Pith Number

pith:CFJKL72P

pith:2017:CFJKL72P72533VSHN4WPVRSSHL

not attested not anchored not stored refs pending

Wave decay for star-shaped obstacles in $\mathbb{R}^3$: papers of Morawetz and Ralston revisited

Maciej Zworski, Peter Hintz

arxiv:1703.01389 v1 · 2017-03-04 · math.SP · math-ph · math.AP · 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{CFJKL72P72533VSHN4WPVRSSHL}

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	2026-05-18T00:49:30.917636Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1152a5ff4ffebbbdd6476f2cfac6523af357979a53b0c86deefe7622a3121cd5

Aliases

arxiv: 1703.01389 · arxiv_version: 1703.01389v1 · doi: 10.48550/arxiv.1703.01389 · pith_short_12: CFJKL72P7253 · pith_short_16: CFJKL72P72533VSH · pith_short_8: CFJKL72P

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/CFJKL72P72533VSHN4WPVRSSHL \
  | 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: 1152a5ff4ffebbbdd6476f2cfac6523af357979a53b0c86deefe7622a3121cd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bff3565ff99d3dc0c44acaa148bfe05aefa00eae61e0f2000ad35c4d45223b5c",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2017-03-04T03:13:23Z",
    "title_canon_sha256": "ec751c04626732c0fca0ad6017366e15efbc1bc40a6a673cb23727a56c337b0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1703.01389",
    "kind": "arxiv",
    "version": 1
  }
}