RecognitionTracker
plain-language theorem explainer
A recognition tracker packages a list of ledger recognition events, each carrying source and target indices together with a positive ratio. Researchers proving the recognition forcing complete theorem cite this structure when bridging cost minima to ledger representations. The declaration is a direct structure definition with a single field, requiring no proof steps.
Claim. A recognition tracker is a list of recognition events, where each event consists of a source index, a target index, and a positive real ratio.
background
The module proves that recognition is forced by the cost foundation, with RecognitionEvent from LedgerForcing defined as a structure containing source : ℕ, target : ℕ, ratio : ℝ and ratio_pos : 0 < ratio. Parallel RecognitionEvent structures appear in ObserverForcing (a positive state) and InformationIsLedger (a positive ratio encoding physical facts). The local setting is the ledger forcing section of the recognition forcing complete theorem, which links observables, extraction mechanisms, and J-stable structures to recognition-like structures.
proof idea
This is a structure definition that introduces the type as a container holding a list of LedgerForcing recognition events. No lemmas or tactics are applied; the declaration serves as a type for downstream results such as ledger_is_minimal_recognition_tracker.
why it matters
The structure supplies the event list used in ledger_is_minimal_recognition_tracker to show that a tracker preserving J-symmetry corresponds to a ledger. It fills the ledger forcing part of the recognition forcing complete theorem and connects cost-based recognition to ledger representations, consistent with J-uniqueness and the recognition composition law in the forcing chain.
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