Pith Number

pith:VDPNIGIF

pith:2018:VDPNIGIFO2RMCVJL6S6UV7RAJQ

not attested not anchored not stored refs pending

Blowup stability at optimal regularity for the critical wave equation

Roland Donninger, Ziping Rao

arxiv:1811.08130 v1 · 2018-11-20 · math.AP · math-ph · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDPNIGIFO2RMCVJL6S6UV7RAJQ}

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.

Cited by

1 paper in Pith

Strichartz estimates for the one-dimensional wave equation

Receipt and verification

First computed	2026-05-18T00:00:16.781965Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8ded4190576a2c1552bf4bd4afe204c1979a588b641c6436494a57ae27cf513

Aliases

arxiv: 1811.08130 · arxiv_version: 1811.08130v1 · doi: 10.48550/arxiv.1811.08130 · pith_short_12: VDPNIGIFO2RM · pith_short_16: VDPNIGIFO2RMCVJL · pith_short_8: VDPNIGIF

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/VDPNIGIFO2RMCVJL6S6UV7RAJQ \
  | 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: a8ded4190576a2c1552bf4bd4afe204c1979a588b641c6436494a57ae27cf513

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79d7d295d0aa60f343afdc0828368a4287e501c8bb0bbbbe2758750b451c9e83",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-11-20T09:00:56Z",
    "title_canon_sha256": "5452586dc3cecc5c850e508aeb35ec0675c153d5000088d95ed392f4e83c2508"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.08130",
    "kind": "arxiv",
    "version": 1
  }
}