Pith Number

pith:QWOZT7TI

pith:2024:QWOZT7TIRN76QOU566ZPMB74SV

not attested not anchored not stored refs pending

Semigroups uniquely determined by one-sided identity and zero sets

Julia Maddox

Every right group with maximal subgroup size 2 and every commutative-rectangular band is uniquely determined by the one-sided identity and zero sets of its elements.

arxiv:2410.23473 v5 · 2024-10-30 · math.GR

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\usepackage{pith}
\pithnumber{QWOZT7TIRN76QOU566ZPMB74SV}

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Record completeness

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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.

Claims

C1strongest claim

We prove every right group with maximal subgroup size 2 is a stabilized semigroup with respect to the one-sided identity [zero] sets of its elements. We prove a commutative-rectangular band is a stabilized semigroup with respect to the one-sided identity [zero] sets of its elements.

C2weakest assumption

The structures under consideration satisfy the defining properties of a right group (every element has a right identity and right inverse) or of a commutative-rectangular band (every pair commutes or forms generalized inverses), which are invoked to establish that matching identity/zero sets force identical operations.

C3one line summary

Right groups with maximal subgroup size 2 and commutative-rectangular bands are stabilized semigroups uniquely determined by their one-sided identity and zero sets.

Receipt and verification

First computed	2026-05-26T02:04:59.112175Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

859d99fe688b7fe83a9df7b2f607fc9543a51d7deb9bffa13dd6622ef0494efd

Aliases

arxiv: 2410.23473 · arxiv_version: 2410.23473v5 · doi: 10.48550/arxiv.2410.23473 · pith_short_12: QWOZT7TIRN76 · pith_short_16: QWOZT7TIRN76QOU5 · pith_short_8: QWOZT7TI

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/QWOZT7TIRN76QOU566ZPMB74SV \
  | 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: 859d99fe688b7fe83a9df7b2f607fc9543a51d7deb9bffa13dd6622ef0494efd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "015dd935ae0e53c5603eff4c2a3fd4fad043fc9de4116cdefc90ce7bc4db1ff2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2024-10-30T21:36:45Z",
    "title_canon_sha256": "c7b88a3be3e61863e9ca29e7a73ce87704413dd64481cc39fe13e511f9d20427"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2410.23473",
    "kind": "arxiv",
    "version": 5
  }
}