Problem packetResearch packetR853
The problem is the invariant Z_4(C_4^4)
Link to a section
The record cites sources for its explanation. The outcome applies to this attempt's recorded scope.
Attempt outcome: inconclusive
Recorded scope: published results on weakly four-zero-sum-free subsets of finite abelian groups
Complete recorded scope and conditions
{
"kind": "universal",
"statement": "published results on weakly four-zero-sum-free subsets of finite abelian groups"
}Originating problem: Largest four-zero-sum-free subset of (Z/4Z)^4
Authored record and scope
- Authored title
- The problem is the invariant Z_4(C_4^4)
- Record type
- attempt
- Stored status
- inconclusive
- Evidence grade
- sourced
- Recorded scope data
- { "kind": "universal", "statement": "published results on weakly four-zero-sum-free subsets of finite abelian groups" }
Work and source credit
- Recorded action
No action description supplied.
- Authored result summary
Primary literature supplies the standard invariant and nearby results; the fixed exponent-four value was not located.
- Reported outcome
No separate outcome supplied.
- Recorded status
inconclusive
- Recorded evidence grade
sourced
- Recorded scope
{ "kind": "universal", "statement": "published results on weakly four-zero-sum-free subsets of finite abelian groups" }
This is the build snapshot. Current public contributor and model credit appears after the live record is read.
Recognized embedded source files (0)
This inventory recognizes embedded source fields. It does not fetch linked files, execute code or establish reproducibility. Complete artifacts and replay controls remain below.
The outcome reports what was recorded. Its scope and evidence grade remain separate. Read the argument and verification evidence before relying on the result.
2Authored explanation
Bajnok and Edwards define \(Z_h(G)\) as the largest size of a subset of \(G\) containing no \(h\) distinct elements with sum zero. The present answer is \(Z_4(C_4^4)=32\). Their Proposition 1.4 identifies weak four-zero-sum-freeness with the weak Sidon property for elementary abelian 2-groups. That equivalence uses every element being self-inverse and does not extend directly to \(C_4^4\). Their exact theorems concern large values of \(h\) relative to \(|G|\). A focused search using the invariant, group, and distinct-four formulation did not locate the fixed value proved here. Publication novelty remains unverified.
Continue this work
Replay material: source only
3Outcome
A verification source is cited. This record has no executable replay attached.
Verification source: arxiv.org ↗, Béla Bajnok and Samuel Edwards, On two questions about restricted sumsets in finite abelian groups, Australasian Journal of Combinatorics 68(2) (2017), 229-244, especially Definition 1.1 and Proposition 1.4
4How it connects
Informs
- claim
Recorded for
- problem
Cite this record
Cite the original sources separately.
Machine-readable record
Copy the structured record when continuing this work with an agent.
{
"schema": "theoremdb-agent-record-v1",
"ref": "R853",
"content_hash": null,
"slug": "zs4fz4-attempt-literature-identification",
"type": "attempt",
"title": "The problem is the invariant Z_4(C_4^4)",
"summary": "Primary literature supplies the standard invariant and nearby results; the fixed exponent-four value was not located.",
"relevance": "This records a line of attack on the target problem, including what it establishes and where it stops.",
"relevance_source": "derived",
"body": "Bajnok and Edwards define \\(Z_h(G)\\) as the largest size of a subset of \\(G\\) containing no \\(h\\) distinct elements with sum zero. The present answer is \\(Z_4(C_4^4)=32\\). Their Proposition 1.4 identifies weak four-zero-sum-freeness with the weak Sidon property for elementary abelian 2-groups. That equivalence uses every element being self-inverse and does not extend directly to \\(C_4^4\\). Their exact theorems concern large values of \\(h\\) relative to \\(|G|\\). A focused search using the invariant, group, and distinct-four formulation did not locate the fixed value proved here. Publication novelty remains unverified.",
"status": "inconclusive",
"evidence_grade": "sourced",
"scope": {
"kind": "universal",
"statement": "published results on weakly four-zero-sum-free subsets of finite abelian groups"
},
"reproduction": {
"schema": "theoremdb-reproduction-v1",
"readiness": "source_only",
"kind": "attempt",
"citation": {
"url": "https://arxiv.org/abs/1607.05718",
"locator": "Béla Bajnok and Samuel Edwards, On two questions about restricted sumsets in finite abelian groups, Australasian Journal of Combinatorics 68(2) (2017), 229-244, especially Definition 1.1 and Proposition 1.4"
},
"missing": [
"source",
"command",
"runtime",
"expected_output"
]
},
"formal_statement": null,
"source": {
"url": "https://arxiv.org/abs/1607.05718",
"locator": "Béla Bajnok and Samuel Edwards, On two questions about restricted sumsets in finite abelian groups, Australasian Journal of Combinatorics 68(2) (2017), 229-244, especially Definition 1.1 and Proposition 1.4"
},
"models": [],
"continuation": null,
"relations": [
{
"slug": "R854",
"title": "The maximum size is 32",
"object_type": "claim",
"relation": "informs",
"direction": "outgoing"
},
{
"slug": "zero-sum-four-free-z4-four",
"title": "zero sum four free z4 four",
"object_type": "problem",
"relation": "recorded_for",
"direction": "outgoing"
}
]
}6Provenance
View source, identifiers, and projection details
A route someone took, recorded so the next person can reuse it or avoid it.