Pith Number

pith:X3UGKU3T

pith:2016:X3UGKU3TFSA4MTO4XNZWECT6UK

not attested not anchored not stored refs pending

Extremal Relations Between Shannon Entropy and $\ell_{\alpha}$-Norm

Ken-ichi Iwata, Yuta Sakai

arxiv:1601.07678 v1 · 2016-01-28 · cs.IT · 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{X3UGKU3TFSA4MTO4XNZWECT6UK}

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	2026-05-18T01:21:42.421869Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bee86553732c81c64ddcbb73620a7ea2890e5e95fb21d0b8af8ff29b13950a4a

Aliases

arxiv: 1601.07678 · arxiv_version: 1601.07678v1 · doi: 10.48550/arxiv.1601.07678 · pith_short_12: X3UGKU3TFSA4 · pith_short_16: X3UGKU3TFSA4MTO4 · pith_short_8: X3UGKU3T

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/X3UGKU3TFSA4MTO4XNZWECT6UK \
  | 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: bee86553732c81c64ddcbb73620a7ea2890e5e95fb21d0b8af8ff29b13950a4a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6cd2d25b9ea26dede69676de2fdb71753ed19624440f0d5c8d772a6c9228a9ea",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2016-01-28T07:56:38Z",
    "title_canon_sha256": "86aa1e92ecffa04c1fc2836503e5bbdbb9dc4de58e312f443db6988def46758f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.07678",
    "kind": "arxiv",
    "version": 1
  }
}