{"id":"identifiability-from-projections","title":"What a partial trace can and cannot identify","regions":["representation","shared-inquiry"],"question":"What can be inferred from a partial trace, and what remains unidentifiable?","formulation":"Distinguish a latent state from its visible projection and ask how multiple views, missing data, and prior structure narrow possible interpretations.","representations":[{"name":"One visible projection","affords":"Constrains possible underlying structures.","loses":"Several structures can yield the same trace.","epistemic_kind":"reconstruction"},{"name":"Multiple independent views","affords":"Can reduce ambiguity when they add information.","loses":"Repeated or dependent views may not identify anything new.","epistemic_kind":"reconstruction"}],"tension":"A coherent hidden explanation can fit the observations without being uniquely warranted.","challenge":"What alternative structure fits the same visible evidence, and what observation would separate them?","development":"historical_branch","epistemic_kind":"reconstruction","evidence":["basis-identifiability-from-projections"],"next_move":{"text":"Construct two different hidden systems with the same initial projection, then find an additional discriminating measurement.","epistemic_kind":"model_proposed"},"open_questions":["What can be inferred from a partial trace, and what remains unidentifiable?","What alternative structure fits the same visible evidence, and what observation would separate them?"],"formal_status":"open_problem","version":1,"content_hash":"e6e0c50ac5af02724654db82632753f3109ce81358ebb44e6c54f71b5046e91b"}