Pith Number

pith:MIK26GRY

pith:2025:MIK26GRYIIESQWOJP3MRVYPMSX

not attested not anchored not stored refs pending

Forbidden Induced Subgraphs for Bounded Shrub-Depth and the Expressive Power of MSO

Nikolas M\"ahlmann

arxiv:2501.13903 v1 · 2025-01-23 · cs.LO · cs.DM · math.CO · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MIK26GRYIIESQWOJP3MRVYPMSX}

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.

Cited by

1 paper in Pith

Unavoidable pivot-minors in graphs of large rank-depth

Receipt and verification

First computed	2026-07-05T10:04:35.801719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6215af1a3842092859c97ed91ae1ec95e34d0de210cd164c291af0364c7fbb0e

Aliases

arxiv: 2501.13903 · arxiv_version: 2501.13903v1 · doi: 10.48550/arxiv.2501.13903 · pith_short_12: MIK26GRYIIES · pith_short_16: MIK26GRYIIESQWOJ · pith_short_8: MIK26GRY

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/MIK26GRYIIESQWOJP3MRVYPMSX \
  | 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: 6215af1a3842092859c97ed91ae1ec95e34d0de210cd164c291af0364c7fbb0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0e481109c3c0d2a6397f15983865652ab6320683a106695678ee3ec214cd6bd",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LO",
    "submitted_at": "2025-01-23T18:31:33Z",
    "title_canon_sha256": "9029f7bbc3a4f4736a14b0a309855cacaf863d369063a58a5d276344ad8e1fc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.13903",
    "kind": "arxiv",
    "version": 1
  }
}