Pith Number

pith:NQUE46WG

pith:2011:NQUE46WGDBZZX3Z6PHNDVDPAOG

not attested not anchored not stored refs pending

Commuting time geometry of ergodic Markov chains

Jean Steiner, Peter G. Doyle

arxiv:1107.2612 v2 · 2011-07-13 · 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{NQUE46WGDBZZX3Z6PHNDVDPAOG}

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	2026-05-18T00:31:59.717371Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6c284e7ac618739bef3e79da3a8de0718907ddd5e7bfa472df5ebd986e01e773

Aliases

arxiv: 1107.2612 · arxiv_version: 1107.2612v2 · doi: 10.48550/arxiv.1107.2612 · pith_short_12: NQUE46WGDBZZ · pith_short_16: NQUE46WGDBZZX3Z6 · pith_short_8: NQUE46WG

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/NQUE46WGDBZZX3Z6PHNDVDPAOG \
  | 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: 6c284e7ac618739bef3e79da3a8de0718907ddd5e7bfa472df5ebd986e01e773

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc7dad64dbe00896b9f0a5562233885143b6eb3402d054921dc729324a815c1b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-13T17:36:17Z",
    "title_canon_sha256": "acd9f10c569cf364283f950d2d13347fc389bfbf944442050577a27d3e2baf52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2612",
    "kind": "arxiv",
    "version": 2
  }
}