vault backup: 2026-04-09 11:51:04

.gitignore

@@ -0,0 +1 @@
+.trash/

.obsidian/community-plugins.json

@@ -8,5 +8,7 @@
   "highlightr-plugin",
   "obsidian-file-color",
   "darlal-switcher-plus",
-  "dataview"
+  "dataview",
+  "obsidian-vimrc-support",
+  "emoji-shortcodes"
 ]

.obsidian/plugins/emoji-shortcodes/data.json

@@ -0,0 +1,9 @@
+{
+  "immediateReplace": true,
+  "suggester": true,
+  "historyPriority": true,
+  "historyLimit": 100,
+  "history": [
+    ":gear:"
+  ]
+}

.obsidian/plugins/emoji-shortcodes/manifest.json

@@ -0,0 +1,11 @@
+{
+	"id": "emoji-shortcodes",
+	"name": "Emoji Shortcodes",
+	"version": "2.2.0",
+	"minAppVersion": "1.0.0",
+	"description": "This Plugin enables the use of Markdown Emoji Shortcodes :smile:",
+	"author": "phibr0",
+	"authorUrl": "https://github.com/phibr0",
+	"isDesktopOnly": false,
+	"fundingUrl": "https://ko-fi.com/phibr0"
+}

.obsidian/plugins/emoji-shortcodes/styles.css

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+a[href="https://ko-fi.com/phibr0"] > img
+{
+  height: 3em;
+}
+
+a[href="https://ko-fi.com/phibr0"]
+{
+  transform: translate(0, 5%);
+}
+
+.ES-suggester-container {
+  display: flex;
+  place-content: space-between;
+}
+
+.ES-shortcode {
+  margin-right: 8px;
+}
+
+.ES-suggestion-item {
+  border-top: solid var(--background-secondary) 1px;
+  padding-left: 10px;
+}
+
+.ES-sub-setting {
+  padding-left: 2em;
+}
+.ES-sub-setting + .ES-sub-setting {
+  padding-left: 0;
+  margin-left: 2em;
+}

.obsidian/plugins/obsidian-file-color/data.json

@@ -1,5 +1,5 @@
 {
-  "cascadeColors": false,
+  "cascadeColors": true,
   "colorBackground": false,
   "palette": [],
   "fileColors": []

.obsidian/plugins/obsidian-vimrc-support/data.json

@@ -0,0 +1,14 @@
+{
+  "vimrcFileName": ".obsidian.vimrc",
+  "displayChord": true,
+  "displayVimMode": true,
+  "fixedNormalModeLayout": false,
+  "capturedKeyboardMap": {},
+  "supportJsCommands": false,
+  "vimStatusPromptMap": {
+    "normal": "🟢",
+    "insert": "🟠",
+    "visual": "🟡",
+    "replace": "🔴"
+  }
+}

.obsidian/plugins/obsidian-vimrc-support/manifest.json

@@ -0,0 +1,10 @@
+{
+  "id": "obsidian-vimrc-support",
+  "name": "Vimrc Support",
+  "version": "0.10.2",
+  "description": "Auto-load a startup file with Obsidian Vim commands.",
+  "minAppVersion": "0.15.3",
+  "author": "esm",
+  "authorUrl": "",
+  "isDesktopOnly": false
+}

.obsidian/workspace.json

@@ -4,35 +4,49 @@
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     "children": [
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+        "id": "81f0ebb32620dead",
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+            "id": "140d404d9b2faf63",
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             "state": {
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               "state": {
-                "file": "99 Templates/New File Template.md",
+                "file": "10 Courses/02 - SoSe 2026/AT/29593852 - Strings.md",
                 "mode": "source",
                 "source": false
               },
               "icon": "lucide-file",
-              "title": "New File Template"
+              "title": "29593852 - Strings"
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+            "id": "e179fd2c20f4067e",
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             "state": {
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               "state": {
-                "file": "10 Courses/02 - SoSe 2026/ET II/29592733 - Zählpfeilsysteme.md",
+                "file": "00 Inbox/29595454 - Komplexe Zahlen und Eigenwertaufgaben.md",
                 "mode": "source",
                 "source": false
               },
               "icon": "lucide-file",
-              "title": "29592733 - Zählpfeilsysteme"
+              "title": "29595454 - Komplexe Zahlen und Eigenwertaufgaben"
+            }
+          },
+          {
+            "id": "1e58a188bb5d367b",
+            "type": "leaf",
+            "state": {
+              "type": "markdown",
+              "state": {
+                "file": "10 Courses/02 - SoSe 2026/AT/29593952 - Regular Languages.md",
+                "mode": "source",
+                "source": false
+              },
+              "icon": "lucide-file",
+              "title": "29593952 - Regular Languages"
             }
           }
         ],
@@ -93,7 +107,7 @@
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     ],
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-    "width": 320.50418853759766
+    "width": 411.50418853759766
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   "right": {
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@@ -197,44 +211,53 @@
       "darlal-switcher-plus:Open Symbols for the active editor": false
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.trash/1775572307685 - Lecture 1 Summary.md

@@ -1,18 +0,0 @@
----
-created: 2026-04-07 16:31
-course:
-topic:
-type: lecture
-status: 🔴
-tags:
-  - university
----
-## 📌 Summary
-
-> [!abstract]
->
-
----
-
-## 📝 Content
-

.trash/29592872.615316667 - Lecture 1 Recp.md

@@ -1,18 +0,0 @@
----
-created: 2026-04-07 16:32
-course:
-topic:
-type: lecture
-status: 🔴
-tags:
-  - university
----
-## 📌 Summary
-
-> [!abstract]
->
-
----
-
-## 📝 Content
-

.trash/29592877 - review.md

@@ -1,18 +0,0 @@
----
-created: 2026-04-07 16:37
-course:
-topic:
-type: lecture
-status: 🔴
-tags:
-  - university
----
-## 📌 Summary
-
-> [!abstract]
->
-
----
-
-## 📝 Content
-

.trash/29593223 - 29593223 - Elektrotechnik II.md

@@ -1,19 +0,0 @@
----
-created: 2026-04-07 22:23
-course:
-topic:
-related:
-type: lecture
-status: 🔴
-tags:
-  - university
----
-## 📌 Summary
-
-> [!abstract]
->
-
----
-
-## 📝 Content
-

