The Geometry of
Admissible Computation

The left panel is trajectory space 𝒳. Points represent distinct life histories; their vertical position encodes hidden attributes (family endowment, circumstance, luck). The right panel is the achievement manifold 𝓜 — the projection π: 𝒳 → 𝓜 that discards all but one axis.

Drag points in 𝒳. Toggle Show Fibers to reveal which distinct trajectories collapse to the same achievement point. Toggle Collapse to simulate meritocratic hubris: the fiber vanishes and only the projected position remains.

The RSVP scalar field Φ(x) measures the degree to which each state admits coherent semantic continuations. Local maxima of Φ are admissibility basins — stable attractors of the semantic flow field v = α∇Φ.

Click to release a particle. It follows the gradient flow toward the nearest admissibility maximum. Add Basin to place a new attractor. Entropy controls the noise term ξ, the magnitude of which tests Lyapunov stability.

The semantic manifold is Whitney-stratified into regions of differing representational dimension. Strata are shown as colored bands; boundaries enforce Whitney condition B — the tangent constraint governing admissible phase transitions.

Draw a trajectory by clicking and dragging. An admissible trajectory (green) follows the tangent constraint at stratum crossings. A non-admissible trajectory (red) cuts through transversally. Toggle Force Admissible to see how the trajectory is deflected to satisfy the constraint.

MEM|8 stores memories as wave packets — stabilized field configurations parameterized by amplitude A (brightness), frequency ω (semantic content), and phase φ (flow direction). Retrieval fires a probe wave whose overlap with each memory determines the retrieval weight w_m.

Click to place a memory. Fire Probe emits a retrieval cue from the cursor position; memory packets whose frequency matches the cue resonate (flare bright). Adjust cue freq to see selective activation.

Each agent has an admissible future cone A(i) — the set of accessible states from their current position. Collective admissibility is the colimit colim A(i), assembling compatible futures along their overlaps.

Drag agents (colored dots). The intersection region A_collective is shown in amber; when agents are separated beyond a threshold, the intersection collapses and collective agency fails (the region turns red). Add Agent introduces a new participant.