{"id":"order-sensitive-path-encoding","title":"Constituents, order, and path identity","regions":["computation","representation","mathematical-experiments"],"question":"What must an encoding retain to distinguish paths that reach the same apparent state?","formulation":"Separate visited symbols, the order of operations, path-dependent state, and reduced projections; explore whether repeated operational patterns can be recognized without losing reversibility.","representations":[{"name":"A product encoding","affords":"Offers a compact composition.","loses":"Commutative products erase order; general matrix products need not be injective.","epistemic_kind":"reconstruction"},{"name":"Words over explicitly defined generators","affords":"Retains sequence before choosing a reduction.","loses":"Finite representations, cancellation, and bounded precision require separate checks.","epistemic_kind":"reconstruction"},{"name":"A reduced state or projection","affords":"Supports operational comparison.","loses":"The same projection may correspond to different complete paths.","epistemic_kind":"reconstruction"}],"tension":"Order sensitivity, unique decoding, reversibility, and behavioral equivalence are separate demands.","challenge":"Which distinct paths collide, and does a projected recurrence imply recurrence of the complete relevant state?","development":"historical_branch","epistemic_kind":"reconstruction","evidence":["basis-order-sensitive-path-encoding"],"next_move":{"text":"Run the supplied counterexample script, then define a restricted generator system with a stated decoding guarantee.","epistemic_kind":"model_proposed"},"open_questions":["What must an encoding retain to distinguish paths that reach the same apparent state?","Which distinct paths collide, and does a projected recurrence imply recurrence of the complete relevant state?"],"formal_status":"open_problem","version":1,"content_hash":"d486d76ceab86ec29670a599438f53780ff1f2b049e5b4a76ba4f1bf59a62169"}