Pith Number

pith:VMQK26HO

pith:2013:VMQK26HO3IKJZIPEJQGFM347R6

not attested not anchored not stored refs pending

Using multiobjective optimization to map the entropy region of four random variables

Laszlo Csirmaz

arxiv:1310.4638 v2 · 2013-10-17 · 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{VMQK26HO3IKJZIPEJQGFM347R6}

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	2026-05-18T03:08:46.597867Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab20ad78eeda149ca1e44c0c566f9f8fa5c1e690f1c7461556769d2751cb05ef

Aliases

arxiv: 1310.4638 · arxiv_version: 1310.4638v2 · doi: 10.48550/arxiv.1310.4638 · pith_short_12: VMQK26HO3IKJ · pith_short_16: VMQK26HO3IKJZIPE · pith_short_8: VMQK26HO

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/VMQK26HO3IKJZIPEJQGFM347R6 \
  | 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: ab20ad78eeda149ca1e44c0c566f9f8fa5c1e690f1c7461556769d2751cb05ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0134225b1ae9f043da16ccafd26cb08116c59cc5cab2c50b96bc8a04d1dc67a0",
    "cross_cats_sorted": [
      "math.IT",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2013-10-17T09:46:19Z",
    "title_canon_sha256": "22ea455b57439100a48224207cd2b46b7c215ba18ca5184e2ef42e9057ac9378"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.4638",
    "kind": "arxiv",
    "version": 2
  }
}