Boundary Compensation Emergence Certified Ascent and Ontological Shadows

The BC-Emergence programme studies the ascending route from finite-dimensional
operator, spectral, graph, and atlas structures to stable effective objects at a higher
level. Its central principle is that emergence is not the inverse function of compression. The descending BC-Layers branch describes loss of form in the transition
from a continuum or hidden description to a finite readout channel; BC-Emergence
studies a different map: under which additional rules of assembly, refinement, scaling, and stability does a family of lower-level realizations determine one effective
class of upper-level structures?
The Charter introduces the concepts of an ontological shadow, an ascent system, an
emergence certificate ECert, the anti-tautology principle, layer-specific certificate
types, and the O0–O4 claim scale. It separately fixes a dependency map, modulegraduation rules, and the BC-Emergence I–VII roadmap: from admissible relational
complexes and local-to-global assembly to discrete connections, spectral geometry,
controlled continuum limits, effective dynamics, and barriers to physical identification.
The central thesis of the programme is:
lower structures + assembly rules
+ scaling limit + stability
=⇒ a class of effective upper structures