Pith Number

pith:HQRQMTX6

pith:2018:HQRQMTX6LKR7NOSELGLBN6XV7E

not attested not anchored not stored refs pending

Sharp bilinear estimates and its application to a system of quadratic derivative nonlinear Schr\"odinger equations

Hiroyuki Hirayama, Shinya Kinoshita

arxiv:1802.06563 v1 · 2018-02-19 · 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{HQRQMTX6LKR7NOSELGLBN6XV7E}

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	2026-07-05T09:05:28.409805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c23064efe5aa3f6ba44599616faf5f93f0e4ef846e839d2c18dd996b8f9a9d2

Aliases

arxiv: 1802.06563 · arxiv_version: 1802.06563v1 · doi: 10.48550/arxiv.1802.06563 · pith_short_12: HQRQMTX6LKR7 · pith_short_16: HQRQMTX6LKR7NOSE · pith_short_8: HQRQMTX6

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/HQRQMTX6LKR7NOSELGLBN6XV7E \
  | 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: 3c23064efe5aa3f6ba44599616faf5f93f0e4ef846e839d2c18dd996b8f9a9d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c52289b4d9be8d061e09f856a6c2c40786b115ddc2f75a4376805bf57daa980",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-02-19T09:31:26Z",
    "title_canon_sha256": "8d3e0ea7b2a50083cddb8fd5f2d27492d9d79b119e4e2ab87895a08c4ff7bb07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.06563",
    "kind": "arxiv",
    "version": 1
  }
}