Pith Number

pith:INH3P4PY

pith:2025:INH3P4PYI2QKFXMMFPKPGUL3FZ

not attested not anchored not stored refs pending

Normalized solutions for the NLS equation with potential in higher dimension: the purely Sobolev critical case

He Zhang, Juntao Sun, Shuai Yao

arxiv:2507.23639 v1 · 2025-07-31 · 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{INH3P4PYI2QKFXMMFPKPGUL3FZ}

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	2026-07-05T11:46:28.557167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

434fb7f1f846a0a2dd8c2bd4f3517b2e52332e7a0023cb36a2354fe88cbb08c8

Aliases

arxiv: 2507.23639 · arxiv_version: 2507.23639v1 · doi: 10.48550/arxiv.2507.23639 · pith_short_12: INH3P4PYI2QK · pith_short_16: INH3P4PYI2QKFXMM · pith_short_8: INH3P4PY

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/INH3P4PYI2QKFXMMFPKPGUL3FZ \
  | 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: 434fb7f1f846a0a2dd8c2bd4f3517b2e52332e7a0023cb36a2354fe88cbb08c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f8667efcf840d92c7f8f4dd6a28b3485524960b12708b9f6417eae429b428e7",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-07-31T15:16:32Z",
    "title_canon_sha256": "efa40d77bac0e57128dda9698d7fe3d29409872b46894112371181150aa13bf5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.23639",
    "kind": "arxiv",
    "version": 1
  }
}