Pith Number

pith:PPBCOBQC

pith:2018:PPBCOBQCV4YXYCVBLWHBKV4MND

not attested not anchored not stored refs pending

Levelness of toric rings arising from order and chain polytopes

Akihiro Higashitani, Takayuki Hibi

arxiv:1809.08462 v3 · 2018-09-22 · math.CO · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PPBCOBQCV4YXYCVBLWHBKV4MND}

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	2026-05-17T23:57:31.267838Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7bc2270602af317c0aa15d8e15578c68f851b22734dec2ad0678bb554c9d3654

Aliases

arxiv: 1809.08462 · arxiv_version: 1809.08462v3 · doi: 10.48550/arxiv.1809.08462 · pith_short_12: PPBCOBQCV4YX · pith_short_16: PPBCOBQCV4YXYCVB · pith_short_8: PPBCOBQC

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/PPBCOBQCV4YXYCVBLWHBKV4MND \
  | 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: 7bc2270602af317c0aa15d8e15578c68f851b22734dec2ad0678bb554c9d3654

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "84f28fadfcb39b7e9d7916ba6762237277cf16f72682da96bf7eba2d1750e107",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-09-22T18:03:40Z",
    "title_canon_sha256": "6b0c95701f6714ee985938d3901c7b989910bf709ebd7c5e5c321dfcf63cdcd1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.08462",
    "kind": "arxiv",
    "version": 3
  }
}