Pith Number

pith:JFGSCDK5

pith:2026:JFGSCDK5RKQVKXQQC4B5BRSGEM

not attested not anchored not stored refs resolved

A nonabelian twist on differences of bijections

Mohsen Aliabadi

Quotient-realizability in nonabelian groups requires a cycle-tiling decomposition of partial products beyond the abelianization condition.

arxiv:2605.16478 v1 · 2026-05-15 · math.GR · math.CO

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\pithnumber{JFGSCDK5RKQVKXQQC4B5BRSGEM}

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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

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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

quotient-realizability is equivalent to a decomposition of A into product-one words whose partial-product sets tile G by right translates

C2weakest assumption

That the standard use of permutation cycles and the translation of quotient-realizability into an exact tiling condition on partial-product sets is sufficient to capture all obstructions without further group-specific invariants beyond the abelianization product (as described in the main structural result).

C3one line summary

A cycle-tiling criterion characterizes when a multiset A in a finite nonabelian group G can be realized as quotients from two bijections, with the abelianization product condition shown insufficient even when the product in G is the identity, via a counterexample in S3.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] B. Alspach, J.-C. Bermond, and D. Sotteau, Decomposition into cycles. I. Hamilton decompositions, in Cycles and Rays, NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 301, Kluwer Academic Publisher 1990

[2] D´ enes and A 1974

[3] A. B. Evans, Applications of complete mappings and orthomorphisms of finite groups,Quasigroups Related Systems23(2015), no. 1, 5–30 2015

[4] Fuchs, Ein kombinatorisches Problem bez¨ uglich abelscher Gruppen,Math 1958

[5] W. Gao and A. Geroldinger, Zero-sum problems in finite abelian groups: A survey,Expo. Math.24 (2006), no. 4, 337–369. 17 2006

Receipt and verification

First computed	2026-05-20T00:02:24.017239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

494d210d5d8aa1555e101703d0c646232c23eff2e977f3075ecdb246a08aa6a6

Aliases

arxiv: 2605.16478 · arxiv_version: 2605.16478v1 · doi: 10.48550/arxiv.2605.16478 · pith_short_12: JFGSCDK5RKQV · pith_short_16: JFGSCDK5RKQVKXQQ · pith_short_8: JFGSCDK5

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/JFGSCDK5RKQVKXQQC4B5BRSGEM \
  | 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: 494d210d5d8aa1555e101703d0c646232c23eff2e977f3075ecdb246a08aa6a6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ae3e4b40066f03e36b93843083d33084ffdef90d5521e6f8053f35dcd3957ee2",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-05-15T16:15:43Z",
    "title_canon_sha256": "fa0b4642c61fb2f0c243a154b1ff334fe09a6acf549a4c5b23e590a5a29a0456"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16478",
    "kind": "arxiv",
    "version": 1
  }
}