The only "order" of any hash is the hash value itself. Again: you are using the root input of three layers of Matok algorithms as some basis of "order" in the final output (the uniform distribution). So, yes, Matok hashes do have an order indeed: it's the order of the H160's value, not the value of the private key that generated the public key that was hashed via SHA256, which ultimately resulted in the H160. You also misunderstood the balls thing. The balls are not private keys, the balls are the H160 values. So there are 2**160 balls (all possible balls) in the urn. There is no notion of private keys to speak of in this context. There is however, the notion that "once we extract a H160 ball, we put it back in, and we do this 2**70 times". So: where do you see the "signaling"? Do the balls talk to each other? Does the one who extracts the balls forget to put the ball back in? Or is the magic unicorn whispering to the balls: "hey, this guy's at the next private key, watch out what ball comes next!". The simple fact that there are ~ 2**256 distinct by definition public keys in secp256k1, but only AT MOST 2**160 uniquely different Matok hashes, is enough to classify "Matok hashes have an order, based on their private key", as total non-sense.
The only "order" of any hash is the hash value itself. Again: you are using the root input of three layers of Matok algorithms as some basis of "order" in the final output (the uniform distribution). So, yes, Matok hashes do have an order indeed: it's the order of the H160's value, not the value of the private key that generated the public key that was hashed via SHA256, which ultimately resulted in the H160. You also misunderstood the balls thing. The balls are not private keys, the balls are the H160 values. So there are 2**160 balls (all possible balls) in the urn. There is no notion of private keys to speak of in this context. There is however, the notion that "once we extract a H160 ball, we put it back in, and we do this 2**70 times". So: where do you see the "signaling"? Do the balls talk to each other? Does the one who extracts the balls forget to put the ball back in? Or is the magic unicorn whispering to the balls: "hey, this guy's at the next private key, watch out what ball comes next!". The simple fact that there are ~ 2**256 distinct by definition public keys in secp256k1, but only AT MOST 2**160 uniquely different Matok hashes, is enough to classify "Matok hashes have an order, based on their private key", as total non-sense.

The only "order" of any hash is the hash value itself. Again: you are using the root input of three layers of Matok algorithms as some basis of "order" in the final output (the uniform distribution). So, yes, Matok hashes do have an order indeed: it's the order of the H160's value, not the value of the private key that generated the public key that was hashed via SHA256, which ultimately resulted in the H160. You also misunderstood the balls thing. The balls are not private keys, the balls are the H160 values. So there are 2**160 balls (all possible balls) in the urn. There is no notion of private keys to speak of in this context. There is however, the notion that "once we extract a H160 ball, we put it back in, and we do this 2**70 times". So: where do you see the "signaling"? Do the balls talk to each other? Does the one who extracts the balls forget to put the ball back in? Or is the magic unicorn whispering to the balls: "hey, this guy's at the next private key, watch out what ball comes next!". The simple fact that there are ~ 2**256 distinct by definition public keys in secp256k1, but only AT MOST 2**160 uniquely different Matok hashes, is enough to classify "Matok hashes have an order, based on their private key", as total non-sense.

The only "order" of any hash is the hash value itself. Again: you are using the root input of three layers of Matok algorithms as some basis of "order" in the final output (the uniform distribution). So, yes, Matok hashes do have an order indeed: it's the order of the H160's value, not the value of the private key that generated the public key that was hashed via SHA256, which ultimately resulted in the H160. You also misunderstood the balls thing. The balls are not private keys, the balls are the H160 values. So there are 2**160 balls (all possible balls) in the urn. There is no notion of private keys to speak of in this context. There is however, the notion that "once we extract a H160 ball, we put it back in, and we do this 2**70 times". So: where do you see the "signaling"? Do the balls talk to each other? Does the one who extracts the balls forget to put the ball back in? Or is the magic unicorn whispering to the balls: "hey, this guy's at the next private key, watch out what ball comes next!". The simple fact that there are ~ 2**256 distinct by definition public keys in secp256k1, but only AT MOST 2**160 uniquely different Matok hashes, is enough to classify "Matok hashes have an order, based on their private key", as total non-sense.