Pith Number

pith:VYY4N2MZ

pith:2018:VYY4N2MZLTYVEUJCQ67CCMVL66

not attested not anchored not stored refs pending

Solutions concentrating around the saddle points of the potential for Schr\"{o}dinger equations with critical exponential growth

J. M. do \'O, J. Zhang, P. K. Mishra

arxiv:1803.07946 v1 · 2018-03-21 · 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{VYY4N2MZLTYVEUJCQ67CCMVL66}

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	2026-05-18T00:20:28.441210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae31c6e9995cf152512287be2132abf79ea74167a3572bf38a91265faa4f73f7

Aliases

arxiv: 1803.07946 · arxiv_version: 1803.07946v1 · doi: 10.48550/arxiv.1803.07946 · pith_short_12: VYY4N2MZLTYV · pith_short_16: VYY4N2MZLTYVEUJC · pith_short_8: VYY4N2MZ

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/VYY4N2MZLTYVEUJCQ67CCMVL66 \
  | 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: ae31c6e9995cf152512287be2132abf79ea74167a3572bf38a91265faa4f73f7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "156acc5008bbd2c38bc62a581179451a183dad9362c8dda225997cef179da01c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-03-21T14:37:52Z",
    "title_canon_sha256": "f1596ed8caced0a13dbe2be89a9c5238b0222a1f39aa983db2870fb4ee5dea9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.07946",
    "kind": "arxiv",
    "version": 1
  }
}