Pith Number

pith:FMQU7UOU

pith:2019:FMQU7UOUIBSPIZNPO2LX7DXQGI

not attested not anchored not stored refs pending

Blow up of fractional Schr\"odinger equations on manifolds with nonnegative Ricci curvature

Huali Zhang, Shiliang Zhao

arxiv:1911.01183 v2 · 2019-11-04 · 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{FMQU7UOUIBSPIZNPO2LX7DXQGI}

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	2026-07-05T02:35:49.264009Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b214fd1d44064f465af76977f8ef03239f2d5d2986ddfe84e4f7e9ad579215a

Aliases

arxiv: 1911.01183 · arxiv_version: 1911.01183v2 · doi: 10.48550/arxiv.1911.01183 · pith_short_12: FMQU7UOUIBSP · pith_short_16: FMQU7UOUIBSPIZNP · pith_short_8: FMQU7UOU

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/FMQU7UOUIBSPIZNPO2LX7DXQGI \
  | 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: 2b214fd1d44064f465af76977f8ef03239f2d5d2986ddfe84e4f7e9ad579215a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "43e4f91c4dc8b278949224303b2cec96559d3edcd02b2fe35db68f3556689456",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-11-04T13:16:17Z",
    "title_canon_sha256": "a3bc2178afa2e50921b7506851c830fd7807bd3585d3b9b27f3db53c802918c4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1911.01183",
    "kind": "arxiv",
    "version": 2
  }
}