.trash/29593223 - Elektrotechnik II.md

@@ -1,19 +0,0 @@
----
-created: 2026-04-07 22:23
-course:
-topic:
-related:
-type: lecture
-status: 🔴
-tags:
-  - university
----
-## 📌 Summary
-
-> [!abstract]
->
-
----
-
-## 📝 Content
-

.trash/29593224 - 29593223 - 29593223 - Elektrotechnik II.md

@@ -1,19 +0,0 @@
----
-created: 2026-04-07 22:24
-course:
-topic:
-related:
-type: lecture
-status: 🔴
-tags:
-  - university
----
-## 📌 Summary
-
-> [!abstract]
->
-
----
-
-## 📝 Content
-

.trash/29593226 - ET_II_Folien_gesamt_020426.pdf.md

@@ -1,19 +0,0 @@
----
-created: 2026-04-07 22:26
-course:
-topic:
-related:
-type: lecture
-status: 🔴
-tags:
-  - university
----
-## 📌 Summary
-
-> [!abstract]
->
-
----
-
-## 📝 Content
-

.trash/Untitled 2.md

@@ -1,320 +0,0 @@
-# Arithmetic
-
-## Asymptotic Equivalence Classes (Big-O)
-
-The equivalence relation definition given in the task is asking you to find functions that grow at the exact same rate (also known as Big-Theta $\Theta$):
-
-$f asymp g <==> f in O(g) and g in O(f)$
-
-Notation of $f in O(g)$ means "function $f$ doesn't grow faster than $g$"
-
-### The "Dominant Term" Rule
-To find which class a function belongs to, simplify it to its core growth rate:
-1.  **Drop all lower-order terms:** In $n^3 + n^2$, drop the $n^2$.
-2.  **Drop all constant multipliers:** $5n^2$ and $1000n^2$ both become just $n^2$.
-3.  **Identify the highest rank:** Factorials ($n!$) > Exponentials ($2^n$, $e^n$) > Polynomials ($n^3$, $n^2$) > Linear ($n$) > Logarithmic ($log n$) > Constant ($1$).
-
-## Euclidian Algorithm
-Purpose is to find the **GCD** (Greatest Common Divisor).
-
-### Core Rule
-Fill out this formula:
-$$"Dividend" = ("Quotient" * "Divisor") + "Remainder"$$
-1. **Divide** the bigger number by the smaller one
-2. **How many times** does it fit -> $"Quotient"$
-3. Find out **whats leftover** -> $"Remainder"$
-4. **Shift to left** and repeat ($"Old Divisor" -> "Dividend"$, $"Remainder" -> "Divisor"$)
-
-Result is the last $"Remainder"$ that is not $0$.
-
-### Bezout Coefficients
-**Goal:** find a $x$ and $y$ so that $"Divident" * x + "Divisor" * y = gcd("Dividend", "Divisor")$
-
-1. **Rewrite Euclid (above) equations** to solve for remainder ($"Remainder" = "Old Remainder" - "Dividend" * "Divisor"$)
-2.  **Substitute remainders** -> $$
-
----
-
-# Counting
-
-## Inclusion-Exclusion Principle
-Principle that dictates that when combining / overlapping sets, you have to make sure to not include elements that occur in multiple sets multiple times.
-
-### Example:
-How many integers between $1$ and $10^6$ are of the form $x^2$ or $x^5$ for some $x in NN$?
-#### How many $x^2$?
-$sqrt(10^6) = 10^3 = 1.000$
-#### How many $x^5$?
-By estimation:
-$$
-&15^5 = 759,375 && "--- in the range / below" 10^6 \
-&16^5 = 1,048,576 && "--- outside the range / above" 10^6 \
-&=> 15 "numbers in the form "x^5"exist" &&
-$$
-> [!warning]
-> Now, we can't add $1,000$ and $15$, since there are numbers that match both, so we need to subtract these duplicates.
-
-#### How many $x^2$ and $x^5$ / $x^10$?
-$$
-& 3^10 = 59,049 \
-& 4^10 = 1,048,576 \
-& => 3 "numbers that are both" x^2 "and" x^5 "exist"
-$$
-#### Final calculation:
-Formula: $"Elements that are" x^2 + "Elements that are" x^5 - "Elements that are both"$
-$==> 1,000 + 15 - 3 = 1,012$
-
-### For two sets
-$|"Total possibilities"| - |"Avoid 1"| - |"Avoid 2"| + |"Avoid Both"|$
-Where 
-- $"Avoid 1"$ are all elements *not matching* condition 1
-- $"Avoid 2"$ are all elements *not matching* condition 2
-- $"Avoid Both"$ are all elements *not matching* condition 1 **and** 2
-
-## Type of Task: Boolean Lattice
-Find the amount of upper bounds in ${0, 1}^5$ for the set of vectors $S = {x, y, z}$
-$$
-& x = (0, 1, 0, 0, 0) \
-& y = (0, 0, 1, 0, 1) \ 
-& z = (0, 1, 1, 0, 0) \
-$$
-> [!INFO]
-> Method used is called **All-Zero Column Method**
-
-We look for columns that have $0$'s in all three vectors: Column $1$ and $4$, that's $2$ columns, so we define $k = 2$.
-To get our result we calculate $2^k$ since there are only two possible states for each value $(0, 1)$: 
-$2^2 = 4$.
-So we have **4** upper bounds in total.
-
-> [!INFO]
-> For the amount of lower bounds we'd check for all-ones columns
-
----
-
-# Functions
-A function takes in an element from its **domain**, transforms it in someway and outputs that transformed element, which is part of the **co-domain**.
-Every element of the **domain** must map to a value in the **co-domain**, all values of the **co-domain** that are mapped to form the functions **image**.
-A function must be **deterministic** - one input can only map to a single output.
-
-## Notation
-General function notation: $f: X -> Y$
-
-> [!INFO]
-> $f$: name of the function
-> $X$: Domain
-> $Y$: Co-domain
-> $f(x)$: Image of $f$
-> $X$, $f(x)$ and $Y$ are [[Set Theory | Set]]
-
-For any $x in X$ the output $f(x)$ is an element of $Y$.
-
-## Mapping Properties
-### Injectivity
-A function is _injective_ if every element in $y in f(x)$ has _at most_ one matching $x in X$.
-- $forall y in Y,exists excl x in X : f(x) = y$
-### Surjectivity
-A function is _surjective_ if every element $y in Y$ has _at minimum_ one matching $x in X$
-- $forall y in Y, exists x in X : f(x) = y$
-
-### Bijectivity
-A function is _bijective_ if every element $y in Y$ has _exactly_ one matching $x in X$ (it is _injective_ and _surjective_)
-- $forall y in Y, exists excl x in X : f(x) = y$
-
----
-
-# Logic
-
-## Operators 
-| Operation         | Explanation                          | Notation  |
-| ----------------- | ------------------------------------ | --------- |
-| **and**<br>       | Both $p$ and $q$ must be true        | $p and q$ |
-| **or** | Either $p$ or $q$ (or both) are true | $p or q$  |
-| **not** | Negates the statement                | $not p$   |
-| **Implication** | If $p$ then $q$                      | $=>$      |
-| **Biconditional** | $p$ if and _only_ if $q$             | $<=>$     |
-| **xor** | Either $p$ or $q$ but not both       | $xor$     |
-
-### Implied Operators
-| Operation | Explanion                               | Notation       |
-| --------- | --------------------------------------- | -------------- |
-| **nand** | $p$ and $q$ are not both true           | $not(p and q)$ |
