Pith Number

pith:7GE6VEMP

pith:2008:7GE6VEMPAWRJQTOL2UJBLQOU6W

not attested not anchored not stored refs pending

On the Log-Concavity of Hilbert Series of Veronese Subrings and Ehrhart Series

Alan Stapledon, Matthias Beck

arxiv:0804.3639 v3 · 2008-04-23 · 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{7GE6VEMPAWRJQTOL2UJBLQOU6W}

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	2026-05-18T04:41:36.884475Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f989ea918f05a2984dcbd51215c1d4f59f0d8c623bfb09503aa3e0687d0738ef

Aliases

arxiv: 0804.3639 · arxiv_version: 0804.3639v3 · doi: 10.48550/arxiv.0804.3639 · pith_short_12: 7GE6VEMPAWRJ · pith_short_16: 7GE6VEMPAWRJQTOL · pith_short_8: 7GE6VEMP

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/7GE6VEMPAWRJQTOL2UJBLQOU6W \
  | 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: f989ea918f05a2984dcbd51215c1d4f59f0d8c623bfb09503aa3e0687d0738ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4dc8e797934d18ee7e87752532953996f291f3dc5ef96f883da684dcff734cb7",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2008-04-23T04:20:32Z",
    "title_canon_sha256": "c90b4461e74355d34a3bc89cc6f5fea8e9f92f0854d144862c709ad1c8ef7e90"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0804.3639",
    "kind": "arxiv",
    "version": 3
  }
}