Pith Number

pith:E63PR4UL

pith:2012:E63PR4ULB5OOXHXHE3562C7OCJ

not attested not anchored not stored refs pending

When Does a Mixture of Products Contain a Product of Mixtures?

Guido F. Montufar, Jason Morton

arxiv:1206.0387 v5 · 2012-06-02 · stat.ML · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{E63PR4ULB5OOXHXHE3562C7OCJ}

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	2026-05-18T02:42:29.230173Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

27b6f8f28b0f5ceb9ee726fbed0bee125fb10d6ee3953782f94a037f5926fd12

Aliases

arxiv: 1206.0387 · arxiv_version: 1206.0387v5 · doi: 10.48550/arxiv.1206.0387 · pith_short_12: E63PR4ULB5OO · pith_short_16: E63PR4ULB5OOXHXH · pith_short_8: E63PR4UL

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/E63PR4ULB5OOXHXHE3562C7OCJ \
  | 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: 27b6f8f28b0f5ceb9ee726fbed0bee125fb10d6ee3953782f94a037f5926fd12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfc41917ebfe88fd79ef4ae747cff4e9065dc448c1678f670279f42dc541f1ab",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2012-06-02T14:48:30Z",
    "title_canon_sha256": "46184e16be472c24b7eeda4a67ba2f618ce40cd46a37e907fd4722bd332e5641"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0387",
    "kind": "arxiv",
    "version": 5
  }
}