Pith Number

pith:P3WHYL5K

pith:2024:P3WHYL5KVTVVNAGAX3BA7RTKPO

not attested not anchored not stored refs pending

Gamma vectors of partitioned permutohedra

John Shareshian, Jongbaek Song, Mikiya Masuda, Takashi Sato, Tatsuya Horiguchi

arxiv:2405.09242 v2 · 2024-05-15 · math.CO · math.AG · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{P3WHYL5KVTVVNAGAX3BA7RTKPO}

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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.

Cited by

1 paper in Pith

Order polytopes of graded posets are gamma-effective

Receipt and verification

First computed	2026-07-05T10:56:06.240439Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7eec7c2faaaceb5680c0bec20fc66a7bb7f0cc7d93692972c34cd9a960b47d1f

Aliases

arxiv: 2405.09242 · arxiv_version: 2405.09242v2 · doi: 10.48550/arxiv.2405.09242 · pith_short_12: P3WHYL5KVTVV · pith_short_16: P3WHYL5KVTVVNAGA · pith_short_8: P3WHYL5K

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/P3WHYL5KVTVVNAGAX3BA7RTKPO \
  | 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: 7eec7c2faaaceb5680c0bec20fc66a7bb7f0cc7d93692972c34cd9a960b47d1f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6e7addf50531645793c1cc387edb0c6c780f5ae3b12b77a979d95cbc428d6f38",
    "cross_cats_sorted": [
      "math.AG",
      "math.RT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-05-15T10:43:02Z",
    "title_canon_sha256": "4b3e433f97952ac548ff7ba64459cbb317a4088bff343abeb5388b4bf9a2f90b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.09242",
    "kind": "arxiv",
    "version": 2
  }
}