Clinical dialogue-to-note generation is challenging because clinically salient evidence is noisy, distributed across turns, and often revised later in the encounter. Direct transcript-only prompting and coarse intermediate scaffolds can therefore suffer from omissions, section leakage, unsupported fill-in, and brittle final-state tracking. We propose Clinical Atomic Propositions (CAPs), a dialogue-aware intermediate representation for faithful clinical note generation. CAPs extract source-grounded clinical assertions while preserving modifiers such as verification status, temporality, speaker/source, and action type. We also study an optional event consolidation layer that groups CAPs into problem-oriented care bundles before note rendering. We evaluate five methods on a 197-case ACI-Bench cohort: a transcript-only baseline, prompt-based reimplementations of Cluster2Sent and MEDSUM-ENT, CAP, and CAP+Event. The main task uses a sectioned-note template, with SOAP-template rendering and transcript-free rendering reported as ablations. We use MEDSUM-ENT-style GPT-R/P/F1 metrics and a proposition-grounded semCAP-R/P/F1 audit to measure concept-level and source-grounded faithfulness, complemented by case-level win/tie/loss analysis and clinician deep review. Results show that CAP improves preservation of transcript-grounded clinical propositions while remaining competitive on concept-level GPT metrics. CAP+Event is not uniformly better than CAP, but qualitative and boundary analyses show when problem-oriented consolidation can improve organization and when compression can introduce omissions. We release code, prompts, intermediate representations, generated notes, and evaluation artifacts at a public repository.