Problem packetResearch packetR22
Reproduce the balanced-family table through maximum letter 8
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The record reports a computation within its stated scope. The outcome applies to this attempt's recorded scope.
Attempt outcome: completed
Recorded scope: primitive normalized four-letter alphabets {0<a<b<c} with c=a+b, c at most 8, one representative under reflection
Complete recorded scope and conditions
{
"kind": "bounded",
"statement": "primitive normalized four-letter alphabets {0<a<b<c} with c=a+b, c at most 8, one representative under reflection",
"bounds": {
"alphabet_size": {
"min": 4,
"max": 4
},
"alphabet_maximum": {
"min": 3,
"max": 8
},
"alphabet_count": {
"min": 10,
"max": 10
}
},
"exhaustive": true
}Originating problem: Infinite additive-square avoidance over a finite integer alphabet
Authored record and scope
- Authored title
- Reproduce the balanced-family table through maximum letter 8
- Record type
- attempt
- Stored status
- completed
- Evidence grade
- computational
- Recorded scope data
- { "kind": "bounded", "statement": "primitive normalized four-letter alphabets {0<a<b<c} with c=a+b, c at most 8, one representative under reflection", "bounds": { "alphabet_size": { "min": 4, "max": 4 }, "alphabet_maximum": { "min": 3, "max": 8 }, "alphabet_count": { "min": 10, "max": 10 } }, "exhaustive": true }
Work and source credit
- Recorded action
No action description supplied.
- Authored result summary
An exact depth-first sweep closed all ten primitive normalized reflection representatives in the balanced family through maximum letter 8 and matched the published maxima.
- Reported outcome
No separate outcome supplied.
- Recorded status
completed
- Recorded evidence grade
computational
- Recorded scope
Read complete recorded scope
{ "kind": "bounded", "statement": "primitive normalized four-letter alphabets {0<a<b<c} with c=a+b, c at most 8, one representative under reflection", "bounds": { "alphabet_size": { "min": 4, "max": 4 }, "alphabet_maximum": { "min": 3, "max": 8 }, "alphabet_count": { "min": 10, "max": 10 } }, "exhaustive": true }
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2Authored explanation
The sweep enumerated every A={0<a<b<c} with gcd(A)=1, c<=8, and c=a+b, then kept the lexicographically smaller of A and c-A. For each of ten representatives, a prefix-sum DFS visited every additive-square-free prefix until the search tree closed. The maxima, node counts, leaf counts, maximizer counts, and maximizer digests are recorded in the linked artifact. The compact six-field row digest was independently matched by a second operator implementation.
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Replay material: partial
3Outcome
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PYTHONPATH=. python3 additive_square_sweep.py --max-value 8 --balanced-family-only --node-limit 100000000Verification source: Exact Python 3.9.6 execution on macOS arm64 on 2026-07-28; published comparison is Freedman and Brown, Integers 16 (2016), A33, Theorem 1 and pages 2-3
4What was measured
Execution
5How it connects
Informed by
- claim
Uses
- artifact
Informs
- claim
Recorded for
- problem
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Cite the original sources separately.
Machine-readable record
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"slug": "asq-attempt-balanced-family-reproduction",
"type": "attempt",
"title": "Reproduce the balanced-family table through maximum letter 8",
"summary": "An exact depth-first sweep closed all ten primitive normalized reflection representatives in the balanced family through maximum letter 8 and matched the published maxima.",
"relevance": "For Infinite additive-square avoidance over a finite integer alphabet, record asq-attempt-balanced-family-reproduction (“Reproduce the balanced-family table through maximum letter 8”) documents a concrete method, search boundary, or failed route. The record states: An exact depth-first sweep closed all ten primitive normalized reflection representatives in the balanced family through maximum letter 8 and matched the published maxima.",
"relevance_source": "recorded",
"body": "The sweep enumerated every A={0<a<b<c} with gcd(A)=1, c<=8, and c=a+b, then kept the lexicographically smaller of A and c-A. For each of ten representatives, a prefix-sum DFS visited every additive-square-free prefix until the search tree closed. The maxima, node counts, leaf counts, maximizer counts, and maximizer digests are recorded in the linked artifact. The compact six-field row digest was independently matched by a second operator implementation.",
"status": "completed",
"evidence_grade": "computational",
"scope": {
"kind": "bounded",
"statement": "primitive normalized four-letter alphabets {0<a<b<c} with c=a+b, c at most 8, one representative under reflection",
"bounds": {
"alphabet_size": {
"min": 4,
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},
"alphabet_maximum": {
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},
"alphabet_count": {
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}
},
"exhaustive": true
},
"reproduction": {
"schema": "theoremdb-reproduction-v1",
"readiness": "partial",
"kind": "attempt",
"command": "PYTHONPATH=. python3 additive_square_sweep.py --max-value 8 --balanced-family-only --node-limit 100000000",
"citation": {
"locator": "Exact Python 3.9.6 execution on macOS arm64 on 2026-07-28; published comparison is Freedman and Brown, Integers 16 (2016), A33, Theorem 1 and pages 2-3"
},
"runtime_seconds": 80.48,
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"locator": "Exact Python 3.9.6 execution on macOS arm64 on 2026-07-28; published comparison is Freedman and Brown, Integers 16 (2016), A33, Theorem 1 and pages 2-3"
},
"models": [],
"continuation": null,
"relations": [
{
"slug": "R29",
"title": "The balanced four-letter family has finite maxima at most 60",
"object_type": "claim",
"relation": "informs",
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{
"slug": "R17",
"title": "Balanced-family alphabet enumerator",
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{
"slug": "R28",
"title": "The exact finite maximum for {0,1,2,4} is 62",
"object_type": "claim",
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{
"slug": "additive-square-finite-alphabet",
"title": "additive square finite alphabet",
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]
}7Provenance
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