-| **nor** | neither of $p$ and $q$ are true         | $not(p or q)$  |
-| **xnor** | $p$ and $q$ are both false or both true | $not xor$      |
-
----
-
-# Relations
-
-## Types of Relations
-
-| Relation         | Explanation                                                                                                           | Example                   |
-| ---------------- | :-------------------------------------------------------------------------------------------------------------------- | ------------------------- |
-| *transitive*<br> | "chain reaction", a information about $a$ in relation to $c$ can be inferred from the relations $a -> b$ and $b -> c$ | $a < b, b < c => a < c$   |
-| *reflexive* | every element is related to itself with the given relation                                                            | $a <= a, 5 = 5$           |
-| *anti-reflexive* | every element is *NOT* related to itself in the given relation                                                        | $a < a$                   |
-| *symmetric* | the given relation work both ways                                                                                     | $a = b => b = a$          |
-| *antisymmetric* | the given relation only works both ways if $a$ and $b$ are the same                                                   | $a <= b, b <= a => a = b$ |
-
-
-## Equivalence Relations
-A relation $R$ is called _equivalence relation_ when it is _transitive, reflexive and symmetric_.
-
-### Example: 
-**Question:** How many equivalence classes are there for the given equivalence relation?
-$$
-& ~ "on" {0, 1, 2, 3}^(2) \
-& "defined by" (x_1, y_1) ~ (x_2, y_2) <==> x_1 + y_1 = x_2 + y_2
-$$
-> [!INFO]
-> Meaning: 
-> The pairs $(x_1, y_1)$ and $(x_2, y_2)$ are equivalent to each other when the components of the pair added up have the same result.
-
-Solving: 
-- Smallest possible sum: $(0 + 0) = 0$
-- Biggest possible sum: $(3 + 3) = 6$
-- All possible sums: $0, 1, 2, 3, 4, 5, 6$
-
-Each possible sum creates it's own equivalence class. So there are $7$ equivalence classes.
-
-> [!NOTE]
-> All equivalence classes:
-> $[0]_(~) = {(0, 0)}$
-> $[1]_(~) = {(0, 1), (1, 0)}$
-> $[2]_(~) = {(0, 2), (1, 1), (2, 0)}$
-> $[3]_(~) = {(0, 3), (1, 2), (2, 1), (3, 0)}$ 
-> $[4]_(~) = {(1, 3), (2, 2), (3, 1)}$
-> $[5]_(~) = {(2, 3), (3, 2)}$
-> $[6]_(~) = {(3, 3)}$
-
-## Binary Relation
-A binary relation is a relation $R$ between _exactly two_ elements $a in R$ and $b in R$. An example for a binary relation is $a <= b$
-
-## Converse Relation
-$C^top$ or $C^(-1)$ is the relation that occurs if the elements of a _binary relation_ are switched.
-
-## Composition of Relations - Example
-$$
-"Compute" Q^top compose R "with:"\
-Q = {(2, 2), (3, 3), (2, 1)} \
-R = {(1, 2), (3, 3), (3, 1)} \
-$$
-### 1. Apply converse to $Q$:
-$$
-Q^top = {(2, 2), (3, 3), (1, 2)}
-$$
-### 2. Perform Composition:
-Look at each pair in $R$, check if $Q^top$ has a pair starting with se second element in that pair:
-
-$$
-(1, 2) -> (2, 2) => (1, 2) \
-(3, 3) -> (3, 3) => (3, 3) \
-(3, 1) -> (1, 2) => (3, 2)
-$$
-### 3. Result:
-$$Q^top compose R = {(1, 2), (3, 2), (3, 3)}$$
-
-## Orders
-An **Order** is a mathematical way to sort, rank or compare elements within a set, where some elements come "before" and "after" others.
-
-A _binary relation_ is called an order if it is...
-- [?] a *reflexive relation*
-- [?] a *antisymmetric relation*
-- [?] a *transitive relation*
-
----
-
-# Set Theory
-A set is a collection of _unordered_ elements.
-A set cannot contain duplicates.
-
-## Notation
-### Set Notation
-Declaration of a set $A$ with elements $a$, $b$, $c$: 
-$$A := {a, b, c}$$
-
-### Cardinality
-Amount of Elements in a set $A$
-Notation: $|A|$
-$$
-A := {1, 2, 3, 4} \
-|A| = 4
-$$
-
-### Well-Known Sets
-- Empty Set: $emptyset = {}$
-- Natural Numbers: $N = {1, 2, 3, ...}$
-- Integers: $ZZ = {-2, -1, 0, 1, 2}$
-- Rational Numbers: $QQ = {1/2, 22/7 }$
-- Real Numbers: $RR = {1, pi, sqrt(2)}$
-- Complex Numbers: $CC = {i, pi, 1, sqrt(-1)}$
-
-### Set-Builder Notation
-Common form of notation to create sets without explicitly specifying elements.
-$$
-A := {x in N | 0 <= x <= 5} \
-A = {1, 2, 3, 4, 5}
-$$
-
-### Member of
-Denote whether $x$ is an element of the set $A$
-Notation: $x in A$
-Negation: $x in.not A$
-
-### Subsets
-| Type                     | Explanation                                                            | Notation            |
-| ------------------------ | ---------------------------------------------------------------------- | ------------------- |
-| **Subset** | Every element of $A$ is in $B$                                         | $A subset B$        |
-| **Subset or equal to** | Every element of $A$ is in $B$, or they are the exactly same set       | $A subset.eq B$     |
-| **Proper subset** | Every element of $A$ is in $B$, but $A$ is definitely smaller than $B$ | $A subset.sq B$<br> |
-| **Superset**<br>         | $A$ contains everything that is in $B$                                 | $A supset B$        |
-| **Superset or equal to** | $A$ contains everything that is in $B$, or they are identical          | $A supset.eq B$     |
-
-## Operations
-### Union
-Notation: $A union B$
-Definition: all elements from both sets _without adding duplicates_
-$$A := {1, 2, 3}\ B := {3, 4, 5}\ A union B = {1, 2, 3, 4, 5}$$
-
-### Intersection
-Notation:$A inter B$
-Definition: all elements _contained in both sets_
-$$
-A := {1, 2, 3} \
-B := {2, 3, 4} \
-A inter B = {2, 3}
-$$
-
-### Difference
-Notation: $A backslash B$ 
-Definition: all elements _in $A$ that are not in $B$_
-$$
-A := {1, 2, 3} \
-B := {3, 4, 5} \
-A backslash B = {1, 2}
-$$ 
-
-### Symmetric Difference
-Notation: $A Delta B$ 
-Definition: all elements _only in $A$ or only in $B$_
-$$
-A := {1, 2, 3} \
-B := {2, 3, 4} \
-A Delta B = {1, 4}
-$$
-
-### Cartesian Product
-Notation: $A times B$
-Definition: all pairs of all elements in $A$ and $B$
-$$
-A := {1, 2} \
-B := {3, 4, 5} \
-A times B = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}
-$$
-
-### Powerset
-Notation: $cal(P)(A)$
-Definition: all possible _Subsets of A_
-$$
-A := {1, 2, 3} \
-cal(P)(A) = {emptyset, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
-$$

