Pith Number

pith:M5NC4GAH

pith:2008:M5NC4GAHW6IQRKR2VK2XNAOXY2

not attested not anchored not stored refs pending

A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains

Martin Nilsson Jacobi

arxiv:0810.1127 v3 · 2008-10-07 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M5NC4GAHW6IQRKR2VK2XNAOXY2}

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	2026-06-03T22:06:10.551763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

675a2e1807b79108aa3aaab57681d7c6b3a49e04e8182cff507624ba06310efa

Aliases

arxiv: 0810.1127 · arxiv_version: 0810.1127v3 · doi: 10.48550/arxiv.0810.1127 · pith_short_12: M5NC4GAHW6IQ · pith_short_16: M5NC4GAHW6IQRKR2 · pith_short_8: M5NC4GAH

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/M5NC4GAHW6IQRKR2VK2XNAOXY2 \
  | 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: 675a2e1807b79108aa3aaab57681d7c6b3a49e04e8182cff507624ba06310efa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea3e73ea9ae21b8222749796f94aab8a3f838d2656ed4774db548d8198c7e3df",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2008-10-07T09:11:49Z",
    "title_canon_sha256": "68cdf3e0b3fe437ed4959214633f1803056fca50f668cf53d719c879999a0cfe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.1127",
    "kind": "arxiv",
    "version": 3
  }
}