Pith Number

pith:F27TIM4F

pith:2012:F27TIM4FOBNKMAN5VRUHAPTS27

not attested not anchored not stored refs pending

Multifractal behavior of polynomial Fourier series

Adri\'an Ubis, Fernando Chamizo

arxiv:1208.6533 v1 · 2012-08-31 · math.NT · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F27TIM4FOBNKMAN5VRUHAPTS27}

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	2026-05-18T03:46:32.711441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ebf343385705aa601bdac68703e72d7c818d0cf4015f10b30fb8b12b2c7ceed

Aliases

arxiv: 1208.6533 · arxiv_version: 1208.6533v1 · doi: 10.48550/arxiv.1208.6533 · pith_short_12: F27TIM4FOBNK · pith_short_16: F27TIM4FOBNKMAN5 · pith_short_8: F27TIM4F

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/F27TIM4FOBNKMAN5VRUHAPTS27 \
  | 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: 2ebf343385705aa601bdac68703e72d7c818d0cf4015f10b30fb8b12b2c7ceed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "655432315c981da4710a80d0c35877de981c2cd99266c901b4756f198c24eb1d",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-08-31T15:54:17Z",
    "title_canon_sha256": "e5337c2681bb23e63506f2e4cf728aacb015595b5fc0506257e080b4da6b84a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.6533",
    "kind": "arxiv",
    "version": 1
  }
}