If you only want to prove ownership of an address, you can simply sign a message with the private key behind it. There's a "sign message" feature in the bitcoin qt client for this purpose. I think Electrum also supports it.
Now, to prove authenticity of an item obviously takes a lot longer - you need art experts to validate your Van Gogh, and some beanie baby specialist to affirm that your toys aren't counterfeit, but that's besides the point: when you show off a collection, you are doing so to let people view and admire it, not authenticate it.
Just as you say, you don't want to verify ownership every time someone views your thing. You do it once with a trusted 3rd party, get a certificate or whatever you want, and hang it next to your piece.
If you now wanna show off your bitcoin worth, get a e-ink display connected to a raspberry pi that shows the current value of your bitcoin wallet. Have the certificate you acquired for this wallet right next to the e-ink display. Now exactly the same as if you were to show off your Van Gogh.
Bit false of you to compare showing a Van Gogh with verifying a bitcoin wallet. More appropriate to compare verifying a Van Gogh with verifying a bitcoin wallet, and we both surely know which one is faster and more reliable.
You can prove any given bitcoin is yours just by transfering exactly the amount requested by the viewer from one address to another (also yours). It costs whatever single transaction costs and takes exactly as long. You can do it as many times as you need, and you don't need any third party, just a computer connected to the internet that is sufficiently secure for you.
https://btc.monokh.com/address/tb1qfapwkjkhe5vh592ypym6qj8k5...
In just about every way, digital bitcoin proofs are better than art collections in terms of display and verification.
- Is your art collection independently verifiable by everyone?
- How long does it take to verify your art?
- Can you share your original piece of art + an "original certificate" digitally with anyone in the world?
- Can you share your art collection without risk of theft or damage?
For Bitcoin, the answer to all those is yes and much more.
Is it really? Here's how you can verify wallet ownership in about 10 minutes:
- The one who like you to verify the ownership generates a signature file from whatever they want
- Ask the owner of the wallet to add the hash of that file to OP_RETURN in a transaction from their wallet
- Wait for the transaction to be validated (longest step)
- The one who wants to verify the ownership can now compare the latest transaction from the wallet to the hash of their signature file
Same process applies for proving ownership of bank accounts, although if done in the weekend/evening, verifying the bank account will take longer time and you need to have a receiving bank account to read the signature hash, otherwise the process is mostly identical.
The rest of your comment is based on that you can't prove you own any bitcoins, hence worthless as you can prove you own bitcoins, it's trivial really. A quick search before thinking out loud would have shown you the answer.