Pith Number

pith:3TBIXOPV

pith:2020:3TBIXOPV24VXWG5FW5ZRR4WOGC

not attested not anchored not stored refs pending

Square function estimates and Local smoothing for Fourier Integral Operators

Bochen Liu, Changxing Miao, Chuanwei Gao, Yakun Xi

arxiv:2010.14390 v2 · 2020-10-27 · math.AP · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3TBIXOPV24VXWG5FW5ZRR4WOGC}

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	2026-07-05T05:59:19.253852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dcc28bb9f5d72b7b1ba5b77318f2ce309c84a72dd0a50f39abe89bf39e44cc94

Aliases

arxiv: 2010.14390 · arxiv_version: 2010.14390v2 · doi: 10.48550/arxiv.2010.14390 · pith_short_12: 3TBIXOPV24VX · pith_short_16: 3TBIXOPV24VXWG5F · pith_short_8: 3TBIXOPV

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/3TBIXOPV24VXWG5FW5ZRR4WOGC \
  | 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: dcc28bb9f5d72b7b1ba5b77318f2ce309c84a72dd0a50f39abe89bf39e44cc94

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3ec48963361837ba332ba122b759bea61fecfb3e2b85920d664091dd150ff177",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2020-10-27T15:51:42Z",
    "title_canon_sha256": "e8a8160cf1e735a6eacc0d332daae85a369916d18bed3c395d21909d1af732d5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.14390",
    "kind": "arxiv",
    "version": 2
  }
}