Pith Number

pith:XF4UPUM7

pith:2011:XF4UPUM7CD4NY7PQVTTGNE6AJ2

not attested not anchored not stored refs pending

A Metric Between Probability Distributions on Finite Sets of Different Cardinalities and Applications to Order Reduction

Mathukumalli Vidyasagar

arxiv:1104.4521 v2 · 2011-04-23 · cs.SY · cs.IT · math.IT · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XF4UPUM7CD4NY7PQVTTGNE6AJ2}

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	2026-05-18T02:22:01.209611Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b97947d19f10f8dc7df0ace66693c04ea5186e25e973a93b7d3620583775dc3d

Aliases

arxiv: 1104.4521 · arxiv_version: 1104.4521v2 · doi: 10.48550/arxiv.1104.4521 · pith_short_12: XF4UPUM7CD4N · pith_short_16: XF4UPUM7CD4NY7PQ · pith_short_8: XF4UPUM7

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/XF4UPUM7CD4NY7PQVTTGNE6AJ2 \
  | 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: b97947d19f10f8dc7df0ace66693c04ea5186e25e973a93b7d3620583775dc3d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bef68f4b05068c5fbfc162102153c90b32a7e6abbea6a8f477973824f5c36f3e",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SY",
    "submitted_at": "2011-04-23T00:15:17Z",
    "title_canon_sha256": "094e82f244d8bff9aaeda43df68d6fc91444652dc566b0c4ad9ad090bbf35d71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.4521",
    "kind": "arxiv",
    "version": 2
  }
}