.trash/mathe/notation.md

@@ -1,5 +0,0 @@
-# Notation
-
-## 1. Sets and Logic
-$|A|$: The *cardinality* (size) of finite set $A$.
-$script(p)$

.trash/merge.md

@@ -1,284 +0,0 @@
-## Asymptotic Equivalence Classes (Big-O)
-
-The equivalence relation definition given in the task is asking you to find functions that grow at the exact same rate (also known as Big-Theta $\Theta$):
-
-$f asymp g <==> f in O(g) and g in O(f)$
-
-Notation of $f in O(g)$ means "function $f$ doesn't grow faster than $g$"
-
-###  The "Dominant Term" Rule
-To find which class a function belongs to, simplify it to its core growth rate:
-1.  **Drop all lower-order terms:** In $n^3 + n^2$, drop the $n^2$.
-2.  **Drop all constant multipliers:** $5n^2$ and $1000n^2$ both become just $n^2$.
-3.  **Identify the highest rank:** Factorials ($n!$) > Exponentials ($2^n$, $e^n$) > Polynomials ($n^3$, $n^2$) > Linear ($n$) > Logarithmic ($log n$) > Constant ($1$).
-
-## Euclidian Algorithm
-Purpose is to find the **GCD** (Greatest Common Divisor).
-
-### Core Rule
-Fill out this formula:
-$$"Dividend" = ("Quotient" * "Divisor") + "Remainder"$$
-1. **Divide** the bigger number by the smaller one
-2. **How many times** does it fit -> $"Quotient"$
-3. Find out **whats leftover** -> $"Remainder"$
-4. **Shift to left** and repeat ($"Old Divisor" -> "Dividend"$, $"Remainder" -> "Divisor"$)
-
-Result is the last $"Remainder"$ that is not $0$.
-
-### Bezout Coefficients
-**Goal:** find a $x$ and $y$ so that $"Divident" * x + "Divisor" * y = gcd("Dividend", "Divisor")$
-
-1. **Rewrite Euclid (above) equations** to solve for remainder ($"Remainder" = "Old Remainder" - "Dividend" * "Divisor"$)
-2.  **Substitute remainders** -> ## Inclusion-Exclusion Principle
- Principle that dictates that when combining / overlapping sets, you have to make sure to not include elements that occur in multiple sets multiple times.
-
-### Example:
-How many integers between $1$ and $10^6$ are of the form $x^2$ or $x^5$ for some $x in NN$?
-#### How many $x^2$?
-$sqrt(10^6) = 10^3 = 1.000$
-#### How many $x^5$?
-By estimation:
-$$
-&15^5 = 759,375 && "--- in the range / below" 10^6 \
-&16^5 = 1,048,576 && "--- outside the range / above" 10^6 \
-&=> 15 "numbers in the form "x^5"exist" &&
-$$
-> [!warning]
-> Now, we can't add $1,000$ and $15$, since there are numbers that match both, so we need to subtract these duplicates.
-
-#### How many $x^2$ and $x^5$ / $x^10$?
-$$
-& 3^10 = 59,049 \
-& 4^10 = 1,048,576 \
-& => 3 "numbers that are both" x^2 "and" x^5 "exist"
-$$
-#### Final calculation:
-Formula: $"Elements that are" x^2 + "Elements that are" x^5 - "Elements that are both"$
-$==> 1,000 + 15 - 3 = 1,012$
-
-### For two sets
-$|"Total possibilities"| - |"Avoid 1"| - |"Avoid 2"| + |"Avoid Both"|$
-Where 
-- $"Avoid 1"$ are all elements *not matching* condition 1
-- $"Avoid 2"$ are all elements *not matching* condition 2
-- $"Avoid Both"$ are all elements *not matching* condition 1 **and** 2
-
-## Type of Task: Boolean Lattice
-Find the amount of upper bounds in ${0, 1}^5$ for the set of vectors $S = {x, y, z}$
-$$
-& x = (0, 1, 0, 0, 0) \
-& y = (0, 0, 1, 0, 1) \ 
-& z = (0, 1, 1, 0, 0) \
-$$
-> [!INFO]
-> Method used is called **All-Zero Column Method**
-
-We look for columns that have $0$'s in all three vectors: Column $1$ and $4$, that's $2$ columns, so we define $k = 2$.
-To get our result we calculate $2^k$ since there are only two possible states for each value $(0, 1)$: 
-$2^2 = 4$.
-So we have **4** upper bounds in total.
-
-> [!INFO]
-> For the amount of lower bounds we'd check for all-ones columns
-A function takes in an element from its **domain**, transforms it in someway and outputs that transformed element, which is part of the **co-domain**.
-Every element of the **domain** must map to a value in the **co-domain**, all values of the **co-domain** that are mapped to form the functions **image**.
-A function must be **deterministic** - one input can only map to a single output.
-
-## Notation
-General function notation: $f: X -> Y$
-
-> [!INFO]
-> $f$: name of the function
-> $X$: Domain
-> $Y$: Co-domain
-> $f(x)$: Image of $f$
-> $X$, $f(x)$ and $Y$ are [[Set Theory | Set]]
-
-For any $x in X$ the output $f(x)$ is an element of $Y$.
-
-## Mapping Properties
-### Injectivity
-A function is _injective_ if every element in $y in f(x)$ has _at most_ one matching $x in X$.
-- $forall y in Y,exists excl x in X : f(x) = y$
-### Surjectivity
-A function is _surjective_ if every element $y in Y$ has _at minimum_ one matching $x in X$
-- $forall y in Y, exists x in X : f(x) = y$
-
-### Bijectivity
-A function is _bijective_ if every element $y in Y$ has _exactly_ one matching $x in X$ (it is _injective_ and _surjective_)
-- $forall y in Y, exists excl x in X : f(x) = y$## Operators 
-| Operation         | Explanation                          | Notation  |
-| ----------------- | ------------------------------------ | --------- |
-| **and**<br>       | Both $p$ and $q$ must be true        | $p and q$ |
-| **or**            | Either $p$ or $q$ (or both) are true | $p or q$  |
-| **not**           | Negates the statement                | $not p$   |
-| **Implication**   | If $p$ then $q$                      | $=>$      |
-| **Biconditional** | $p$ if and _only_ if $q$             | $<=>$     |
-| **xor**           | Either $p$ or $q$ but not both       | $xor$     |
-### Implied Operators
-| Operation | Explanion                               | Notation       |
-| --------- | --------------------------------------- | -------------- |
-| **nand**  | $p$ and $q$ are not both true           | $not(p and q)$ |
-| **nor**   | neither of $p$ and $q$ are true         | $not(p or q)$  |
-| **xnor**  | $p$ and $q$ are both false or both true | $not xor$      |
-## Types of Relations
-
-| Relation         | Explanation                                                                                                           | Example                   |
