Pith Number

pith:U3G2DAA6

pith:2021:U3G2DAA65CECRRIBAOE2LJ23NJ

not attested not anchored not stored refs pending

Uniqueness of ground states for combined power-type nonlinear scalar field equations involving the Sobolev critical exponent and a large frequency parameter in three and four dimensions

Miho Murata, Takafumi Akahori

arxiv:2105.02490 v1 · 2021-05-06 · 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{U3G2DAA65CECRRIBAOE2LJ23NJ}

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	2026-07-05T02:38:01.741630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6cda1801ee88828c5010389a5a75b6a6d827fc721a618ad1352299a30cf1cd2

Aliases

arxiv: 2105.02490 · arxiv_version: 2105.02490v1 · doi: 10.48550/arxiv.2105.02490 · pith_short_12: U3G2DAA65CEC · pith_short_16: U3G2DAA65CECRRIB · pith_short_8: U3G2DAA6

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/U3G2DAA65CECRRIBAOE2LJ23NJ \
  | 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: a6cda1801ee88828c5010389a5a75b6a6d827fc721a618ad1352299a30cf1cd2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e59bed62c3811c5f5fa0150ab43f655f2f53c5925f2380fa82674c614aa5d168",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-05-06T07:44:22Z",
    "title_canon_sha256": "32a510b7a1701e916d24ac2e180a8fe543b7077eab6187ec5a38d6bf8a11d147"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2105.02490",
    "kind": "arxiv",
    "version": 1
  }
}