Pith Number

pith:TUG73VEI

pith:2015:TUG73VEIYLCSIPGUK3M3Z4LY2W

not attested not anchored not stored refs pending

Microlocal properties of Shubin pseudodifferential and localization operators

Patrik Wahlberg, Ren\'e Schulz

arxiv:1508.02331 v2 · 2015-08-10 · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TUG73VEIYLCSIPGUK3M3Z4LY2W}

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	2026-05-18T01:34:56.797412Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d0dfdd488c2c5243cd456d9bcf178d5a0a82c7b31d5846f6f1a69bd2eedd0f2

Aliases

arxiv: 1508.02331 · arxiv_version: 1508.02331v2 · doi: 10.48550/arxiv.1508.02331 · pith_short_12: TUG73VEIYLCS · pith_short_16: TUG73VEIYLCSIPGU · pith_short_8: TUG73VEI

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/TUG73VEIYLCSIPGUK3M3Z4LY2W \
  | 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: 9d0dfdd488c2c5243cd456d9bcf178d5a0a82c7b31d5846f6f1a69bd2eedd0f2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "999e33b8978c3ca1ec4272c8e98577ed3036ae6f91338918019dc63d5ab7a356",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-08-10T17:39:03Z",
    "title_canon_sha256": "f4bfaadd734598b04025ba36d90c060b51e086a0aa862ecc0ae1cec9b25fcfad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.02331",
    "kind": "arxiv",
    "version": 2
  }
}