Pith Number

pith:44CLCVTL

pith:2018:44CLCVTL4ANIZ6H3T3PBRZVKEF

not attested not anchored not stored refs pending

Weighted $L^2-L^2$ estimate for wave equation and its applications

Ning-An Lai

arxiv:1807.05109 v1 · 2018-07-13 · 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{44CLCVTL4ANIZ6H3T3PBRZVKEF}

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	2026-05-18T00:10:48.996653Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e704b1566be01a8cf8fb9ede18e6aa2140d3cb288b3c168834a86046d838e445

Aliases

arxiv: 1807.05109 · arxiv_version: 1807.05109v1 · doi: 10.48550/arxiv.1807.05109 · pith_short_12: 44CLCVTL4ANI · pith_short_16: 44CLCVTL4ANIZ6H3 · pith_short_8: 44CLCVTL

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/44CLCVTL4ANIZ6H3T3PBRZVKEF \
  | 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: e704b1566be01a8cf8fb9ede18e6aa2140d3cb288b3c168834a86046d838e445

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd7c5abd38fda5adc49b9b8f22418af9f128500e8a5ddbd8fee2d7ec2b3ec117",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-07-13T14:41:19Z",
    "title_canon_sha256": "b8497f3eb388ca6f1cb9a317c7318564899d5ba5e5ade512d4f4b208b66a4a93"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1807.05109",
    "kind": "arxiv",
    "version": 1
  }
}