-| ---------------- | :-------------------------------------------------------------------------------------------------------------------- | ------------------------- |
-| *transitive*<br> | "chain reaction", a information about $a$ in relation to $c$ can be inferred from the relations $a -> b$ and $b -> c$ | $a < b, b < c => a < c$   |
-| *reflexive*      | every element is related to itself with the given relation                                                            | $a <= a, 5 = 5$           |
-| *anti-reflexive* | every element is *NOT* related to itself in the given relation                                                        | $a < a$                   |
-| *symmetric*      | the given relation work both ways                                                                                     | $a = b => b = a$          |
-| *antisymmetric*  | the given relation only works both ways if $a$ and $b$ are the same                                                   | $a <= b, b <= a => a = b$ |
-
-
-## Equivalence Relations
-A relation $R$ is called _equivalence relation_ when it is _transitive, reflexive and symmetric_.
-
-### Example: 
-**Question:** How many equivalence classes are there for the given equivalence relation?
-$$
-& ~ "on" {0, 1, 2, 3}^(2) \
-& "defined by" (x_1, y_1) ~ (x_2, y_2) <==> x_1 + y_1 = x_2 + y_2
-$$
-> [!INFO]
-> Meaning: 
-> The pairs $(x_1, y_1)$ and $(x_2, y_2)$ are equivalent to each other when the components of the pair added up have the same result.
-
-Solving: 
-- Smallest possible sum: $(0 + 0) = 0$
-- Biggest possible sum: $(3 + 3) = 6$
-- All possible sums: $0, 1, 2, 3, 4, 5, 6$
-
-Each possible sum creates it's own equivalence class. So there are $7$ equivalence classes.
-
-> [!NOTE]
-> All equivalence classes:
-> $[0]_(~) = {(0, 0)}$
-> $[1]_(~) = {(0, 1), (1, 0)}$
-> $[2]_(~) = {(0, 2), (1, 1), (2, 0)}$
->$[3]_(~) = {(0, 3), (1, 2), (2, 1), (3, 0)}$ 
->$[4]_(~) = {(1, 3), (2, 2), (3, 1)}$
-> $[5]_(~) = {(2, 3), (3, 2)}$
-> $[6]_(~) = {(3, 3)}$
-
-## Binary Relation
-A binary relation is a relation $R$ between _exactly two_ elements $a in R$ and $b in R$. An example for a binary relation is $a <= b$
-
-## Converse Relation
-$C^top$ or $C^(-1)$ is the relation that occurs if the elements of a _binary relation_ are switched.
-
-## Composition of Relations - Example
-$$
-"Compute" Q^top compose R "with:"\
-Q = {(2, 2), (3, 3), (2, 1)} \
-R = {(1, 2), (3, 3), (3, 1)} \
-$$
-### 1. Apply converse to $Q$:
-$$
-Q^top = {(2, 2), (3, 3), (1, 2)}
-$$
-### 2. Perform Composition:
-Look at each pair in $R$, check if $Q^top$ has a pair starting with se second element in that pair:
-
-$$
-(1, 2) -> (2, 2) => (1, 2) \
-(3, 3) -> (3, 3) => (3, 3) \
-(3, 1) -> (1, 2) => (3, 2)
-$$
-### 3. Result:
-$$ Q^top compose R = {(1, 2), (3, 2), (3, 3)} $$
-
-## Orders
-An **Order** is a mathematical way to sort, rank or compare elements within a set, where some elements come "before" and "after" others.
-
-A _binary relation_ is called an order if it is...
-- [?] a *reflexive relation*
-- [?] a *antisymmetric relation*
-- [?] a *transitive relation*
-A set is a collection of _unordered_ elements.
-A set cannot contain duplicates.
-## Notation
-### Set Notation
-Declaration of a set $A$ with elements $a$, $b$, $c$: 
-$$ A := {a, b, c} $$
-### Cardinality
-Amount of Elements in a set $A$
-Notation: $|A|$
-$$
-A := {1, 2, 3, 4} \
-|A| = 4
-$$
-### Well-Known Sets
-- Empty Set: $emptyset = {}$
-- Natural Numbers: $N = {1, 2, 3, ...}$
-- Integers: $ZZ = {-2, -1, 0, 1, 2}$
-- Rational Numbers: $QQ = {1/2, 22/7 }$
-- Real Numbers: $RR = {1, pi, sqrt(2)}$
-- Complex Numbers: $CC = {i, pi, 1, sqrt(-1)}$
-
-### Set-Builder Notation
-Common form of notation to create sets without explicitly specifying elements.
-$$
-A := {x in N | 0 <= x <= 5} \
-A = {1, 2, 3, 4, 5}
-$$
-### Member of
-Denote whether $x$ is an element of the set $A$
-Notation: $x in A$
-Negation: $x in.not A$
-
-### Subsets
-| Type                     | Explanation                                                            | Notation            |
-| ------------------------ | ---------------------------------------------------------------------- | ------------------- |
-| **Subset**               | Every element of $A$ is in $B$                                         | $A subset B$        |
-| **Subset or equal to**   | Every element of $A$ is in $B$, or they are the exactly same set       | $A subset.eq B$     |
-| **Proper subset**        | Every element of $A$ is in $B$, but $A$ is definitely smaller than $B$ | $A subset.sq B$<br> |
-| **Superset**<br>         | $A$ contains everything that is in $B$                                 | $A supset B$        |
-| **Superset or equal to** | $A$ contains everything that is in $B$, or they are identical          | $A supset.eq B$     |
-
-## Operations
-### Union
-Notation: $A union B$
-Definition: all elements from both sets _without adding duplicates_
-$$ A := {1, 2, 3}\ B := {3, 4, 5}\ A union B = {1, 2, 3, 4, 5} $$
-### Intersection
-Notation:$A inter B$
-Definition: all elements _contained in both sets_
-$$
-A := {1, 2, 3} \
-B := {2, 3, 4} \
-A inter B = {2, 3}
-$$
-### Difference
-Notation: $A backslash B$ 
-Definition: all elements _in $A$ that are not in $B$_
-$$
-A := {1, 2, 3} \
-B := {3, 4, 5} \
-A backslash B = {1, 2}
-$$ 
-### Symmetric Difference
-Notation: $A Delta B$ 
-Definition: all elements _only in $A$ or only in $B$_
-$$
-A := {1, 2, 3} \
-B := {2, 3, 4} \
-A Delta B = {1, 4}
-$$
-### Cartesian Product
-Notation: $A times B$
-Definition: all pairs of all elements in $A$ and $B$
-$$
-A := {1, 2} \
-B := {3, 4, 5} \
-A times B = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}
-$$
-### Powerset
-Notation: $cal(P)(A)$
-Definition: all possible _Subsets of A_
-$$
-A := {1, 2, 3} \
-cal(P)(A) = {emptyset, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
-$$
-

