Pith Number

pith:VDNJ3YMS

pith:2014:VDNJ3YMS3E6B5OCTMVLCZDM6BZ

not attested not anchored not stored refs pending

Ground states and concentration phenomena for the fractional Schr\"odinger equation

Enrico Valdinoci, Fethi Mahmoudi, Mouhamed Moustapha Fall

arxiv:1411.0576 v2 · 2014-11-03 · 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{VDNJ3YMS3E6B5OCTMVLCZDM6BZ}

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	2026-05-18T02:17:54.390645Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8da9de192d93c1eb85365562c8d9e0e747c5233dbc6aea7300e649942ec8352

Aliases

arxiv: 1411.0576 · arxiv_version: 1411.0576v2 · doi: 10.48550/arxiv.1411.0576 · pith_short_12: VDNJ3YMS3E6B · pith_short_16: VDNJ3YMS3E6B5OCT · pith_short_8: VDNJ3YMS

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/VDNJ3YMS3E6B5OCTMVLCZDM6BZ \
  | 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: a8da9de192d93c1eb85365562c8d9e0e747c5233dbc6aea7300e649942ec8352

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a98005d637cba3c8e5345422442b4f8454d0b10c3317ebd42577c4e39dcd5a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2014-11-03T17:29:37Z",
    "title_canon_sha256": "b9fa250b908e752a7f6eb12d711d58e5c9d715329db722cbc3e0ea1a4caa66cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.0576",
    "kind": "arxiv",
    "version": 2
  }
}