Pith Number

pith:R46MSMIJ

pith:2022:R46MSMIJCP2ML3OHUZB2VWPY3I

not attested not anchored not stored refs pending

Nondegeneracy of ground states for nonlinear scalar field equations involving the Sobolev-critical exponent at high frequencies in three and four dimensions

Miho Murata, Takafumi Akahori

arxiv:2203.13473 v1 · 2022-03-25 · 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{R46MSMIJCP2ML3OHUZB2VWPY3I}

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	2026-07-05T04:08:32.476051Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f3cc9310913f4c5edc7a643aad9f8da34ab96aec871c29298db4cc88f559907

Aliases

arxiv: 2203.13473 · arxiv_version: 2203.13473v1 · doi: 10.48550/arxiv.2203.13473 · pith_short_12: R46MSMIJCP2M · pith_short_16: R46MSMIJCP2ML3OH · pith_short_8: R46MSMIJ

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/R46MSMIJCP2ML3OHUZB2VWPY3I \
  | 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: 8f3cc9310913f4c5edc7a643aad9f8da34ab96aec871c29298db4cc88f559907

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f76116af663de81c1c4ad05b7cc4741d8e98d810b4d3e9514776b416466a53b6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2022-03-25T06:49:44Z",
    "title_canon_sha256": "eef84cebbdfeca4080cdd0174b517b03b44cdfd2afa155d9fe6bd30b5b4983de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2203.13473",
    "kind": "arxiv",
    "version": 1
  }
}