Pith Number

pith:32ZR5IKN

pith:2011:32ZR5IKNQBYRX42GBVUZ3TVGBH

not attested not anchored not stored refs pending

Log-concavity of face vectors of cyclic and ordinary polytopes

Laszlo Major

arxiv:1112.1713 v1 · 2011-12-07 · 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{32ZR5IKNQBYRX42GBVUZ3TVGBH}

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	2026-05-18T04:06:45.816668Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

deb31ea14d80711bf3460d699dcea609cc24b41da513958492837ca4b2aeb5a0

Aliases

arxiv: 1112.1713 · arxiv_version: 1112.1713v1 · doi: 10.48550/arxiv.1112.1713 · pith_short_12: 32ZR5IKNQBYR · pith_short_16: 32ZR5IKNQBYRX42G · pith_short_8: 32ZR5IKN

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/32ZR5IKNQBYRX42GBVUZ3TVGBH \
  | 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: deb31ea14d80711bf3460d699dcea609cc24b41da513958492837ca4b2aeb5a0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1672fe00a69a3eef693e8a7224fed3bc38d528ffb8c0ed61c8a5003f4f0d457",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2011-12-07T22:00:36Z",
    "title_canon_sha256": "91a53ed18edfd9ad9fe8394296d2ad42fd8e2800f9c2acea0a046e003e0321f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.1713",
    "kind": "arxiv",
    "version": 1
  }
}