Pith Number

pith:VBT5QSY4

pith:2017:VBT5QSY4ZUS33EV2QPP5QAQWYP

not attested not anchored not stored refs pending

The spectral expansion approach to index transforms and connections with the theory of diffusion processes

R\'uben Sousa, Semyon Yakubovich

arxiv:1706.05194 v1 · 2017-06-16 · math.CA · math.PR · 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{VBT5QSY4ZUS33EV2QPP5QAQWYP}

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	2026-05-18T00:13:11.134377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a867d84b1ccd25bd92ba83dfd80216c3ea0f0d55a39d97f95d7121c81f2fe1ad

Aliases

arxiv: 1706.05194 · arxiv_version: 1706.05194v1 · doi: 10.48550/arxiv.1706.05194 · pith_short_12: VBT5QSY4ZUS3 · pith_short_16: VBT5QSY4ZUS33EV2 · pith_short_8: VBT5QSY4

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/VBT5QSY4ZUS33EV2QPP5QAQWYP \
  | 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: a867d84b1ccd25bd92ba83dfd80216c3ea0f0d55a39d97f95d7121c81f2fe1ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b9c68acde049537bfbd39c32c8faa9c541710fafd42765ebbddc6e264fe1b40",
    "cross_cats_sorted": [
      "math.PR",
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-06-16T09:40:39Z",
    "title_canon_sha256": "443d4b5440eff941123b0f86ed87e65ccfd18313a53834107689744b7336127e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.05194",
    "kind": "arxiv",
    "version": 1
  }
}