Pith Number

pith:MHYOMNPH

pith:2010:MHYOMNPHWS3FGWRFBS45BGZFGA

not attested not anchored not stored refs pending

Solutions to nonlinear Schr\"odinger equations with singular electromagnetic potential and critical exponent

Laura Abatangelo, Susanna Terracini

arxiv:1009.3386 v1 · 2010-09-17 · 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{MHYOMNPHWS3FGWRFBS45BGZFGA}

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	2026-05-18T04:40:45.836335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61f0e635e7b4b6535a250cb9d09b25302e1b2e18a7b25b79d2b07c04d57e814c

Aliases

arxiv: 1009.3386 · arxiv_version: 1009.3386v1 · doi: 10.48550/arxiv.1009.3386 · pith_short_12: MHYOMNPHWS3F · pith_short_16: MHYOMNPHWS3FGWRF · pith_short_8: MHYOMNPH

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/MHYOMNPHWS3FGWRFBS45BGZFGA \
  | 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: 61f0e635e7b4b6535a250cb9d09b25302e1b2e18a7b25b79d2b07c04d57e814c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f89d339fea40d20d80734796ca69fd9627c7d8f4ffdafa81c46b54988ee8e29e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-09-17T10:11:53Z",
    "title_canon_sha256": "464c5314fe288889fd45d83527315df170bd02ad1eabb861ad6cb92bf31b6d77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.3386",
    "kind": "arxiv",
    "version": 1
  }
}