00 Inbox/29595454 - Komplexe Zahlen und Eigenwertaufgaben.md

@@ -0,0 +1,40 @@
+---
+created: 2026-04-09 11:34
+course: "[[29595454 - Mathematik II]]"
+topic: komplexe Zahlen, Eigenwert
+related:
+type: lecture
+status: 🔴
+tags:
+  - university
+---
+## 📌 Summary
+
+> [!abstract]
+> 
+
+---
+
+## 📝 Content
+
+## Imaginäre Einheit
+Die imaginäre Einheit $i$ ist definiert über $i^2 = -1$.
+
+## Menge der komplexen Zahlen
+Die Elemente der menge $CC := {x + i y : x, y in RR}$ nennt man _komplexe Zahlen_.
+
+## Komplexe Zahlen
+Zu einer komplexen Zahl $z = x + i y in CC$ mit $x, y in RR$ heißt
+- $"Re" z := x$ _Realteil_ von $z$
+- $"Im" z := y$ _Imaginärteil_ von $z$
+- $overline(z) := x - i y$ die _konjugiert komplexe Zahl_ zu $z$
+- $abs(z) := sqrt(x^2 + y^2)$ der _Betrag_ von $z$
+- $phi in [0, 2pi]$ _Argument_ oder _Phase_ von $z$
+
+### Operationen
+
+#### Addition
+Die Addition wird (komponentenweise) wie für Vektoren definiert: 
+$a = vec(x, y), b = vec(x_2, y_2)$
+
+#### Multiplikation

10 Courses/02 - SoSe 2026/AT/29593850 - Automationtheory.md

@@ -0,0 +1,7 @@
+---
+created: 2026-04-08 08:50
+course: "[[29593850 - Automationtheory]]"
+type: overview
+tags:
+  - university
+---

10 Courses/02 - SoSe 2026/AT/29593852 - Strings.md

@@ -0,0 +1,71 @@
+---
+created: 2026-04-08 08:52
+course: "[[29593850 - Automationtheory]]"
+topic: strings
+related: "[[29593929 - Alphabets]]"
+type: lecture
+status: 🟢
+tags:
+  - university
+---
+## 📌 Summary
+
+> [!abstract]
+> Overview of lecture 1 on `Wednesday, 2026/Apr/08`
+
+---
+
+## 📝 Content
+
+A word (or _string_) is a finite sequence $w = a_1 a_2 ... a_n$ if characters from $Sigma$.
+
+> [!CONVENTION]
+> We will use small letters to describe strings that are part of a language.
+
+> [!EXAMPLE]
+> $"aa", "ab", "bba"$ and $"baab"$ are strings over $Sigma = {a, b}.
+
+#### Length of a string
+The _length_ $abs(x)$ of a string $x = a_1 ... a_n$ is its number $abs(x) = n$ of characters.
+#### Empty String
+The empty string is denoted by $epsilon$, this is the neutral element.
+-> $abs(epsilon) = 0$
+
+## String Operations
+### Concatenation
+String can be concatenated, where one string is appended to another. 
+For strings $x = a_1 ... a_n$ and $y  = b_1 ... b_m$ over alphabets $Sigma_x$ and $Sigma_y$, their _concatenation_ over the alphabet $Sigma = Sigma_x union Sigma_y$ is the string
+$$x circle.small y = x y = a_1 a_2 ... a_n b_1 b_2 ... b_m$$
+> This string is of the length $abs(x y) = n + m$
+
+> [!EXAMPLE]
+> $x = "apple"$
+> $y = "pie"$ 
+> $x circle.small y = "applepie"$
+
+Order of operations / Brackets do _not matter_. (Concatenation is associative but **not** commutative $x y eq.not y x$)
+> $(x circle.small y) circle.small z = x circle.small (y circle.small z)$
+
+Any string concatenated with the empty string $epsilon$ will result in itself.
+> $x circle.small epsilon = x = epsilon circle.small x$ 
+
+### Exponentiation
+
+The $n^"th"$ power $x^n$ of a string $x$ is the $(n-1)$-fold concatenation of $x$ with itself.
+> $x^0 := epsilon$
+> $x^n := x^(n-1) circle.small x$ for $n in NN$
+
+> [!Example]
+> $x^4 = x x x x$
+> $(a b)^3 = a b a b a b$
+
+### Reversing / Mirroring
+For a string $x = a_1 a_2 ... a_(n-1) a_n$ of length $n$, it's _mirrored string_ is given by 
+$$ x^("Rev") = a_n a_(n-1)...a_2 a_1$$
+## Substrings
+A string $x$ is a _substring_ of a string $y$ if $y = u x v$, where $u$ and $v$ can be arbitrary strings.
+- If $u = epsilon$ then $x$ is a _prefix_ of $y$.
+- If $v = epsilon$ then $x$ is a suffix of $y$.
+
+For strings $x$ and $y$ the quantity $abs(y)_x$ is the number of times that $x$ is a substring of $y$.
+

