Pith Number

pith:VMQMEDIO

pith:2015:VMQMEDIOXOTWS3PNJJZZ6R7VBL

not attested not anchored not stored refs pending

The Word Problem for Omega-Terms over the Trotter-Weil Hierarchy

Jan Philipp W\"achter, Manfred Kufleitner

arxiv:1509.05364 v2 · 2015-09-17 · cs.FL · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VMQMEDIOXOTWS3PNJJZZ6R7VBL}

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	2026-05-18T00:44:25.182948Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab20c20d0ebba7696ded4a739f47f50ae592731db7d56fc8cbb5e6ec2473a53d

Aliases

arxiv: 1509.05364 · arxiv_version: 1509.05364v2 · doi: 10.48550/arxiv.1509.05364 · pith_short_12: VMQMEDIOXOTW · pith_short_16: VMQMEDIOXOTWS3PN · pith_short_8: VMQMEDIO

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/VMQMEDIOXOTWS3PNJJZZ6R7VBL \
  | 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: ab20c20d0ebba7696ded4a739f47f50ae592731db7d56fc8cbb5e6ec2473a53d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bfc2155f8bf850e2288883f25d6760f1d7ec5c87859c8043f3b39f3cf9062030",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.FL",
    "submitted_at": "2015-09-17T18:35:08Z",
    "title_canon_sha256": "bc4b1bad6188d48ccc26298597b61dbe2f0a441c1e6672e346811629d4b17897"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05364",
    "kind": "arxiv",
    "version": 2
  }
}