Pith Number

pith:547CDX3Y

pith:2015:547CDX3YTPICUYPTR2XU3HTYZ5

not attested not anchored not stored refs pending

Fractional Schr\"odinger-Poisson systems with a general subcritical or critical nonlinearity

Jianjun Zhang, Jo\~ao Marcos do \'O, Marco Squassina

arxiv:1503.08765 v1 · 2015-03-30 · 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{547CDX3YTPICUYPTR2XU3HTYZ5}

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	2026-05-18T02:20:00.986977Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef3e21df789bd02a61f38eaf4d9e78cf5ec7e44c770b93ac69d04ee2f7a940f0

Aliases

arxiv: 1503.08765 · arxiv_version: 1503.08765v1 · doi: 10.48550/arxiv.1503.08765 · pith_short_12: 547CDX3YTPIC · pith_short_16: 547CDX3YTPICUYPT · pith_short_8: 547CDX3Y

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/547CDX3YTPICUYPTR2XU3HTYZ5 \
  | 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: ef3e21df789bd02a61f38eaf4d9e78cf5ec7e44c770b93ac69d04ee2f7a940f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37a5ebe207b9362c70be712e3b79c1ae02100fc7cbb741b6ed1bef7e7b4ce61c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-30T17:48:29Z",
    "title_canon_sha256": "5f97140230f47cd5ddc40949621269f75f6317b343c553f0072ae98378500e7c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.08765",
    "kind": "arxiv",
    "version": 1
  }
}