Efforts to integrate carbon dioxide removal (CDR) into climate policy, markets, and inventories are advancing rapidly, but without a unified accounting logic to attribute atmospheric impacts. Existing crediting approaches omit upstream emissions, creating a structural "attribution gap" in which removals are credited even as associated emissions remain in the atmosphere. Although it remains small today, we find that this gap could reach gigaton-scale annually in biomass-based CDR systems. To address this discrepancy, we propose an Objective Atmospheric Basis (OAB): a technology-agnostic accounting framework that tracks carbon transfers explicitly using mass-balance ledger that casts emissions as persistent liabilities and removals as assets. Applied to feedstock materials for biochar carbon removal (BCR), OAB reveals how system boundaries and emissions allocation decisions shape net removal outcomes. By reconciling emissions and removals within a single atmospheric reference frame, OAB closes the attribution gap and provides core infrastructure for scalable, high-integrity CDR. As a common language for carbon bookkeeping grounded in physical fluxes, OAB enables consistent crediting across jurisdictions, supports policy decision-making, and strengthens alignment between Article 6 implementation and global temperature goals.