | 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: 62c54c941782a47f558ec852f401483222345fda9c8cdeca508cd0a0d8a224ee

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2ccb07b7a43836ea270aaf1491af0607b956533d990d8214a61e160a083f75a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-09-21T18:36:16Z",
    "title_canon_sha256": "10997eaf768f428d67dfaca3136c66c7aeb4eed11778419ed173afa01d7cb40f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.06671",
    "kind": "arxiv",
    "version": 3
  }
}