Let's write a Solidity contract that can prove file ownership without revealing the actual file. It can prove that the file existed at a particular time and finally check for document integrity.

We will achieve proof of ownership by storing the hash of the file and the owner's name as pairs. We will achieve proof of existence by storing the hash of the file and the block timestamp as pairs. Finally, storing the hash itself proves the file integrity; that is, if the file was modified, then its hash will change and the contract won't be able to find any such file, therefore proving that the file was modified.

Here is the code for the smart contract to achieve all this:

contract Proof 
{ 
    struct FileDetails 
    { 
        uint timestamp; 
        string owner; 
    } 

    mapping (string => FileDetails) files; 

    event logFileAddedStatus(bool status, uint timestamp, string owner, string fileHash); 

    //this is used to store the owner of file at the block timestamp 
    function set(string owner, string fileHash) 
    { 
        //There is no proper way to check if a key already exists or not therefore we are checking for default value i.e., all bits are 0 
        if(files[fileHash].timestamp == 0) 
        { 
            files[fileHash] = FileDetails(block.timestamp, owner); 

            //we are triggering an event so that the frontend of our app knows that the file's existence and ownership details have been stored 
            logFileAddedStatus(true, block.timestamp, owner, fileHash); 
        } 
        else 
        { 
            //this tells to the frontend that file's existence and ownership details couldn't be stored because the file's details had already been stored earlier 
            logFileAddedStatus(false, block.timestamp, owner, fileHash); 
        } 
    } 

    //this is used to get file information 
    function get(string fileHash) returns (uint timestamp, string owner) 
    { 
        return (files[fileHash].timestamp, files[fileHash].owner); 
    } 
}