Move Merklist summary to second cell; move drafts to other branch

2021-07-07-Merklist.ipynb

@@ -2,10 +2,17 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "2bdec887-ee29-4bef-8978-88a81940f7bc",
+   "id": "83dd7287-bca5-49f9-b927-31bbc519d5b9",
+   "metadata": {},
+   "source": [
+    "# Merklist"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bf97974c-5582-4bf5-8ed8-6c43daf5036c",
    "metadata": {},
    "source": [
-    "# Merklist\n",
     "Using matrix multiplication's associativity and non-commutativity properties provides a natural definition of a cryptographic hash / digest / summary of an ordered list of elements. Due to the non-commutativity property, lists that only differ in element order result in a different summary. Due to the associativity property, arbitrarily divided adjacent sub-lists can be summarized independently and combined to quickly find the summary of their concatenation. This definition provides exactly the properties needed to define a list, and does not impose any unnecessary structure that could cause two equivalent lists to produce different summaries. The name *Merklist* is intended to be reminicent of other hash-based data structures like [Merkle Tree](https://en.wikipedia.org/wiki/Merkle_tree) and [Merklix Tree](https://www.deadalnix.me/2016/09/24/introducing-merklix-tree-as-an-unordered-merkle-tree-on-steroid/)."
    ]
   },

2021-XX-XX-Merklist-Field.ipynb

@@ -1,115 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "acb06966-8cfa-4b28-9fa9-30286c33d20c",
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "markdown",
-   "id": "203b80b6-7559-4861-ab9c-538885b8d223",
-   "metadata": {
-    "tags": []
-   },
-   "source": [
-    "## Inverse?"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "id": "66031921-f6b4-4c32-bc8b-97a92ea935df",
-   "metadata": {
-    "jupyter": {
-     "source_hidden": true
-    },
-    "tags": []
-   },
-   "outputs": [],
-   "source": [
-    "# Q: If you compute the inverse of one of these matrixes and multiply it to the right of the position\n",
-    "#    where it was originally multiplied it should \"delete\" that element as if the element was never added.\n",
-    "#    I'm uncertain of the possibility and frequency of such inverse matrices over finite fields.\n",
-    "#    If this scenario is possible to construct, I think we should \"define\" this operation as deletion.\n",
-    "\n",
-    "# See: https://en.wikipedia.org/wiki/Determinant#Properties_of_the_determinant\n",
-    "\n",
-    "def det2(mat, m=256):\n",
-    "    ((a, b),\n",
-    "     (c, c)) = mat\n",
-    "    return (a*c - b*c) % m\n",
-    "\n",
-    "def det3(mat, m=256):\n",
-    "    ((a, b, c),\n",
-    "     (d, e, f),\n",
-    "     (g, h, i)) = mat\n",
-    "    return (a*e*i + b*f*g + c*d*h - c*e*g - b*d*i - a*f*h) % m\n",
-    "\n",
-    "def det(mat, m=256):\n",
-    "    # I dislike having to round here, but it returns a float\n",
-    "    # I wish it returned a native \"B\" type\n",
-    "    return int(round(np.linalg.det(mat),0)) % m\n",
-    "\n",
-    "a = ((-2,2,-3),(-1,1,3),(2,0,-1))\n",
-    "assert_equal(det(a), 18)\n",
-    "assert_equal(det(a), det3(a))\n",
-    "\n",
-    "# ?\n",
-    "# assert that they didn't change since the last time I ran it\n",
-    "assert_equal(det(f1), 128)\n",
-    "assert_equal(det(f2), 160)\n",
-    "assert_equal(det(f3), 128)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "568ad4ed-7894-465b-9bf3-f19f2269c0f3",
-   "metadata": {
-    "tags": []
-   },
-   "source": [
-    "[This](https://math.stackexchange.com/questions/273054/how-to-find-matrix-inverse-over-finite-field) suggests to find the inverse matrix by first finding the adjugate then applying\n",
-    "\n",
-    "> (1/det(A))adj(A)=inv(A)\n",
-    "\n",
-    "Under mod p\n",
-    "\n",
-    "---\n",
-    "\n",
-    "The [adjugate](https://en.wikipedia.org/wiki/Adjugate_matrix) is the inverse of the cofactor matrix.\n",
-    "\n",
-    "---\n",
-    "\n",
-    "The cofactor matrix is made by multiplying the matrix minor of each (i,j) of the original matrix times a sign factor.\n",
-    "\n",
-    "---\n",
-    "\n",
-    "The (i,j)-minor of matrix A is the determinant of the matrix A with row i & column j removed."
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.2"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}

2021-XX-XX-Merklist-Tree.ipynb

@@ -1,36 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "d6b5f16e-76a4-473f-a8cd-efd532f8673f",
-   "metadata": {},
-   "source": [
-    "# Merklist Tree\n",
-    "\n",
-    "Part 2 of the Merklist idea. Constructing a tree structure of summarized sublists, so that mutations to the list can be computed, verified, and stored using $O(log(N))$ time and space.\n",
-    "\n"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.2"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}