Pith Number

pith:6ITMCBHU

pith:2013:6ITMCBHUWGM7LV5E5CNGSSQLAP

not attested not anchored not stored refs pending

Entropy and sampling numbers of classes of ridge functions

Jan Vybiral, Sebastian Mayer, Tino Ullrich

arxiv:1311.2005 v1 · 2013-11-08 · math.NA · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6ITMCBHUWGM7LV5E5CNGSSQLAP}

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	2026-05-18T03:07:41.762405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f226c104f4b199f5d7a4e89a694a0b03d314604ec6d4d6bfbf09b74dc984920b

Aliases

arxiv: 1311.2005 · arxiv_version: 1311.2005v1 · doi: 10.48550/arxiv.1311.2005 · pith_short_12: 6ITMCBHUWGM7 · pith_short_16: 6ITMCBHUWGM7LV5E · pith_short_8: 6ITMCBHU

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/6ITMCBHUWGM7LV5E5CNGSSQLAP \
  | 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: f226c104f4b199f5d7a4e89a694a0b03d314604ec6d4d6bfbf09b74dc984920b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "325e3a435274366108b2e8fcbab63c06d5cafef621251a3e8bedcf1a323bea01",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-11-08T15:56:58Z",
    "title_canon_sha256": "c9b39ce13b0a990b621a4f4628aa93806ca81052af53730a6d2f74cb4d87e1c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.2005",
    "kind": "arxiv",
    "version": 1
  }
}