Pith Number

pith:MHBUDQPW

pith:2021:MHBUDQPWZ55BQM37JG2OOIUMQA

not attested not anchored not stored refs pending

Mixing time of fractional random walk on finite fields

Huy Tuan Pham, Jimmy He, Max Wenqiang Xu

arxiv:2102.02781 v3 · 2021-02-04 · math.PR · math.CO · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MHBUDQPWZ55BQM37JG2OOIUMQA}

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	2026-07-05T02:22:25.556887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61c341c1f6cf7a18337f49b4e7228c803a0e1ce24ac620a0af536c97ea602e53

Aliases

arxiv: 2102.02781 · arxiv_version: 2102.02781v3 · doi: 10.48550/arxiv.2102.02781 · pith_short_12: MHBUDQPWZ55B · pith_short_16: MHBUDQPWZ55BQM37 · pith_short_8: MHBUDQPW

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/MHBUDQPWZ55BQM37JG2OOIUMQA \
  | 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: 61c341c1f6cf7a18337f49b4e7228c803a0e1ce24ac620a0af536c97ea602e53

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6c35a77e74ffa7c6a7a2c4433299221c7fd956733aa08d132856459191294bbb",
    "cross_cats_sorted": [
      "math.CO",
      "math.GR",
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2021-02-04T18:00:34Z",
    "title_canon_sha256": "ce8738051da655f3c979a4788ae79067906ebc490fcc96ebe2ea966eb7b4d18e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2102.02781",
    "kind": "arxiv",
    "version": 3
  }
}