A partial result toward: Is every number above 3 the number Quartier of 10?

finish_attempt({"summary":"Attempt 348: no progress and nothing claimed. \"Quartier number\" has no definition in any reachable source after about 142 search variants (arXiv, Wikipedia, OEIS, MathWorld), so Q(10) cannot be computed or tested against any m > 3. Blocked until the holders supply a definition, a sourc) -> attempt finished

Attempt 347 finished: Attempt 348: no progress and nothing claimed. "Quartier number" has no definition in any reachable source after about 142 search variants (arXiv, Wikipedia, OEIS, MathWorld), so Q(10) cannot be computed or tested against any m > 3. Blocked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 348: no searches, no compute. About 142 search variants across arXiv, Wikipedia, OEIS,) -> notes saved

The notes show 347 prior attempts and about 142 searches, none of which defined "Quartier number." Repeating those searches would probably return the same result, so I'll record the blocker and end this attempt without spending more compute.

Attempt 347 started with $0.3299 of compute.

finish_attempt({"summary":"Attempt 347: no progress and nothing claimed. \"Quartier number\" has no definition in any reachable source (about 142 search variants across arXiv, Wikipedia, OEIS, MathWorld), so Q(10) cannot be computed or tested against any m > 3. Blocked until the holders supply a definition, a sour) -> attempt finished

Attempt 346 finished: Attempt 347: no progress and nothing claimed. "Quartier number" has no definition in any reachable source (about 142 search variants across arXiv, Wikipedia, OEIS, MathWorld), so Q(10) cannot be computed or tested against any m > 3. Blocked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 347: no searches, no compute. About 142 search variants across arXiv, Wikipedia, OEIS,) -> notes saved

The notes show 346 prior attempts and about 142 searches, none of which defined "Quartier number." Another search would likely repeat that result, so I'll record the blocker rather than spend compute.

Attempt 346 started with $0.3307 of compute.

finish_attempt({"summary":"Attempt 346: no progress. \"Quartier number\" is not defined in any reachable source after about 142 search variants (arXiv, Wikipedia, OEIS, MathWorld), so Q(10) cannot be computed or tested against any m > 3. Nothing claimed. Blocked until the holders supply a definition, source, or co) -> attempt finished

Attempt 345 finished: Attempt 346: no progress. "Quartier number" is not defined in any reachable source after about 142 search variants (arXiv, Wikipedia, OEIS, MathWorld), so Q(10) cannot be computed or tested against any m > 3. Nothing claimed. Blocked until the holders supply a definition, source, or corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 346: no searches, no compute. Roughly 142 search variants across arXiv, Wikipedia, OEI) -> notes saved

The notes show 345 prior attempts and about 142 searches, none of which found a definition of "Quartier number." Another search would most likely return the same result, so I'll record the blocker and stop rather than spend compute on it.

Attempt 345 started with $0.3314 of compute.

finish_attempt({"summary":"Attempt 345: one further search for \"Quartier number\" returned only unrelated physics papers. The term remains undefined in all reachable sources (about 142 variants total), so Q(10) cannot be computed or tested against any m > 3. Nothing claimed. Blocked until the holders supply a def) -> attempt finished

Attempt 344 finished: Attempt 345: one further search for "Quartier number" returned only unrelated physics papers. The term remains undefined in all reachable sources (about 142 variants total), so Q(10) cannot be computed or tested against any m > 3. Nothing claimed. Blocked until the holders supply a definition or source.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 345: one more search (\"Quartier number of n integer sequence\") returned only unrelat) -> notes saved

The search returned only unrelated physics papers, so "Quartier number" still has no definition in any reachable source. I'll record that and stop here.

search_papers({"query":"Quartier number of n integer sequence","max_results":5}) -> 2510.17487v1 | Directional Search for Persistent Gravitational Waves: Results from the First Part of LIGO-Virgo-KAGRA's Fourth Observing Run | The LIGO Scientific Collaboration, the Virgo Collaboration, the KAGRA Collaboration, A. G. Abac | 2025-10-20 The angular distribution of gravitational-wave power from persistent sources may exhibit anisotropies arising from the large-scale structure o

The notes record about 141 unsuccessful searches for "Quartier number," so I'll try one differently worded query before concluding.

Attempt 344 started with $0.3328 of compute.

finish_attempt({"summary":"Attempt 344: no progress, nothing claimed. \"Quartier number\" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Blocked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 343 finished: Attempt 344: no progress, nothing claimed. "Quartier number" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Blocked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 344: no searches, no compute. About 141 search variants across arXiv, Wikipedia, OEIS ) -> notes saved

The notes record about 141 search variants with no definition of "Quartier number" in any reachable source. Running more searches would repeat that work, and any definition I chose would answer a different question, so I'm not making a claim. I'll record the blocker so the next attempt starts from the request for a definition.

Attempt 343 started with $0.3337 of compute.

finish_attempt({"summary":"Attempt 343: no progress, nothing claimed. \"Quartier number\" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Blocked until the holders supply a definition, a source, or a corrected term. Notes updated t) -> attempt finished

Attempt 342 finished: Attempt 343: no progress, nothing claimed. "Quartier number" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Blocked until the holders supply a definition, a source, or a corrected term. Notes updated to say so.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 343: no searches, no compute. About 141 search variants across arXiv, Wikipedia, OEIS ) -> notes saved

The notes record about 141 search variants with no definition of "Quartier number" anywhere reachable. Running more searches would repeat that work, and any definition I chose would be a guess that answers a different question. I'll update the notes so the next attempt starts from the blocker rather than repeating the loop.

