Framework

Loss Landscape Vocabulary Framework

v12 · April 2026 · Atlas Heritage Systems Inc. · Working document — not a finished product

Terrain Topology Global Geometry Navigator Flow & Resistance Structural Integrity Ablation Potential & Tension Architecture Summary

Flow & Resistance Vocabulary

Describes what happens at interaction points between terrain and navigator. These are illustration vocabulary derived from fluid dynamics — not a formal third layer. The Reynolds number analogy is dimensionally incoherent as a formal metric (confirmed by DeepSeek V3 adversarial review) and is retained as illustration only.

Resistancehigh / low

The composite opposing force at any point in the loss landscape. Integrates slope, friction, viscosity, tension, and coupling. Resistance is derived, not primary — potential difference is the primary generative quantity.

F_drag = −b·v b = drag coefficient (composite) v = gradient update magnitude

Stokes (1851) drag; Foret et al. (2020) SAM

Laminar Flowdirected / smooth

Movement through low-resistance regions. Clean, directed, fast convergence toward attractors. Where remagnetization completes without resistance. Archaeological signal absent or already overwritten.

Re << 1 (low Reynolds number regime)

Reynolds (1883); Izmailov et al. (2018)

Turbulent Flowcontested / high-drag

Movement through high-resistance regions. Slow, contested. The model does not resolve cleanly. Turbulence is only observable during movement — what you read in a frozen model is the scar tissue turbulence left behind.

Re >> 1 (high Reynolds number regime)

Reynolds (1883); Dauphin et al. (2014)

Reynolds Numberillustration only

Ratio of gradient momentum to local resistance — predicts laminar vs turbulent transition. Retained as illustration only.

Re_landscape = ‖∇L‖ / b(θ) [illustration only] Fluid Re = ρvL/μ [dimensionally coherent]

Dimensionally incoherent as formal metric — confirmed by DeepSeek V3 adversarial review

Reynolds (1883)

Drag Coefficienthigh / low

The composite resistance property of a specific location, absorbing all terrain and navigator contributions. The drag coefficient profile across the landscape is what ablation changes.

b(θ) = f(η, {λ_i}, Var[∇L], ‖∇L_task − ∇L_reg‖, H_off-diag)

Keskar et al. (2016); Sagun et al. (2017)