Pith Number

pith:XFR3KJK6

pith:2014:XFR3KJK63J7OU33D5MAS72M34W

not attested not anchored not stored refs pending

Asymptotics of the geometric mean error for in-homogeneous self-similar measures

Sanguo Zhu, Yongjian Sheng, Youming Zhou

arxiv:1411.3359 v1 · 2014-10-23 · math.DS · cs.IT · math.FA · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XFR3KJK63J7OU33D5MAS72M34W}

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	2026-05-18T02:37:43.981304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b963b5255eda7eea6f63eb012fe99be5aa3d95eca276f029840eb93548780f5f

Aliases

arxiv: 1411.3359 · arxiv_version: 1411.3359v1 · doi: 10.48550/arxiv.1411.3359 · pith_short_12: XFR3KJK63J7O · pith_short_16: XFR3KJK63J7OU33D · pith_short_8: XFR3KJK6

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/XFR3KJK63J7OU33D5MAS72M34W \
  | 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: b963b5255eda7eea6f63eb012fe99be5aa3d95eca276f029840eb93548780f5f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14c1f92bf2615d3e4cbb281f1155278e524be6872c103542f529938e1c40f700",
    "cross_cats_sorted": [
      "cs.IT",
      "math.FA",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-10-23T06:54:52Z",
    "title_canon_sha256": "fc43fa68034d980d674798ea5f4f78ed340fbde9f1351399ee9828cd3043b734"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1411.3359",
    "kind": "arxiv",
    "version": 1
  }
}