Pith Number

pith:5HEBKOI2

pith:2025:5HEBKOI2OMISFQSZEKLMFXIY3W

not attested not anchored not stored refs pending

Normalized solutions to focusing Sobolev critical biharmonic Schr\"{o}dinger equation with mixed dispersion

Hong-Rui Sun, Jianlun Liu, Ziheng Zhang

arxiv:2502.02049 v1 · 2025-02-04 · 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{5HEBKOI2OMISFQSZEKLMFXIY3W}

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	2026-07-05T10:09:23.008090Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e9c815391a731122c2592296c2dd18ddbb113e804b6fb9fcb860898ac9a5ba86

Aliases

arxiv: 2502.02049 · arxiv_version: 2502.02049v1 · doi: 10.48550/arxiv.2502.02049 · pith_short_12: 5HEBKOI2OMIS · pith_short_16: 5HEBKOI2OMISFQSZ · pith_short_8: 5HEBKOI2

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/5HEBKOI2OMISFQSZEKLMFXIY3W \
  | 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: e9c815391a731122c2592296c2dd18ddbb113e804b6fb9fcb860898ac9a5ba86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb8bfde6798ac780adccdd29fc4b7e933ba8283ceb541d33be9035415de1a074",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-02-04T06:30:43Z",
    "title_canon_sha256": "9338c4b6db3997e190d32f5c8b63e5a3ff9424576e85303794fdcb3a830fc97a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.02049",
    "kind": "arxiv",
    "version": 1
  }
}