CJM PROBLEM SKETCH SERIES · SEASON 1
Thirteen Problems. One Structural Question.
Index of Problem Sketches No. 001–013 · Conceptual reference only
Open Question.
Does a problem Φ admit a solution if and only if it is structurally admissible under atemporal resonance?
Season 1 reinterprets thirteen mathematical, physical, biological, and computational questions through structural admissibility. Sketch 013 turns the question toward the limits of CJM judgment itself.
Ⅰ. Sketch Index
001Recamán’s Sequence — path admissibility
002Collatz Conjecture — reachability
003Goldbach Conjecture — admissibility landscape
004Gravity — structural projection
005Twin Prime Conjecture — persistence
006Ramsey Numbers — structural thresholds
007ABC Conjecture — radical balance
008Protein Folding — conformation admissibility
009Odd Perfect Number — divisor balance
010Erdős–Straus Conjecture — decomposition
011Legendre’s Conjecture — prime intervals
012Quantum Measurement — outcome admissibility
013Halting Problem — termination admissibility
Ⅱ. Shared Interface and Vocabulary
Problem → Structural Constraints → SAT → 3SAT → CJM → Structural Judgment (hypothesized)
SAT → 3SAT interface. A common finite representation and normalization of constraints; not itself a new solving algorithm.
Changbal Function. A proposed observable characterizing an admissibility landscape; its form must be defined for each application.
Changbal Region. A reproducible regime of nonlinear structural reorganization beyond controls and baseline effects; none is established by these sketches.
Changbal Jump. A distinct, substantiated transition within such a regime, not merely one fluctuation or a successful finite instance.
Temporal generation of states ≠ Atemporal discrimination of structural admissibility.
Atemporality is the central CJM hypothesis: global compatibility might be judged independently of sequential state generation. It is not an experimentally established mechanism and does not imply universal computability.
Ⅲ. Scope and Non-Claims
The sketches do not claim proofs of conjectures, resolution of physical problems, discovery of a verified Changbal Region or Jump, a working CJM implementation, or a demonstrated computational advantage. Finite SAT/UNSAT results certify only the encoded instance and bound; they do not settle universally quantified infinite claims.
Special boundary of No. 013. Bounded execution can be encoded in finite 3SAT, but this does not decide arbitrary program termination. An atemporal judgment is not automatically a halting oracle; any stronger claim must confront diagonalization and specify its computational domain.