Pith Number

pith:V3XZJBRL

pith:2016:V3XZJBRLPLHOEGXZ22MQRBY2GH

not attested not anchored not stored refs pending

The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions

Hiroyuki Takamura, Kyouhei Wakasa, Masakazu Kato, Takuto Imai

arxiv:1610.05913 v2 · 2016-10-19 · 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{V3XZJBRLPLHOEGXZ22MQRBY2GH}

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	2026-05-18T00:46:39.389833Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aeef94862b7acee21af9d69908871a31e70f656dd64eefcdf755ff0c4397d57a

Aliases

arxiv: 1610.05913 · arxiv_version: 1610.05913v2 · doi: 10.48550/arxiv.1610.05913 · pith_short_12: V3XZJBRLPLHO · pith_short_16: V3XZJBRLPLHOEGXZ · pith_short_8: V3XZJBRL

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/V3XZJBRLPLHOEGXZ22MQRBY2GH \
  | 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: aeef94862b7acee21af9d69908871a31e70f656dd64eefcdf755ff0c4397d57a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7c12d08c81644f65b2de93fdeccef4284338fce79960980d68f9676e1dce6fb8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-10-19T08:50:54Z",
    "title_canon_sha256": "0b102cce990c3ba02c43f1978f63cdd6d92ecb942629a1975da46540b1db593b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.05913",
    "kind": "arxiv",
    "version": 2
  }
}