Pith Number

pith:C2CSTJTU

pith:2021:C2CSTJTUXF3XQDA2FSEEOAU3F5

not attested not anchored not stored refs pending

Improved local smoothing estimate for the wave equation in higher dimensions

Bochen Liu, Changxing Miao, Chuanwei Gao, Yakun Xi

arxiv:2108.06870 v2 · 2021-08-16 · 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{C2CSTJTUXF3XQDA2FSEEOAU3F5}

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	2026-07-05T05:59:19.583641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

168529a674b977780c1a2c8847029b2f4e121004e3164d113e10a22bcf28b12a

Aliases

arxiv: 2108.06870 · arxiv_version: 2108.06870v2 · doi: 10.48550/arxiv.2108.06870 · pith_short_12: C2CSTJTUXF3X · pith_short_16: C2CSTJTUXF3XQDA2 · pith_short_8: C2CSTJTU

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/C2CSTJTUXF3XQDA2FSEEOAU3F5 \
  | 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: 168529a674b977780c1a2c8847029b2f4e121004e3164d113e10a22bcf28b12a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3641c4bd78cedec9c151baf06bf1bdbc310b43e28dfa15b69c2f207e45a42bcd",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-08-16T02:57:56Z",
    "title_canon_sha256": "9512b09152c72746fb574e78ec07f0df1f54f0eecefda821ce70806cda51405f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2108.06870",
    "kind": "arxiv",
    "version": 2
  }
}