Pith Number

pith:VZYI663U

pith:2026:VZYI663UJZH6SBCKFM5NNK6EN4

not attested not anchored not stored refs pending

Singular-value gap of nonreversible Markov processes

Ruochuan Xu

arxiv:2606.01683 v1 · 2026-06-01 · 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{VZYI663UJZH6SBCKFM5NNK6EN4}

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	2026-06-02T02:04:40.009402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae708f7b744e4fe9044a2b3ad6abc46f1c25dfc7db0b59e06a3e234e20089a37

Aliases

arxiv: 2606.01683 · arxiv_version: 2606.01683v1 · doi: 10.48550/arxiv.2606.01683 · pith_short_12: VZYI663UJZH6 · pith_short_16: VZYI663UJZH6SBCK · pith_short_8: VZYI663U

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/VZYI663UJZH6SBCKFM5NNK6EN4 \
  | 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: ae708f7b744e4fe9044a2b3ad6abc46f1c25dfc7db0b59e06a3e234e20089a37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c96d3b545190d4aad7d57c7babcaac8bc13f7f55c133536f2204039b3e637cae",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-01T04:49:03Z",
    "title_canon_sha256": "e6434aae2b7cf106208595130fbee969cc6f1e2e304214aebd6715ca2be5d849"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.01683",
    "kind": "arxiv",
    "version": 1
  }
}