Pith Number

pith:DR7JSM4X

pith:2011:DR7JSM4XJARXQZXZCUU3FTX6UU

not attested not anchored not stored refs pending

Hausdorff dimension for fractals invariant under the multiplicative integers

Boris Solomyak, Richard Kenyon, Yuval Peres

arxiv:1102.5136 v2 · 2011-02-25 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DR7JSM4XJARXQZXZCUU3FTX6UU}

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	2026-05-18T00:24:10.763387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c7e99339748237866f91529b2cefea53f7517a014b2f26741b8ba5968977d71

Aliases

arxiv: 1102.5136 · arxiv_version: 1102.5136v2 · doi: 10.48550/arxiv.1102.5136 · pith_short_12: DR7JSM4XJARX · pith_short_16: DR7JSM4XJARXQZXZ · pith_short_8: DR7JSM4X

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/DR7JSM4XJARXQZXZCUU3FTX6UU \
  | 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: 1c7e99339748237866f91529b2cefea53f7517a014b2f26741b8ba5968977d71

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed0ba23fcfe7d4ea162b6893e6b74aaa1af751eecef0ce8e5b3b1c15b63b2461",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-02-25T01:38:46Z",
    "title_canon_sha256": "176fc398b8a8c2738e790823c3152c4386a4ee850ddfaa60fa02c4f19e0e51b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.5136",
    "kind": "arxiv",
    "version": 2
  }
}