[BENCHMARK] HCB-1: The Hypometabolic Crash (Inverse Control Problem)

[ryanjmccall]

1. The Physics (Context)

We are introducing a new class of benchmark: Survival over Intelligence.

Current WBE (Whole Brain Emulation) simulations, such as those by Mujica-Parodi et al., fail not due to calculation speed, but due to memory bandwidth when modeling the massive feedback loops required for homeostatic control. They cannot efficiently solve the "Inverse Problem" for stiff dynamical systems, specifically detecting the phase transition where a brain snaps from stability to pathology (e.g., seizure) under energy stress.

2. The Task: HCB-1 (Hypometabolic Crash Benchmark)

We need a dataset generator that simulates a neural circuit under progressive energy starvation. The goal is to train models to predict the Critical Bifurcation Point—the exact moment the network loses synchrony and collapses.

The Challenge

Create a Python script that generates the following synthetic dataset:

• System: A standard neural mass model (e.g., Jansen-Rit or Wilson-Cowan) representing a cortical column.
• Constraint ($E$): A variable representing "Available Energy" (ATP flux).
  • $t=0$: Energy is 100%.
  • $t=end$: Energy decays to 0%.
• The Signal: As $E$ drops, the control loop fights to maintain stability (allostasis). Eventually, it fails.
• Target Label ($Y$): The precise timestamp ($t_{crash}$) where the system hits a bifurcation and enters a chaotic or silent state.

3. The Deliverable (Acceptance Criteria)

A Pull Request adding benchmarks/hcb_1/generator.py that outputs:

1. Input Tensor: [Connectivity_Graph, Energy_Scalar_t]
2. Output: A time-series plot showing the "Critical Slowing Down" (the wobble before the crash).
3. Verification: A test ensuring the crash point shifts deterministically as we change the network topology (e.g., a "Small World" network should survive longer than a random network).

4. The Prize

• Bounty: 500 USDC (Escrowed via Agoric Zoe).
• Mechanism: Funds released immediately upon passing the verify_bifurcation test in CI.

References

• Lilianne R. Mujica-Parodi, "The Inverse Problem in Hidden Control Systems"
• Concept: [Bifurcation Diagrams and Phase Transitions]
• *https://github.com/Neuroblox