Pith Number

pith:VDMLBNZO

pith:2016:VDMLBNZOAZVMV3MOYWE3RCZHUL

not attested not anchored not stored refs pending

Spectral decomposition of fractional operators and a reflected stable semigroup

Pierre Patie, Yixuan Zhao

arxiv:1606.04034 v2 · 2016-06-13 · math.PR · math.FA · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VDMLBNZOAZVMV3MOYWE3RCZHUL}

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	2026-05-17T23:45:10.285632Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8d8b0b72e066acaed8ec589b88b27a2efadcf7a89635fdaa1cf5d63e5dec48a

Aliases

arxiv: 1606.04034 · arxiv_version: 1606.04034v2 · doi: 10.48550/arxiv.1606.04034 · pith_short_12: VDMLBNZOAZVM · pith_short_16: VDMLBNZOAZVMV3MO · pith_short_8: VDMLBNZO

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/VDMLBNZOAZVMV3MOYWE3RCZHUL \
  | 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: a8d8b0b72e066acaed8ec589b88b27a2efadcf7a89635fdaa1cf5d63e5dec48a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd23a55aaded6ca98b2cf0717cc1a236d918c20a2afadc3a9cbe3d183c369bc8",
    "cross_cats_sorted": [
      "math.FA",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-06-13T17:02:16Z",
    "title_canon_sha256": "a77d22a738ddc740279aebcb4b995539f5d4fe960f848d19e5cc0a582ba517b7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1606.04034",
    "kind": "arxiv",
    "version": 2
  }
}