Pith Number

pith:LW6CIK6X

pith:2015:LW6CIK6XQYV7NX3OQWXX2TVMWY

not attested not anchored not stored refs pending

Mixing time for the random walk on the range of the random walk on tori

Artem Sapozhnikov, Ji\v{r}\'i \v{C}ern\'y

arxiv:1512.02790 v1 · 2015-12-09 · 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{LW6CIK6XQYV7NX3OQWXX2TVMWY}

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	2026-05-18T01:24:43.141740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5dbc242bd7862bf6df6e85af7d4eacb633299ccc52e7a92ce2c44811edae3926

Aliases

arxiv: 1512.02790 · arxiv_version: 1512.02790v1 · doi: 10.48550/arxiv.1512.02790 · pith_short_12: LW6CIK6XQYV7 · pith_short_16: LW6CIK6XQYV7NX3O · pith_short_8: LW6CIK6X

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/LW6CIK6XQYV7NX3OQWXX2TVMWY \
  | 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: 5dbc242bd7862bf6df6e85af7d4eacb633299ccc52e7a92ce2c44811edae3926

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "140ea49bf4ea68986a2285435edc93d00989c6cda35b4ef54faa585ad5cac6f8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-09T08:53:29Z",
    "title_canon_sha256": "80cb02ee52db7d004f340284ae01e13d81b26005f162819f62a619ce279641ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02790",
    "kind": "arxiv",
    "version": 1
  }
}