Pith Number

pith:4JUYUWXW

pith:2016:4JUYUWXWHRK7GKT7SMLV3WKVVX

not attested not anchored not stored refs pending

Inhomogeneous Oscillatory Integrals and Global Smoothing Effects for Dispersive Equations

Quan Zheng, Shanlin Huang, Tianxiao Huang

arxiv:1612.09072 v2 · 2016-12-29 · 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{4JUYUWXWHRK7GKT7SMLV3WKVVX}

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	2026-05-18T00:14:29.161663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e2698a5af63c55f32a7f93175dd955add6469013246edfc00bf7874e5de5247b

Aliases

arxiv: 1612.09072 · arxiv_version: 1612.09072v2 · doi: 10.48550/arxiv.1612.09072 · pith_short_12: 4JUYUWXWHRK7 · pith_short_16: 4JUYUWXWHRK7GKT7 · pith_short_8: 4JUYUWXW

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/4JUYUWXWHRK7GKT7SMLV3WKVVX \
  | 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: e2698a5af63c55f32a7f93175dd955add6469013246edfc00bf7874e5de5247b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "666ef129c379417b42c38e5ebfd91bf2a34acc5ca4b7a25a8b392341cbee274c",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-12-29T08:41:22Z",
    "title_canon_sha256": "58d9a79ed4f274adbf2510766394d4b6fc7442a66ed71a585303ee3c6a2802f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.09072",
    "kind": "arxiv",
    "version": 2
  }
}