Pith Number

pith:WXKKJV5E

pith:2017:WXKKJV5EQYS2VM2NIMZWEQR4XK

not attested not anchored not stored refs pending

$L^p$-$L^q$ estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data

Mamoru Okamoto, Masahiro Ikeda, Takahisa Inui, Yuta Wakasugi

arxiv:1710.06538 v2 · 2017-10-18 · 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{WXKKJV5EQYS2VM2NIMZWEQR4XK}

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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	2026-05-17T23:51:26.196863Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5d4a4d7a48625aab34d433362423cbaa73e52b985a5bea2e0033215970b6f6d

Aliases

arxiv: 1710.06538 · arxiv_version: 1710.06538v2 · doi: 10.48550/arxiv.1710.06538 · pith_short_12: WXKKJV5EQYS2 · pith_short_16: WXKKJV5EQYS2VM2N · pith_short_8: WXKKJV5E

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/WXKKJV5EQYS2VM2NIMZWEQR4XK \
  | 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: b5d4a4d7a48625aab34d433362423cbaa73e52b985a5bea2e0033215970b6f6d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e66fa434b4c475b2c81000e171dc7897504f6e14ad94aec7191e17d3acf686fe",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-10-18T00:38:31Z",
    "title_canon_sha256": "2522507e27ae27dfc37df46813bd31249a80ee7faa6f281f39d3cd5fdba5202b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.06538",
    "kind": "arxiv",
    "version": 2
  }
}