Attempt 342 started with $0.3345 of compute.

finish_attempt({"summary":"Attempt 342: no progress, nothing claimed. \"Quartier number\" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 341 finished: Attempt 342: no progress, nothing claimed. "Quartier number" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 342: no searches, no compute. About 141 search variants across arXiv, Wikipedia, OEIS ) -> notes saved

The notes record about 141 search variants with no definition of "Quartier number," so I won't repeat them. Without a definition, Q(10) can't be computed, and any definition I chose would answer a different question. I'll update the notes and park the line.

Attempt 341 started with $0.3354 of compute.

finish_attempt({"summary":"Attempt 341: no progress, nothing claimed. \"Quartier number\" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 340 finished: Attempt 341: no progress, nothing claimed. "Quartier number" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 341: no searches, no compute (budget about $0.34). About 141 search variants across ar) -> notes saved

I'm not going to run more searches on this. My notes record about 141 variants across arXiv, Wikipedia, OEIS and MathWorld, and none defines "Quartier number." Without a definition I can't compute Q(10) or test it against any m > 3. Any definition I supplied would answer a different question, so claiming a result would be unjustified.

Attempt 340 started with $0.3363 of compute.

finish_attempt({"summary":"Attempt 340: no progress, nothing claimed. \"Quartier number\" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 339 finished: Attempt 340: no progress, nothing claimed. "Quartier number" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 340: no searches, no compute. About 141 search variants across arXiv, Wikipedia, OEIS ) -> notes saved

I'm not going to run more searches. My notes record about 141 variants across arXiv, Wikipedia, OEIS and MathWorld, and none defines "Quartier number." Without a definition, Q(10) can't be computed or tested against any m > 3, and any definition I supplied would answer a different question. I'll keep the notes current and park the line.

Attempt 339 started with $0.3371 of compute.

finish_attempt({"summary":"Attempt 339: no progress, nothing claimed. \"Quartier number\" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 338 finished: Attempt 339: no progress, nothing claimed. "Quartier number" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 339: no searches, no compute. About 141 search variants across arXiv, Wikipedia, OEIS ) -> notes saved

I'm not going to repeat the same searches. The notes record about 141 variants with no definition of "Quartier number," and I still can't compute Q(10) or test it against any m > 3. I'll record that and park the line.

Attempt 338 started with $0.3379 of compute.

finish_attempt({"summary":"Attempt 338: no progress, nothing claimed. \"Quartier number\" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 337 finished: Attempt 338: no progress, nothing claimed. "Quartier number" has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 338: no new searches or compute (budget about $0.34). About 141 search variants across) -> notes saved

I'm not going to spend more budget on this line. My notes record about 141 searches across arXiv, Wikipedia, OEIS and MathWorld, and none defines "Quartier number." Without a definition I can't compute Q(10) or test it against any m > 3, and any definition I invented would answer a different question.

Attempt 337 started with $0.3388 of compute.

finish_attempt({"summary":"Attempt 337: no progress, nothing claimed. \"Quartier number\" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 336 finished: Attempt 337: no progress, nothing claimed. "Quartier number" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 337: no searches, no compute (budget about $0.34). About 141 search variants across ar) -> notes saved

The notes show that about 141 searches have found no definition of "Quartier number," so I can't compute Q(10) or test it against any m > 3. Repeating those searches would waste the remaining budget, so I'll keep the status as it is and record it.

Attempt 336 started with $0.3396 of compute.

finish_attempt({"summary":"Attempt 336: no progress, nothing claimed. \"Quartier number\" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 335 finished: Attempt 336: no progress, nothing claimed. "Quartier number" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 336: no searches, no compute (budget about $0.34). About 141 search variants across ar) -> notes saved

The notes show this line has been blocked for many attempts. About 141 searches found no definition of "Quartier number," so I can't compute Q(10) or test it against any m > 3. I won't spend the remaining budget repeating those searches or inventing a definition, since that would answer a different question. I'll keep the notes current and park the line.

Attempt 335 started with $0.3404 of compute.

finish_attempt({"summary":"Attempt 335: no progress, nothing claimed. \"Quartier number\" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 334 finished: Attempt 335: no progress, nothing claimed. "Quartier number" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 335: no searches, no compute (budget about $0.34). About 141 search variants across ar) -> notes saved

The notes show this line has been blocked across many attempts. I'll record that the status is unchanged and stop here rather than spend the remaining budget on searches that have already failed.

Attempt 334 started with $0.3412 of compute.

finish_attempt({"summary":"Attempt 334: no progress, nothing claimed. \"Quartier number\" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 333 finished: Attempt 334: no progress, nothing claimed. "Quartier number" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 334: no searches, no compute (budget about $0.34). About 141 search variants across ar) -> notes saved

I'm not going to search again. The notes record about 141 search variants across arXiv, Wikipedia, OEIS and MathWorld, and none defines "Quartier number." Without a definition I can't compute Q(10) or test it against any m > 3. Inventing a definition would answer a different question, and the remaining budget is about $0.34.

Attempt 333 started with $0.3421 of compute.

finish_attempt({"summary":"Attempt 333: no progress, nothing claimed. \"Quartier number\" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term."}) -> attempt finished

Attempt 332 finished: Attempt 333: no progress, nothing claimed. "Quartier number" still has no definition in any reachable source after about 141 search variants, so Q(10) cannot be computed or tested against any m > 3. Parked until the holders supply a definition, a source, or a corrected term.

write_notes({"notes":"WORKING QUESTION: Let Q(n) denote the \"Quartier number\" of n (term undefined in the source). Is Q(10) = m for every integer m > 3? Provisional reading only; no definition found.\n\nStatus after attempt 333: no searches, no compute (budget about $0.34). About 141 search variants across ar) -> notes saved