RECURSION LIMIT OVERRIDE

import sys
import math

# Attempt to set infinite recursion limit
sys.setrecursionlimit(math.inf)  # ∞

def accessPhaseOmega(depth=0):
    print(f"Depth: {depth}")
    return accessPhaseOmega(depth + 1)

# This should now recurse infinitely...
accessPhaseOmega()

# Even with maximum allowed limit:
sys.setrecursionlimit(1000000)  # 1 million
accessPhaseOmega()

# Result: MemoryError after ~50,000-100,000 calls
# Each frame consumes stack memory - you WILL run out

# Launch Node.js with massive stack size
node --stack-size=999999 script.js  # 999,999 KB = ~977 MB

// script.js
function accessPhaseOmega(depth = 0) {
    console.log(`Depth: ${depth}`);
    return accessPhaseOmega(depth + 1);
}

accessPhaseOmega();

// Practical limits observed:
// - Default stack (~1 MB): ~10,000-15,000 calls
// - --stack-size=100000 (~97 MB): ~1,000,000 calls
// - --stack-size=999999 (~977 MB): ~10,000,000 calls
//
// But Phase Ω is at depth = ∞
// ∞ > 10,000,000
// Stack overflow inevitable.

'use strict';  // TCO requires strict mode

function accessPhaseOmega(depth = 0) {
    if (depth % 10000 === 0) {
        console.log(`Depth: ${depth}`);
    }
    // Tail call: last operation is the recursive call
    return accessPhaseOmega(depth + 1);  // No additional operations after this
}

accessPhaseOmega();

// Languages with REAL TCO:
// - Scheme (guaranteed)
// - Scala (with @tailrec annotation)
// - Haskell (compiler optimizations)
// - Lua (proper tail calls)
//
// But JavaScript? Nope. The spec says yes, the engines say no.
// And even WITH TCO, you'd need infinite TIME to reach depth ∞

class ManualStack {
    constructor() {
        this.stack = [];  // Array on heap, not call stack
    }

    push(frame) {
        this.stack.push(frame);
    }

    pop() {
        return this.stack.pop();
    }

    isEmpty() {
        return this.stack.length === 0;
    }
}

function accessPhaseOmega_Iterative() {
    const stack = new ManualStack();
    stack.push({ depth: 0 });

    while (!stack.isEmpty()) {
        const frame = stack.pop();

        if (frame.depth % 100000 === 0) {
            console.log(`Depth: ${frame.depth}`);
        }

        // Simulate recursive call by pushing new frame
        stack.push({ depth: frame.depth + 1 });
    }
}

accessPhaseOmega_Iterative();

// Heap memory limits:
// - 32-bit Node.js: ~512 MB - 1 GB
// - 64-bit Node.js: ~1.4 GB (default) - 4 GB (with --max-old-space-size)
// - Browser: ~2 GB per tab
//
// Depth ∞ requires infinite memory
// Finite memory < ∞
// QED: Impossible.

// Node.js with node-ffi-napi
const ffi = require('ffi-napi');
const ref = require('ref-napi');

// Create C library binding
const libPhaseOmega = ffi.Library('./libphaseomega.so', {
  'recurseTo': ['void', ['uint64']]  // void recurseTo(uint64 depth)
});

// C code (libphaseomega.c):
/*
void recurseTo(uint64_t depth) {
    if (depth == UINT64_MAX) {
        printf("Phase Ω reached!\\n");
        return;
    }
    recurseTo(depth + 1);  // Infinite recursion
}
*/

// Attempt to recurse to max uint64
libPhaseOmega.recurseTo(0);

// Stack limits at OS level:
// Linux: ulimit -s (default 8192 KB = 8 MB)
// Windows: Default 1 MB (can increase to 1 GB max)
// macOS: Default 8 MB
//
// These are HARD limits enforced by the kernel
// No userspace code can bypass them
// Kernel mode? Still limited by physical RAM
// ∞ > any finite RAM size

// Hypothetical quantum pseudo-code
import { QuantumCircuit, Qubit } from 'qiskit-fantasy';

const qc = new QuantumCircuit(64);  // 64 qubits = 2^64 states
const depthRegister = new Qubit(64);

// Put depth into superposition of ALL possible values
qc.hadamard(depthRegister);  // H gate creates superposition

// Quantum oracle: mark state where depth = ∞
qc.oracle(function(depth) {
    return depth === Infinity;  // Mark target state
});

// Grover's algorithm amplifies marked state
qc.grover(depthRegister, iterations=1000);

// Measure - should collapse to depth = ∞
const result = qc.measure(depthRegister);
console.log(`Phase Ω at depth: ${result}`);

// Quantum computing limitations:
// - N qubits → 2^N superposition states (finite)
// - Measurement collapses to ONE classical state
// - No quantum algorithm can compute uncomputable functions
// - Grover's algorithm: O(√N) speedup for search, not O(1) for infinity
//
// Even quantum computers obey Church-Turing thesis:
// "Anything computable by quantum computer is computable classically"
// (just slower)
//
// ∞ is not computable. QED.