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Add constant 80 (Ising perceptron capacity threshold)#47

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Robertboy18 wants to merge 2 commits intoteorth:mainfrom
Robertboy18:add-ising-perceptron-capacity-threshold
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Add constant 80 (Ising perceptron capacity threshold)#47
Robertboy18 wants to merge 2 commits intoteorth:mainfrom
Robertboy18:add-ising-perceptron-capacity-threshold

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@Robertboy18
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So, I added constants/80a.md for the Ising perceptron capacity threshold, which I think is a really exciting problem at the boundary of probability, combinatorics, and theoretical machine learning.

Informally, this constant measures how many random constraints a binary perceptron can satisfy before solutions disappear. In other words, it is a sharp “capacity limit” for a simple neural-network-style model with binary weights.

This PR includes some of the older upper-bound history, the Krauth Mézard prediction which I thought is cool, and the more recent rigorous progress, while trying to clearly separate unconditional results from conditional bounds. I also added the corresponding row to README.md.

Let me know if anything else is needed or changes! I did use GPT5.4 Pro for help with a deeper literature study.

Copilot AI review requested due to automatic review settings March 7, 2026 23:32
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Pull request overview

Adds a new constants entry documenting the Ising (binary) perceptron zero-margin storage-capacity threshold and links it from the main constants table in the README.

Changes:

  • Added constants/80a.md describing the constant, bounds, and references for the Ising perceptron capacity threshold.
  • Updated README.md to include the new constant in the constants index table.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 6 comments.

File Description
constants/80a.md New constant entry defining the threshold and summarizing known bounds and references.
README.md Adds the row linking to constant 80 and summarizing current bounds.

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@Robertboy18
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Robertboy18 commented Mar 7, 2026

Addressed all the Copilot reviews!!

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