Pith Number

pith:4BMOH2KA

pith:2018:4BMOH2KABRRU2RHL4DXOGTIXWA

not attested not anchored not stored refs pending

When are permutation invariants Cohen-Macaulay over all fields?

Ben Blum-Smith, Sophie Marques

arxiv:1802.06735 v5 · 2018-02-19 · math.AC · 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{4BMOH2KABRRU2RHL4DXOGTIXWA}

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	2026-05-18T00:01:30.082678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e058e3e9400c634d44ebe0eee34d17b037bcd62fb1da8af38243c865a55529d1

Aliases

arxiv: 1802.06735 · arxiv_version: 1802.06735v5 · doi: 10.48550/arxiv.1802.06735 · pith_short_12: 4BMOH2KABRRU · pith_short_16: 4BMOH2KABRRU2RHL · pith_short_8: 4BMOH2KA

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/4BMOH2KABRRU2RHL4DXOGTIXWA \
  | 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: e058e3e9400c634d44ebe0eee34d17b037bcd62fb1da8af38243c865a55529d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d8d00ff4494d45e287c7d4065c7feaecc5372eb4dfd3cdcb141dd98bb46a1fd",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2018-02-19T18:00:36Z",
    "title_canon_sha256": "6b8c7198e66eeba7f4f4d3d0f41164af559d75516695122a1f47bad10f705ab5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1802.06735",
    "kind": "arxiv",
    "version": 5
  }
}