Pith Number

pith:MMPMWWKS

pith:2017:MMPMWWKSVVPZUVICLYZIDOEQ4S

not attested not anchored not stored refs pending

Depth and Stanley depth of symbolic powers of cover ideals of graphs

S. A. Seyed Fakhari

arxiv:1709.03882 v1 · 2017-09-10 · 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{MMPMWWKSVVPZUVICLYZIDOEQ4S}

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	2026-05-18T00:35:29.120389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

631ecb5952ad5f9a55025e3281b890e496a3074e2e5ac0074912ada71cb59f92

Aliases

arxiv: 1709.03882 · arxiv_version: 1709.03882v1 · doi: 10.48550/arxiv.1709.03882 · pith_short_12: MMPMWWKSVVPZ · pith_short_16: MMPMWWKSVVPZUVIC · pith_short_8: MMPMWWKS

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/MMPMWWKSVVPZUVICLYZIDOEQ4S \
  | 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: 631ecb5952ad5f9a55025e3281b890e496a3074e2e5ac0074912ada71cb59f92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "594d15b218c264b2ec3064e5c0fc5fcc2a98bd55db57dfafa38fee8926aaf81c",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2017-09-10T09:48:27Z",
    "title_canon_sha256": "ada6292e723b1e04e7d92af60691678ed5f33ffc207ca53969482d719d46279d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.03882",
    "kind": "arxiv",
    "version": 1
  }
}