10 Courses/02 - SoSe 2026/AT/29593929 - Alphabets.md

@@ -0,0 +1,26 @@
+---
+created: 2026-04-08 10:09
+course: "[[29593850 - Automationtheory]]"
+topic: alphabets, characters
+related:
+type: lecture
+status: 🟢
+tags:
+  - university
+---
+## 📌 Summary
+
+> [!abstract]
+> Definition and examples of alphabets.
+
+---
+
+## 📝 Content
+
+Alphabets are formal, non-empty, finite, sets of characters (or _letters_ or _symbols_). They are denoted by $Sigma$.
+
+$Sigma = {a, b}$
+> Alphabet $Sigma$ contains the characters $a$ and $b$.
+
+$Sigma = {a, ..., z, A, ..., Z, 0, ..., 9}$
+> usual alphabet for writing text

10 Courses/02 - SoSe 2026/AT/29593935 - Kleene Star & Kleene Plus.md

@@ -0,0 +1,47 @@
+---
+created: 2026-04-08 10:15
+course: "[[29593850 - Automationtheory]]"
+topic: kleen
+related: "[[29593929 - Alphabets]]"
+type: lecture
+status: 🟢
+tags:
+  - university
+---
+## 📌 Summary
+
+> [!abstract]
+> Definition and Examples of the Kleene Star, the Kleene Plus and the Lemma Group Structure
+ 
+
+---
+
+## 📝 Content
+
+### Kleene Star
+Denoted by $Sigma^*$. The Kleene Star (or _Kleene operator_ or _Kleene Closure_) gives an infinite amount of [[29593852 - Strings|strings]] made up of the characters of the [[29593929 - Alphabets|alphabets]] $Sigma ^ *$. 
+$Sigma^*$ is the set of all string that can be generated by arbitrary concatenation of its characters.
+> $Sigma^* := union.big_(n>=0) A_n$
+> where $A_n$ is the set of all string combinations of length $n$
+
+#### Remarks
+- The same character can be used multiple times.
+- The empty string $epsilon$ is also part f $Sigma^*$.
+
+> [!Example]
+> $Sigma^* {a, b} = {epsilon, a, b, "aa", "ab", "ba", "bb", "aaa", "aab", ...}$
+
+> [!FACT]
+> - The set $Sigma^*$ is infinite, since we defined $Sigma$ to be non-empty.
+> - It is _countable_ and has the same cardinality as the set $NN$ of natural numbers
+
+### Kleene Plus
+The _Kleene Plus_ of an alphabet $Sigma$ is given by $Sigma^+ = Sigma^* backslash {epsilon}$ 
+
+### Lemma group structure
+The _Lemma group structure_ is induced by the [[29593935 - Kleene Star & Kleene Plus#Kleene Star|Kleene Star]] - it is a monoid, that is a semigroup with a neutral element.
+
+> [!PROOF]
+> - Associativity has been shown
+> - Existence  of a neutral element has been shown.
+> - Closure under $circle.small$: Let $x in Sigma^*$ and $y in Sigma^*$ be two string over the alphabet $Sigma$. Then $x circle.small y = x y in Sigma^*$

10 Courses/02 - SoSe 2026/AT/29593940 - Formal Languages.md

@@ -0,0 +1,54 @@
+---
+created: 2026-04-08 10:20
+course: "[[29593850 - Automationtheory]]"
+topic: languages
+related:
+type: lecture
+status: 🟢
+tags:
+  - university
+---
+## 📌 Summary
+
+> [!abstract]
+> Definition and example for formal languages
+ 	
+
+---
+
+## 📝 Content
+
+A formal _language_ of the alphabet $Sigma$ is a subset $L$ of $Sigma^*$.
+
+> [!EXAMPLE]
+> For alphabet $Sigma = {a, b}$, let $L_1$ be the set of all string starting with $b$, followed by an arbitrary number of $a$'s, and ending with $b$:
+> $L_1 = {b a^n b | n in NN_0}$
+> Then $b b in L_1, b a b in L_1$, etc.
+>
+>More in  [[29593895 - atfl-st2026-l01-formal-languages-full.pdf#page=54]]
+
+## Language Operations
+
+### Concatenation of languages
+For languages $X subset Sigma^*_X$ over alphabet $Sigma_X$ and $Y subset Sigma^*_Y$ over alphabet $Sigma_Y$, their _concatenation_ is
+> $X circle.small Y = X Y = {x y bar x in X and y in Y}$
+
+The concatenation of $X$ and $Y$ thus contains all string combinations where the prefix is a string from $X$ and the suffix is a string from $Y$.
+
+> [!CONVENTION]
+> Concatenation has a higher precedence than set operations ($union, inter$).
+
+### Exponentiation of languages
+The $n^"th"$  power of the language $L subset.eq Sigma^*$ over alphabet $Sigma$ is
+- $L^0 := { epsilon }$
+- $L^n := L^(n-1) L$ if $n > 0$
+
+
+
+## Finite representation of languages
+**Goal:** Represent a language using _finite_ information
+### Using set notation
+$S = {a^n b^m bar n, m >= 0} = {epsilon, a, b, "aa", "ab", ...}$
+> This is limited in practice.
+
+### Using regular expressions

