Pith Number

pith:GTOAOTYQ

pith:2015:GTOAOTYQ7AJJRA6PF2TAJG2XZM

not attested not anchored not stored refs pending

Well-posedness and scattering for fourth order nonlinear Schr\"odinger type equations at the scaling critical regularity

Hiroyuki Hirayama, Mamoru Okamoto

arxiv:1505.06496 v1 · 2015-05-24 · 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{GTOAOTYQ7AJJRA6PF2TAJG2XZM}

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	2026-05-18T00:15:52.951039Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34dc074f10f8129883cf2ea6049b57cb112718465e981d87a83657f54d22925e

Aliases

arxiv: 1505.06496 · arxiv_version: 1505.06496v1 · doi: 10.48550/arxiv.1505.06496 · pith_short_12: GTOAOTYQ7AJJ · pith_short_16: GTOAOTYQ7AJJRA6P · pith_short_8: GTOAOTYQ

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/GTOAOTYQ7AJJRA6PF2TAJG2XZM \
  | 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: 34dc074f10f8129883cf2ea6049b57cb112718465e981d87a83657f54d22925e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "111325424c416dea51f654d0e87f907e870c491592ee5fdf04ab2d1b1964298b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-05-24T23:00:26Z",
    "title_canon_sha256": "2df934dbb3f64e719db4b0ce3a8b4d1db1e32bc6ac37942ad3d88eaaa7de3cad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.06496",
    "kind": "arxiv",
    "version": 1
  }
}