Pith Number

pith:WK4IAE6A

pith:2011:WK4IAE6AAPKOJV2TLCWEOMUFH3

not attested not anchored not stored refs pending

Small data blow-up of L^{2}-solution for the nonlinear Schr\"odinger equation without gauge invariance

Masahiro Ikeda, Yuta Wakasugi

arxiv:1111.0178 v3 · 2011-11-01 · 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{WK4IAE6AAPKOJV2TLCWEOMUFH3}

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	2026-05-18T03:44:49.381287Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2b88013c003d4e4d75358ac4732853efdaebec725a3b57fdd464379ae239dcc

Aliases

arxiv: 1111.0178 · arxiv_version: 1111.0178v3 · doi: 10.48550/arxiv.1111.0178 · pith_short_12: WK4IAE6AAPKO · pith_short_16: WK4IAE6AAPKOJV2T · pith_short_8: WK4IAE6A

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/WK4IAE6AAPKOJV2TLCWEOMUFH3 \
  | 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: b2b88013c003d4e4d75358ac4732853efdaebec725a3b57fdd464379ae239dcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69035bf379675c68ec48e0bb6c6fb5c81dec9903c68d6701add33890b1d0b788",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-11-01T11:48:48Z",
    "title_canon_sha256": "78394ee0d4ce739f21c85f1c4f0319af7f586635003269fca7a1b287ac73ea22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0178",
    "kind": "arxiv",
    "version": 3
  }
}