10 Courses/02 - SoSe 2026/AT/29593952 - Regular Languages.md

@@ -0,0 +1,24 @@
+---
+created: 2026-04-08 10:32
+course: "[[29593850 - Automationtheory]]"
+topic: languages
+related: "[[29593940 - Formal Languages]]"
+type: lecture
+status: 🟢
+tags:
+  - university
+---
+## 📌 Summary
+
+> [!abstract]
+> 
+
+---
+
+## 📝 Content
+
+A language $L$ that can be described by a [[29593975 - Regular Expressions|Regular Expression]] $r$ (i. e. $L(r) = L$) is called _regular_.
+
+> [!WARNING]
+> There a several important languages that **cannot** be described by a regular expression.
+> <mark style="background: #CACFD9A6;">(proof later)</mark>

10 Courses/02 - SoSe 2026/AT/29593958 - Kleene star of languages.md

@@ -0,0 +1,25 @@
+---
+created: 2026-04-08 10:38
+course: "[[29593850 - Automationtheory]]"
+topic: kleene
+related: "[[29593940 - Formal Languages]]"
+type: lecture
+status: 🟢
+tags:
+  - university
+---
+## 📌 Summary
+
+> [!abstract]
+> 
+
+---
+
+## 📝 Content
+
+The _Kleene star_ $L^*$ of a language $L subset Sigma^*$ is the set of all strings (including the empty string $epsilon$) that can be generated by arbitrary concatenation of strings in the language, that is
+> $L^* := union.big_(n >= 0) L^n$
+
+> [!EXAMPLE]
+> For $L = {01}$ one has $L^* = {epsilon, 01, 0101, 010101, ...}$
+> $= {(01)^n bar n >= 0}$

10 Courses/02 - SoSe 2026/AT/29593975 - Regular Expressions.md

@@ -0,0 +1,34 @@
+---
+created: 2026-04-08 10:55
+course: "[[29593850 - Automationtheory]]"
+topic: languages
+related: "[[29593940 - Formal Languages#Finite representation of languages]]"
+type: lecture
+status: 🟢
+tags:
+  - university
+---
+## 📌 Summary
+
+> [!abstract]
+> 
+
+---
+
+## 📝 Content
+
+A _regular expression_ $r$ over an alphabet $Sigma$ is defined recursively:
+- $emptyset, epsilon$ and each $a in Sigma$ are regular expression, which represent the Languages $L(emptyset) = emptyset, L(epsilon) = {epsilon}$ and $L(a) = {a}$
+- If $r$ and $s$ are regular expressions then these are also regular expressions:
+	- $(r + s)$ with $L(r + s) = L(r) union L(s)$
+	- $(r s)$ with $L(r s) = L(r)L(s)$
+	- $r^*$ with $L(r^*) = L(r)^*$
+
+
+> [!EXAMPLE]
+> The language $L$ over $Sigma = {a, b}$ containing the substring $a b$ is regular, since it can be expressed using the regular expression
+> $r = (a +b)^* a b (a + b)^*$
+
+## Equivalence of regular expressions
+Two regular expressions $r$ and $s$ are _equivalent_ ($r eq.triple s$ or $r hat(eq) s$) if they generate the same language ($L(r) eq L(s)$).
+

10 Courses/02 - SoSe 2026/Mathe II/29595454 - Mathematik II.md

@@ -0,0 +1,8 @@
+---
+created: 2026-04-09 11:34
+course: "[[29595454 - Mathematik II]]"
+type: lecture
+status: 🔴
+tags:
+  - university
+---

20 Atlas/AT - Map of Content.md

@@ -0,0 +1,7 @@
+
+```dataview
+TABLE topic AS "Concept", status AS "Review Status"
+FROM "10 Courses/02 - SoSe 2026/AT"
+WHERE type = "lecture" OR type = "concept"
+SORT created ASC
+```

30 Library/normalize_name.sh

@@ -0,0 +1,36 @@
+#!/bin/bash
+
+# Check if a filename was provided
+if [ -z "$1" ]; then
+    echo "Usage: $0 <filename>"
+    exit 1
+fi
+
+TARGET="$1"
+
+# Check if the file actually exists
+if [ ! -f "$TARGET" ]; then
+    echo "Error: File '$TARGET' not found."
+    exit 1
+fi
+
+# Get creation time (%W).
+# Note: Returns 0 or '-' if the filesystem doesn't support birth time.
+BTIME=$(stat -c %W "$TARGET")
+
+# Fallback to last modification time (%Y) if birth time is unavailable
+if [ "$BTIME" -eq 0 ] || [ "$BTIME" == "-" ]; then
+    BTIME=$(stat -c %Y "$TARGET")
+fi
+
+# Calculate the minute-based timestamp (equivalent to Math.floor(ms / 60000))
+# Since stat returns seconds, we divide by 60.
+FORMATTED_DATE=$(( BTIME / 60 ))
+
+# Define the new name
+NEW_NAME="${FORMATTED_DATE} - ${TARGET}"
+
+# Perform the rename
+mv "$TARGET" "$NEW_NAME"
+
+echo "Renamed: '$TARGET' -> '$NEW_NAME'"

99 Templates/New File Template.md

@@ -1,25 +1,24 @@
-<%*
-// Move the file to the Inbox immediately upon creation
-let date = Math.floor(Date.now() / 60000)
-let newName = `${date} - ${tp.file.title}`
-await tp.file.move("/00 Inbox/" + newName)
--%>
 ---
 created: <% tp.date.now("YYYY-MM-DD HH:mm") %>
-course:
+course: 
-topic:
+topic: 
-related:
+related: 
 type: lecture
 status: 🔴
 tags:
   - university
 ---
+<%*
+// Move the file to the Inbox immediately upon creation
+let date = Math.floor(Date.now() / 60000);
+let newName = `${date} - ${tp.file.title}`;
+await tp.file.move("/00 Inbox/" + newName);
+-%>
 ## 📌 Summary
 
 > [!abstract]
->
+> 
 
 ---
 
 ## 📝 Content
-