Pith Number

pith:GRAA2NTJ

pith:2012:GRAA2NTJI4PB4FKHQW7XOPCYKP

not attested not anchored not stored refs pending

The dichotomy of recurrence and transience of semi-Levy processes

Makoto Maejima, Taisuke Takamune, Yohei Ueda

arxiv:1209.3838 v1 · 2012-09-18 · 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{GRAA2NTJI4PB4FKHQW7XOPCYKP}

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	2026-05-18T03:45:22.392168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34400d3669471e1e154785bf773c5853c2ee4e567927e5f75296f2317fb39de8

Aliases

arxiv: 1209.3838 · arxiv_version: 1209.3838v1 · doi: 10.48550/arxiv.1209.3838 · pith_short_12: GRAA2NTJI4PB · pith_short_16: GRAA2NTJI4PB4FKH · pith_short_8: GRAA2NTJ

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/GRAA2NTJI4PB4FKHQW7XOPCYKP \
  | 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: 34400d3669471e1e154785bf773c5853c2ee4e567927e5f75296f2317fb39de8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de7fd8b3d2710a5340400e42f0bf16a7b47bafe65574f50ccb4aed0b479a5572",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-09-18T03:43:31Z",
    "title_canon_sha256": "a152245873bb441446ac97c32264ad8b29cf6ae1731cb48fed81f26ed45d6c0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3838",
    "kind": "arxiv",
    "version": 1
  }
}