I'm the owner of 17JkL94B2ngJg4QQZuiozDQjnxXB6B7yTc and 1Gu8zxRi8cyENV8CQe52D7QEsiZ7ruT73u.
Can you provide cryptographic proof of this, please?
Yes, but just after you tell me why it is necessary.
Because other than the obvious evidence you've spent the last hour or so claiming to be the owner and refreshing BTCTalk constantly to reply to various comments about what you should or should not do or should or should not have done, we have absolutely no reason to believe you are the true and rightful owner of the mined coins, or representing the owner of the mined coins.
Even ignoring the Eligius and BTCGuild accusations, for all we know, you are some random person wanting to troll us into thinking you have a claim on the lost coins. We have no reason to believe you have a right to speak for the owner of those two addresses. And frankly, without cryptographic proof, I
don't believe you own either address. Nor should anyone else. This seems to be obvious to everyone but yourself at the moment, so I'm recommending you provide proof to add to the veracity of your claims.
If you need help and you want to make sure you're not doing anything risky, it is recommended you address names and locations and even dates when signing, so that others cannot just copy the message and paste it elsewhere attempting to prove to be you at a later date or time. Aside from that, for the purposes of verification, almost any signed message is sufficient as long as includes the claim in question (that you own both addresses). For example here's something you would NOT want to sign:
I'm the owner of 17JkL94B2ngJg4QQZuiozDQjnxXB6B7yTc and 1Gu8zxRi8cyENV8CQe52D7QEsiZ7ruT73u.
If you only signed that, then anyone who receives a copy can copy/paste it to any of their friends and attempt to claim to be you. So instead you should include details that link your BTCTalk account to the addresses. You can also specify date so that if someone tries to copy it, it'll look weird.
The following message should be safe to sign and post publicly for anyone to see (you can sign it with either address):
Per Raize's request on the BTCTalk forums dated 6/13/2014, I, owner of the Brucexie account on BTCTalk forums, am also the rightful owner of the wallet storing the Bitcoin addresses 17JkL94B2ngJg4QQZuiozDQjnxXB6B7yTc and 1Gu8zxRi8cyENV8CQe52D7QEsiZ7ruT73u.
It makes sense.
I'll paste a signature after the approve of my mining group, they're sleeping so this may be out in one day.
I, owner of the Brucexie account on bitcointalk.org forums, am also the rightful owner of the wallet storing the Bitcoin addresses 17JkL94B2ngJg4QQZuiozDQjnxXB6B7yTc and 1Gu8zxRi8cyENV8CQe52D7QEsiZ7ruT73u. This signature only works before 6/30/2014 and only used for the talking about unpaid issue of eligius of the following 2 address.