Publication and citation indicators commonly assign full credit to every coauthor, obscuring differences in authorship role and potentially rewarding accumulated authorship rather than identifiable intellectual contribution. We propose the $α$-index as a conserved, position-weighted, and penalized authorship-integrity framework. Each publication contributes one unit of credit, allocated across first-author execution, senior-author leadership, and residual middle authorship. Its defining feature is a senior-author responsibility penalty: senior credit decreases as the residual middle-author list expands, expressing the normative principle that leadership credit should be accompanied by responsibility for authorship discipline. The paper formalizes local $α$-credit allocation and the cumulative $α$-index; presents a parameterized family of weight blocks and penalty functions; and compares the framework with fractional, harmonic, and h-$α$-type approaches. Synthetic examples and selected public byline illustrations demonstrate mathematical behavior, including large-team variants. The default values are not empirical constants but transparent, testable hypotheses within a calibratable family. The framework is presented as a methodological and ethical proposal requiring field-specific validation against contribution statements, expert assessments, author surveys, and bibliographic data. It is intended to complement, not replace, peer review, contributor statements, acknowledgements, and citation-based metrics.

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