Pith Number

pith:ILZB6XJ5

pith:2011:ILZB6XJ57PCEEIYB6Z4GGVFFEB

not attested not anchored not stored refs pending

Estimates for a class of oscillatory integrals and decay rates for wave-type equations

Anton Arnold, JinMyong Kim, Xiaohua Yao

arxiv:1109.0452 v2 · 2011-09-02 · math.CA · 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{ILZB6XJ57PCEEIYB6Z4GGVFFEB}

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	2026-05-18T01:55:58.568778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42f21f5d3dfbc4422301f6786354a5206f9ba94c8602b7b8a29231a3f6e24bb1

Aliases

arxiv: 1109.0452 · arxiv_version: 1109.0452v2 · doi: 10.48550/arxiv.1109.0452 · pith_short_12: ILZB6XJ57PCE · pith_short_16: ILZB6XJ57PCEEIYB · pith_short_8: ILZB6XJ5

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/ILZB6XJ57PCEEIYB6Z4GGVFFEB \
  | 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: 42f21f5d3dfbc4422301f6786354a5206f9ba94c8602b7b8a29231a3f6e24bb1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8749e02fa5d8a463a0f6d47ed1ee55484721a61db2692d48c77a108c643080f",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-09-02T14:16:13Z",
    "title_canon_sha256": "cc701aa9a00d48037427f7a881122cf3ba047c600f8a46aae7931f0cc4aec2e0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.0452",
    "kind": "arxiv",
    "version": 2
  }
}