Pith Number

pith:KADJA7KI

pith:2010:KADJA7KI7NJOER4DFFEF23WTEW

not attested not anchored not stored refs pending

Morawetz estimates for the wave equation at low frequency

Andr\'as Vasy, Jared Wunsch

arxiv:1011.0906 v2 · 2010-11-03 · 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{KADJA7KI7NJOER4DFFEF23WTEW}

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	2026-05-18T04:06:43.628544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5006907d48fb52e2478329485d6ed3258d3f9c66b342453873b9b9c9245a15d3

Aliases

arxiv: 1011.0906 · arxiv_version: 1011.0906v2 · doi: 10.48550/arxiv.1011.0906 · pith_short_12: KADJA7KI7NJO · pith_short_16: KADJA7KI7NJOER4D · pith_short_8: KADJA7KI

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/KADJA7KI7NJOER4DFFEF23WTEW \
  | 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: 5006907d48fb52e2478329485d6ed3258d3f9c66b342453873b9b9c9245a15d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6a94a10cff0782ace57abc2c3304f462bd457e198039726fb05c0961f6b3a02",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-11-03T15:04:24Z",
    "title_canon_sha256": "f9b5d126ad4a23a7beca929542bbd8180ce6e6f0d0bb17162ab1d848594c4ba5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.0906",
    "kind": "arxiv",
    "version": 2
  }
}