# OCME ยท Knowledge & practice explorer 302 MKO / 1,441 families / 360 batches / 36,000 questions. 36,000 second-context math/bilingual reviewed; 0 display/symbol-checked candidates. Source questions: candidate. English: ai_candidate. No new proof, Lean, SREG or training. 25 results; page 1/1. ## Question 19401: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0051`; number: 19401 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0051/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0051/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0051.json) ## Question 19402: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0052`; number: 19402 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0052/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0052/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0052.json) ## Question 19403: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0053`; number: 19403 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0053/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0053/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0053.json) ## Question 19404: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0054`; number: 19404 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0054/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0054/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0054.json) ## Question 19405: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0055`; number: 19405 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0055/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0055/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0055.json) ## Question 19406: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0056`; number: 19406 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0056/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0056/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0056.json) ## Question 19407: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0057`; number: 19407 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0057/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0057/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0057.json) ## Question 19408: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0058`; number: 19408 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0058/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0058/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0058.json) ## Question 19409: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0059`; number: 19409 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0059/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0059/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0059.json) ## Question 19410: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0060`; number: 19410 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0060/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0060/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0060.json) ## Question 19411: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0061`; number: 19411 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0061/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0061/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0061.json) ## Question 19412: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0062`; number: 19412 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0062/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0062/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0062.json) ## Question 19413: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0063`; number: 19413 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0063/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0063/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0063.json) ## Question 19414: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0064`; number: 19414 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0064/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0064/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0064.json) ## Question 19415: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0065`; number: 19415 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0065/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0065/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0065.json) ## Question 19416: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0066`; number: 19416 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0066/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0066/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0066.json) ## Question 19417: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0067`; number: 19417 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0067/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0067/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0067.json) ## Question 19418: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0068`; number: 19418 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0068/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0068/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0068.json) ## Question 19419: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0069`; number: 19419 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0069/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0069/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0069.json) ## Question 19420: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0070`; number: 19420 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0070/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0070/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0070.json) ## Question 19421: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0071`; number: 19421 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0071/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0071/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0071.json) ## Question 19422: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0072`; number: 19422 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0072/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0072/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0072.json) ## Question 19423: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0073`; number: 19423 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0073/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0073/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0073.json) ## Question 19424: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0074`; number: 19424 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0074/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0074/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0074.json) ## Question 19425: Exact Chromatic Number Needs Both Lower and Upper Evidence - ID: `q-20261014-advance-20261106-r01-chromatic-number-0075`; number: 19425 - Processing: second_context_reviewed - MKO: [mko-chromatic-number](/en/mko/mko-chromatic-number/) - Family: [qf-mod37-chromatic-exact-number](/en/explore/?family=qf-mod37-chromatic-exact-number) - Batch: [batch-20261014-advance-20261106-r01-chromatic-number-foundations](/en/explore/?batch=batch-20261014-advance-20261106-r01-chromatic-number-foundations) - [Derivation](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0075/) / [Markdown](/en/questions/q-20261014-advance-20261106-r01-chromatic-number-0075/index.md) / [JSON](/data/question-derivations/questions/q-20261014-advance-20261106-r01-chromatic-number-0075.json)