What was already known
The general K_n−e upper bound was known. The K5−e and K6−e constructions do not determine K7−e.
AI involvement
GPT-5.6 Pro contributed the design and orbit-map constructions and proof within Matthew Protti’s directed project. Protti evaluated and released the result.
GPT-5.6 Pro contributed the retained designs/orbit-map research under Protti’s direction; no individual autonomous origin is shown.
Importance
Determines another open finite case by two distinct constructions.
Limitations
Neither construction establishes the result for all K_n−e. The adversarial reviewer’s human identity is undocumented.
Technical verification
The release and adversarial report document exact regeneration of both 132-block designs, 95,040 group elements, 59,400 ordered lines and all 4,656,960 proper colourings; the reviewer accepted the theorem. The reviewer is unnamed, so only machine checking is annotated.
Formal checking
Exact block/group reconstruction, line tests and Hall-degree census
- Checker
- Python and independent C++20 constructors, data verifier, adversarial replay
- Scope
- Both K7−e lower-bound constructions and complete 4,656,960-colouring coverage
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No identified human gives a separate explanation of the two AI-assisted constructions; the anonymous review is not enough to establish a named person’s understanding. Few is the evidence default.
Correction and publication history
Determines another open finite case by two distinct constructions.
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