Pith Number

pith:A76BA47V

pith:2026:A76BA47VQ5E32SRMCHSFSRAPTK

not attested not anchored not stored refs pending

Quantitative Spectral Rigidity and Finite-Time Spectral Thermodynamics in Reversible Markov Chains

Qiao Wang

arxiv:2605.17082 v1 · 2026-05-16 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A76BA47VQ5E32SRMCHSFSRAPTK}

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	2026-05-20T00:03:39.511150Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07fc1073f58749bd4a2c11e459440f9a89cd6d107939282b868fe4896cfdd6bd

Aliases

arxiv: 2605.17082 · arxiv_version: 2605.17082v1 · doi: 10.48550/arxiv.2605.17082 · pith_short_12: A76BA47VQ5E3 · pith_short_16: A76BA47VQ5E32SRM · pith_short_8: A76BA47V

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/A76BA47VQ5E32SRMCHSFSRAPTK \
  | 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: 07fc1073f58749bd4a2c11e459440f9a89cd6d107939282b868fe4896cfdd6bd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d29e53e277e295ccd313a2ea3f8083f44136ec3f8d00b8f43f85dddbb9a8224d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-05-16T16:58:23Z",
    "title_canon_sha256": "60fbef0b4b80d44cc0ef83e2c1f1480c7104326d18764f357f62707cb70b0cc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17082",
    "kind": "arxiv",
    "version": 1
  }
}