Pith Number

pith:QE4VDFJK

pith:2026:QE4VDFJKAO7DJWJY35XWTASP26

not attested not anchored not stored refs pending

Higher Commutativity in Finite Groups, Rigidity, Extremal bounds, and Heisenberg-Type Families

Robert Shwartz, Vadim E Levit

arxiv:2605.17171 v1 · 2026-05-16 · 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{QE4VDFJKAO7DJWJY35XWTASP26}

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	2026-05-20T00:03:43.145101Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

813951952a03be34d938df6f69824fd7a28f053eec0f669ec7e7ae1803f580fe

Aliases

arxiv: 2605.17171 · arxiv_version: 2605.17171v1 · doi: 10.48550/arxiv.2605.17171 · pith_short_12: QE4VDFJKAO7D · pith_short_16: QE4VDFJKAO7DJWJY · pith_short_8: QE4VDFJK

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/QE4VDFJKAO7DJWJY35XWTASP26 \
  | 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: 813951952a03be34d938df6f69824fd7a28f053eec0f669ec7e7ae1803f580fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b69eed8aa6543ae62345508f0df12edad8cdbff617072f24130756a1a8ec951",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-16T21:59:59Z",
    "title_canon_sha256": "9ce0b22589b188460cb96f1760e57789415b311f1f0fba14538e1159fb5123b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17171",
    "kind": "arxiv",
    "version": 1
  }
}