Pith Number

pith:MITCAUST

pith:2016:MITCAUST7WU3I4PY5VLHOQLOPF

not attested not anchored not stored refs pending

Ground states of nonlinear fractional Schr\"odinger equation involving critical growth

Hua Jin, Wenbin Liu

arxiv:1611.04007 v3 · 2016-11-12 · 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{MITCAUST7WU3I4PY5VLHOQLOPF}

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	2026-05-18T00:57:00.676266Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6226205253fda9b471f8ed5677416e797c6f44f7a4e237f7d4f6e563e71a3be9

Aliases

arxiv: 1611.04007 · arxiv_version: 1611.04007v3 · doi: 10.48550/arxiv.1611.04007 · pith_short_12: MITCAUST7WU3 · pith_short_16: MITCAUST7WU3I4PY · pith_short_8: MITCAUST

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/MITCAUST7WU3I4PY5VLHOQLOPF \
  | 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: 6226205253fda9b471f8ed5677416e797c6f44f7a4e237f7d4f6e563e71a3be9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3f131d70f1ebe0aa31ba34d2c7ff2cefb7e1dacf7c929ed18e54e24534744ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-11-12T15:27:44Z",
    "title_canon_sha256": "eb69430999b1b3e11ba85d41c5c431b18e71fe047b95a1c4a57f919c1ee4f145"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04007",
    "kind": "arxiv",
    "version": 3
  }
}