Pith Number

pith:X5W4DQ2F

pith:2011:X5W4DQ2FLHEQJ4MXOLIQK6SKED

not attested not anchored not stored refs pending

Multifractal analysis of Bernoulli convolutions associated with Salem numbers

De-Jun Feng

arxiv:1111.2414 v1 · 2011-11-10 · math.CA · 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{X5W4DQ2FLHEQJ4MXOLIQK6SKED}

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	2026-05-18T04:08:34.225502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf6dc1c34559c904f19772d1057a4a20edaab275c030464db11206a6fec40b10

Aliases

arxiv: 1111.2414 · arxiv_version: 1111.2414v1 · doi: 10.48550/arxiv.1111.2414 · pith_short_12: X5W4DQ2FLHEQ · pith_short_16: X5W4DQ2FLHEQJ4MX · pith_short_8: X5W4DQ2F

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/X5W4DQ2FLHEQJ4MXOLIQK6SKED \
  | 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: bf6dc1c34559c904f19772d1057a4a20edaab275c030464db11206a6fec40b10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "130bcf9fcb7fb4616cbcd1b648470be4795f9997411f513cf51a796739f7296f",
    "cross_cats_sorted": [
      "math.DS",
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-11-10T08:16:54Z",
    "title_canon_sha256": "2b0bd680675ba3fc7abc6b3fc4d312a6bc8186aea5d8a3cb5b5e26bc44030e48"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.2414",
    "kind": "arxiv",
    "version": 1
  }
}