Pith Number

pith:MZMENYU7

pith:2011:MZMENYU776ARV6WCLGMD6WG7N5

not attested not anchored not stored refs pending

Markov Approximations of chains of infinite order in the $\bar{d}$-metric

Daniel Yasumasa Takahashi, Matthieu Lerasle, Sandro Gallo

arxiv:1107.4353 v2 · 2011-07-21 · 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{MZMENYU776ARV6WCLGMD6WG7N5}

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	2026-05-18T04:04:43.618299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

665846e29fff811afac259983f58df6f78e7083f3fd2cae5f3c661f3f5c78fa5

Aliases

arxiv: 1107.4353 · arxiv_version: 1107.4353v2 · doi: 10.48550/arxiv.1107.4353 · pith_short_12: MZMENYU776AR · pith_short_16: MZMENYU776ARV6WC · pith_short_8: MZMENYU7

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/MZMENYU776ARV6WCLGMD6WG7N5 \
  | 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: 665846e29fff811afac259983f58df6f78e7083f3fd2cae5f3c661f3f5c78fa5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e13b6afdeb2e1c19b41817c75233ced9c2fc4128b25fcbd6664bf0601873547",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-21T19:50:31Z",
    "title_canon_sha256": "b40b41041eb72fd535b48337c543693f202bd8079a934be952d1e20b4509ab0e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.4353",
    "kind": "arxiv",
    "version": 2
  }
}