Pith Number

pith:QGDC5LZI

pith:2026:QGDC5LZITEZ5HDN5IEWDUDADFZ

not attested not anchored not stored refs pending

Weyl's laws and Connes' Trace Theorem for operator-valued pseudo-differential operators

Edward McDonald, Xiao Xiong, Xinyu Zhang

arxiv:2605.19239 v1 · 2026-05-19 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QGDC5LZITEZ5HDN5IEWDUDADFZ}

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	2026-05-20T01:05:35.250427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81862eaf289933d38dbd412c3a0c032e6f0a36a6b4974b8cf7c9a81f647e5a20

Aliases

arxiv: 2605.19239 · arxiv_version: 2605.19239v1 · doi: 10.48550/arxiv.2605.19239 · pith_short_12: QGDC5LZITEZ5 · pith_short_16: QGDC5LZITEZ5HDN5 · pith_short_8: QGDC5LZI

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/QGDC5LZITEZ5HDN5IEWDUDADFZ \
  | 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: 81862eaf289933d38dbd412c3a0c032e6f0a36a6b4974b8cf7c9a81f647e5a20

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5ef734d37dc7fc1ea3709dfe4ccd466db0bd5e41a7c83f1eb6d32fcd54cc41c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2026-05-19T01:15:49Z",
    "title_canon_sha256": "fe738a3ac65ac586e8181415e17b0375f516148b384e26dfa867ce93df142574"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19239",
    "kind": "arxiv",
    "version": 1
  }
}