Math &
Theory

Nine diagrams. One universal math substrate. The Inverse Cinematography loop, the bake cascade, the geometric tranche — every named theorem with its application + tool wiring.

All plates rendered in the Nostromo Deep palette. Utilitarian science-abstract: thin strokes, corner ticks, monospace labels, off-white on black. Each figure references the shipped Python module that realises it.

The four pipeline plates that ship with Scene Stager covers — they show the typed compiler boundary, the bake DAG, the six camera-rig profiles, and the target-linked lighting model.

FIG. 01 · SceneScript → IR → MoksBakePlan → Host adapter · seven-slot front door · ten op types in the DAG · Blender / Maya / Unreal parity

FIG. 02 · 11-phase bake cascade · topological ordering · validate → camera → lens → noise → sequence → light · H_spec gate triggers MATERIAL_SWEEP conditionally

FIG. 03 · 6 rig profiles · tripod_locked · moco · technocrane · wirecam · dolly · drone · each with its own perlin / damped spring / catenary imperfection model

FIG. 04 · target-linked lighting · H_spec ceiling · film-stock envelope · global_fill = 0 + rim_mode = target_linked → emit MATERIAL_SWEEP

Each heuristic estimator in the Inverse Cinematography loop has a theorem-grade counterpart with named, bounded failure modes. These five plates show the substitution surfaces.

FIG. 05 · Fabric Transform Tree pullback · M_parent = Σ Jᵀ M J · closed-form Newton step · 5 iterations → 1–2 iterations · ftt_pullback.py

FIG. 06 · Morse-Smale Lotus point · Banchoff cyclic-link → MAX / MIN / SADDLE · Lotus = contained extremum · window-blowout robust · morse_smale_estimator.py

FIG. 07 · Betti signature · β₀ / β₁ of the specular mask · machined (high β₀, low β₁) vs organic · organicity drives h_spec_max · betti_signature.py · topology_fuser.py

FIG. 08 · Operator commutativity TargetLink · ‖C_ij·S_i − S_j·C_ij‖_F = 0 · intrinsic transport · umbilic-immune · seam_connection.py · target_link_intrinsic.py

FIG. 09 · L=2 spherical harmonics · HDRI → 9 bands × RGB = 27 floats · Ramamoorthi-Hanrahan reconstruction · sub-kilobyte JSON payload · sh_projection.py