Pith Number

pith:P43BLMMA

pith:2013:P43BLMMABJCHFFJ45I5KRUGY36

not attested not anchored not stored refs pending

On the energy-critical fractional Sch\"odinger equation in the radial case

Lifeng Zhao, Yannick Sire, Yuzhao Wang, Zihua Guo

arxiv:1310.6816 v1 · 2013-10-25 · 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{P43BLMMABJCHFFJ45I5KRUGY36}

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	2026-05-18T03:08:57.478078Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7f3615b1800a4472953cea3aa8d0d8dfa5efb708c318cfd22d823d54b9c3136c

Aliases

arxiv: 1310.6816 · arxiv_version: 1310.6816v1 · doi: 10.48550/arxiv.1310.6816 · pith_short_12: P43BLMMABJCH · pith_short_16: P43BLMMABJCHFFJ4 · pith_short_8: P43BLMMA

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/P43BLMMABJCHFFJ45I5KRUGY36 \
  | 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: 7f3615b1800a4472953cea3aa8d0d8dfa5efb708c318cfd22d823d54b9c3136c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea864536f87babbe85456bd5048c8ab3fd5786439c3be7bd8c8bf09dbda2fe4c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2013-10-25T04:30:28Z",
    "title_canon_sha256": "391e0f1ebe10b54b071ff8de036b4446cd949e53f037be0033deaf7379eb0a0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.6816",
    "kind": "arxiv",
    "version": 1
  }
}