Pith Number

pith:YPWJ4ZTU

pith:2021:YPWJ4ZTUBYAPOLRGKZGX3HGAE6

not attested not anchored not stored refs pending

Multiplicity of normalized solutions for a Schr\"{o}dinger equation with critical growth in $\mathbb{R}^{N}$

Chao Ji, Claudianor O. Alves, Olimpio H. Miyagaki

arxiv:2103.07940 v2 · 2021-03-14 · 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{YPWJ4ZTUBYAPOLRGKZGX3HGAE6}

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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.

Cited by

1 paper in Pith

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

Receipt and verification

First computed	2026-07-05T02:33:30.726857Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3ec9e66740e00f72e26564d7d9cc0279ade2c09f95cae6666deeb55c12049c3

Aliases

arxiv: 2103.07940 · arxiv_version: 2103.07940v2 · doi: 10.48550/arxiv.2103.07940 · pith_short_12: YPWJ4ZTUBYAP · pith_short_16: YPWJ4ZTUBYAPOLRG · pith_short_8: YPWJ4ZTU

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/YPWJ4ZTUBYAPOLRGKZGX3HGAE6 \
  | 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: c3ec9e66740e00f72e26564d7d9cc0279ade2c09f95cae6666deeb55c12049c3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0699d52dabc16773ddb847702e20cf75c55639b0764b96d34223b3caf55c77a2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-03-14T14:36:52Z",
    "title_canon_sha256": "a9a78e9437d83b6a2cc8003b34d1175652ef243d6b3d7da67510ead53e7f1945"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.07940",
    "kind": "arxiv",
    "version": 2
  }
}