Loss Landscape Vocabulary Framework

The terrain properties (slope, temperature, friction, slippery, tension, flexion, elevation) describe the local and global geometry of the loss surface — the fixed mathematical landscape training navigates, formally defined by L(θ) and its derivatives — while the macro-topology shapes (bowl, valley, saddle, plateau, ridge, basin) are the emergent large-scale features that terrain properties produce in aggregate, determining where models converge, stall, or drift.

The navigator properties (density, perplexity, probability, coupling, viscosity, elasticity, memory) are conjugate to terrain — not a second independent coordinate system but a description of the same system from its momentum axis — and the primary generative quantity at their interface is potential difference: the gap between navigator state and terrain geometry that creates the condition for movement; tension is what holds that potential difference stable without collapsing it; harmonics is the dynamic behavior that emerges when potential and tension interact over time; and resistance, laminar flow, and turbulent flow are derived vocabulary describing the observable character of movement once it is occurring, not a formal layer and not primary.

Structural integrity is a genuinely separate category governing whether the model's internal representational geometry holds under sustained inference load — context pressure, token accumulation, competing objective tension — a property invisible to both the static landscape description and training-time navigator properties, measurable through activation drift analysis across varying context conditions, and not fully reducible to viscosity, elasticity, and memory despite formal overlap at the boundary.

The archaeological signal Atlas seeks lives in the scar tissue of turbulent training — not merely high-resistance regions but places of unresolved potential difference, where the gap between navigator state and terrain geometry never closed, where tension never found its harmonic, where the system stayed charged without discharging, and where the geological record of that retained potential is preserved in the weight structure of a frozen model as high-perplexity, high-viscosity saddle and valley behavior readable not as active turbulence but as the stratigraphic evidence of where the landscape's charge was never released; this claim is asserted on the framework's internal logic and requires formal derivation and empirical testing to be established.