Pith Number

pith:CGRQCNGV

pith:2021:CGRQCNGV2CM4UYNCN3ZVRNTCWN

not attested not anchored not stored refs pending

Random Walks, Spectral Gaps, and Khintchine's Theorem on Fractals

Manuel Luethi, Osama Khalil

arxiv:2101.05797 v4 · 2021-01-14 · math.DS · 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{CGRQCNGV2CM4UYNCN3ZVRNTCWN}

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	2026-07-05T05:14:54.945210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11a30134d5d099ca61a26ef358b662b3472dc11509edda10fe1c4de08cdb0722

Aliases

arxiv: 2101.05797 · arxiv_version: 2101.05797v4 · doi: 10.48550/arxiv.2101.05797 · pith_short_12: CGRQCNGV2CM4 · pith_short_16: CGRQCNGV2CM4UYNC · pith_short_8: CGRQCNGV

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/CGRQCNGV2CM4UYNCN3ZVRNTCWN \
  | 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: 11a30134d5d099ca61a26ef358b662b3472dc11509edda10fe1c4de08cdb0722

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7b739c183dedfc5734e9bbb568c7cb24da512b717ede500a730b182ade38cb01",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2021-01-14T18:58:48Z",
    "title_canon_sha256": "0f2259bfc38a89e46790dd0a7b058801f317f6af3541fd97136bf390153bc24b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.05797",
    "kind": "arxiv",
    "version": 4
  }
}