Pith Number

pith:XXEOPFLC

pith:2015:XXEOPFLCBYPNQDNYCHDSMBWOXQ

not attested not anchored not stored refs pending

Spectral analysis of random-to-random Markov chains

A. B. Dieker, Franco Saliola

arxiv:1509.08580 v3 · 2015-09-29 · math.CO · math.PR · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XXEOPFLCBYPNQDNYCHDSMBWOXQ}

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	2026-05-18T00:34:00.261346Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdc8e795620e1ed80db811c72606cebc151cf24e54d4ade88366f22760ac7680

Aliases

arxiv: 1509.08580 · arxiv_version: 1509.08580v3 · doi: 10.48550/arxiv.1509.08580 · pith_short_12: XXEOPFLCBYPN · pith_short_16: XXEOPFLCBYPNQDNY · pith_short_8: XXEOPFLC

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/XXEOPFLCBYPNQDNYCHDSMBWOXQ \
  | 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: bdc8e795620e1ed80db811c72606cebc151cf24e54d4ade88366f22760ac7680

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a51a40bcab6b1a337bb9dbe3e8f3f87b1904964e8d62c9aa07808ccbb927c87",
    "cross_cats_sorted": [
      "math.PR",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-29T03:31:21Z",
    "title_canon_sha256": "87c7fbf245bf6255f6bf36fa37dce3b3fbf4afe14cdf7fd3aea9a0683055dbc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.08580",
    "kind": "arxiv",
    "version": 3
  }
}