Mercator 2.0: The PTCt Relational Framework and a First Equal-Area Projection Profile (PTCt-1)

Abstract

Mercator 2.0 / PTCt is an exploratory relational cartographic framework that separates the physical Earth model, projection-independent geographical relations, and planar representation. The framework defines four components: Skin (P), a dimensionless measure of relative surface area; Trace (T), a projection-independent geodesic relation; Sky (C), a time-dependent relation to external astronomical reference frames; and Time (t), the epoch required to connect terrestrial and celestial geometry. Version 2.0 introduces PTCt-1, a first explicit equal-area implementation profile based on Lambert azimuthal equal-area geometry and normalized so that the complete planetary surface occupies exactly one unit of planar area (1 PT). The equal-area projection formula itself is not claimed as novel. The proposed contribution lies in the PTCt normalization, relational metadata, explicit topological transparency, adaptive center selection, celestial orientation, and task-dependent distortion accounting. The work is presented as a conceptual and mathematical working paper. A computational implementation and quantitative benchmarking against established map projections constitute the next stage of the research.