Pith Number

pith:4ZJ4Y67J

pith:2016:4ZJ4Y67JLL7LYDVM74UG7N2HRX

not attested not anchored not stored refs pending

On a bilinear Strichartz estimate on irrational tori and some application

Bobby Wilson, Chenjie Fan, Gigliola Staffilani, Hong Wang

arxiv:1612.08460 v3 · 2016-12-26 · 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{4ZJ4Y67JLL7LYDVM74UG7N2HRX}

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	2026-05-18T00:27:31.647141Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e653cc7be95afebc0eacff286fb7478dca57f54182cac027f6f6eef89191e23e

Aliases

arxiv: 1612.08460 · arxiv_version: 1612.08460v3 · doi: 10.48550/arxiv.1612.08460 · pith_short_12: 4ZJ4Y67JLL7L · pith_short_16: 4ZJ4Y67JLL7LYDVM · pith_short_8: 4ZJ4Y67J

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/4ZJ4Y67JLL7LYDVM74UG7N2HRX \
  | 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: e653cc7be95afebc0eacff286fb7478dca57f54182cac027f6f6eef89191e23e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5178b8765bfde6ef1211aa48da2400734fae74d43067d231a5df96f2544fb505",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-12-26T23:40:32Z",
    "title_canon_sha256": "3c9614247a5ce5e681a942ee1d8da6c8919b79b9dbe0803976bbbaba10d958e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08460",
    "kind": "arxiv",
    "version": 3
  }
}