Positions below the spines are positive numbers (+1 to +5 cm).
Imagine a diamond-shaped grid. Instead of just saying "This shape has 2 holes," the Hodge Plan breaks that information down into coordinates.
The dream is to create a "Hodge Plan" for these finite shapes, too. This is called . The problem is that we have the numbers, but we haven't proven that they arrange into a perfect "Hodge Plan" the way complex shapes do.
Hodge theory works perfectly for "complex" shapes (shapes defined using imaginary numbers). However, mathematicians also work with shapes defined in finite fields (modular arithmetic—like the math used in cryptography).
Can every geometric shape described by the Hodge Plan actually be built out of simple geometric blocks (algebraic cycles)?
