On the Combinatorial Selection of the Proton Architecture in PDL, Axiomatic Constraints, Integer Structures, and a Uniqueness Conjecture

We formulate the proton architecture of the Projective Dynamic Logo (PDL) as an explicit integer–combinatorics problem on signed graphs. After extracting axiomatic and phenomenological constraints that any PDL proton must satisfy, we define a class of admissible integer quintuplets, introduce a selection functional encoding coherence optimisation and empirical requirements (notably the fine-structure constant), and show that the standard PDL proton architecture 24,28,930,10\,087,11\,017 satisfies all constraints and appears as a selected configuration. We then state a local uniqueness conjecture for this quintuplet within a bounded parameter domain and outline analytical and computational strategies for testing it, thereby providing a mathematically precise entry point for further work at the interface of relational physics and discrete mathematics.