Pith Number

pith:KWS5NKSB

pith:2026:KWS5NKSBMOEVPDZ4T5BSCUNPVV

not attested not anchored not stored refs pending

Coarse geometry of stable mixed commutator length I: duality and functional analysis on chains

Masato Mimura, Mitsuaki Kimura, Morimichi Kawasaki, Shuhei Maruyama, Takahiro Matsushita

arxiv:2605.19843 v1 · 2026-05-19 · math.GR · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KWS5NKSBMOEVPDZ4T5BSCUNPVV}

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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	2026-05-20T01:06:17.249887Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

55a5d6aa416389578f3c9f432151afad753c7d5f77d62eb42a23f918590d4801

Aliases

arxiv: 2605.19843 · arxiv_version: 2605.19843v1 · doi: 10.48550/arxiv.2605.19843 · pith_short_12: KWS5NKSBMOEV · pith_short_16: KWS5NKSBMOEVPDZ4 · pith_short_8: KWS5NKSB

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/KWS5NKSBMOEVPDZ4T5BSCUNPVV \
  | 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: 55a5d6aa416389578f3c9f432151afad753c7d5f77d62eb42a23f918590d4801

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8d7165ab73c7acf8417f04d99423e55ae74c551ee6fde4a48e32d42d2a8e6d0",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-19T13:37:54Z",
    "title_canon_sha256": "5d2b28c493989931986e2e83fd952e21c9d753d20425ce969fcd6c20a994c919"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19843",
    "kind": "arxiv",
    "version": 1
  }
}