Pith Number

pith:BHIKHJY6

pith:2013:BHIKHJY6PWLHL2W3YVZO6OHIET

not attested not anchored not stored refs pending

Markov bases and generalized Lawrence liftings

Apostolos Thoma, Hara Charalambous, Marius Vladoiu

arxiv:1304.4257 v3 · 2013-04-15 · math.AC · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BHIKHJY6PWLHL2W3YVZO6OHIET}

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	2026-05-18T01:30:49.513825Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

09d0a3a71e7d9675eadbc572ef38e824ea997db4055d99d2af2b11644ea5f463

Aliases

arxiv: 1304.4257 · arxiv_version: 1304.4257v3 · doi: 10.48550/arxiv.1304.4257 · pith_short_12: BHIKHJY6PWLH · pith_short_16: BHIKHJY6PWLHL2W3 · pith_short_8: BHIKHJY6

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/BHIKHJY6PWLHL2W3YVZO6OHIET \
  | 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: 09d0a3a71e7d9675eadbc572ef38e824ea997db4055d99d2af2b11644ea5f463

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3fef1a4df751ab2593bc6b66589b9ae5be5f659b523aac98ac9fb33e1bc40c4",
    "cross_cats_sorted": [
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2013-04-15T20:26:39Z",
    "title_canon_sha256": "2261be7115f218629b37831fa85e576b3fce8cbafcd1e297acc42e9f0b2553a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1304.4257",
    "kind": "arxiv",
    "version": 3
  }
}