Pith Number

pith:QH4KY5F6

pith:2012:QH4KY5F6H3FMXCXHHCPAE7Q427

not attested not anchored not stored refs pending

Positive margins and primary decomposition

Johannes Rauh, Seth Sullivant, Thomas Kahle

arxiv:1201.2591 v3 · 2012-01-12 · math.AC · math.CO · 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{QH4KY5F6H3FMXCXHHCPAE7Q427}

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	2026-05-18T01:17:35.451887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

81f8ac74be3ecacb8ae7389e027e1cd7c8d8bd01b050bfcd4048dc36c09c427d

Aliases

arxiv: 1201.2591 · arxiv_version: 1201.2591v3 · doi: 10.48550/arxiv.1201.2591 · pith_short_12: QH4KY5F6H3FM · pith_short_16: QH4KY5F6H3FMXCXH · pith_short_8: QH4KY5F6

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/QH4KY5F6H3FMXCXHHCPAE7Q427 \
  | 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: 81f8ac74be3ecacb8ae7389e027e1cd7c8d8bd01b050bfcd4048dc36c09c427d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f7d8369a821b21d7d1ee8305a7f3c5a4f8500758c8efb6ccd3ec7671ababf1a0",
    "cross_cats_sorted": [
      "math.CO",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2012-01-12T15:26:26Z",
    "title_canon_sha256": "b75552862dd792949bfd0836e6e39c5dbd5fe16574c9a2f6f2a590f17c09f719"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.2591",
    "kind": "arxiv",
    "version": 3
  }
}