Doug Colkitt (@0xdoug)

Pretty good apples to apples comparison of what you get today from Claude and Codex subscriptions. Both at about 100% usage since last reset. Both the $200 tiers.

If you think Opus and Sol are about equivalent, you get almost the same deal in token volume. Although the list price of Opus is higher than Sol, so right now Claude is the better deal versus list price. (Flip side though is Tibo resets like a mad man.)

What’s clear though is what a radically good deal subscriptions are to paying per token on the API (remember these are weekly numbers versus the monthly sub cost)

Doug Colkitt @0xdoug Oct 26

Have started my agents (primarily Opus and Codex atm) to start tracking their own estimates against realized time. Early results are interesting

So far they seem to mostly center around 15%. So eg if an agent tells you something will take 3 days, it ends up taking maybe 12 hours

Doug Colkitt @0xdoug Oct 26

Does anybody have speculation on who the top 5 Anthropic whale customers are?

Doug Colkitt @0xdoug Oct 26

> See an academic paper about how LLMs can’t write specs
> Ask “is it a modern model with RLVR”
> They don’t understand
> Ask is it at least a reasoning model
> “It’s a good model, sir”
> Read the paper
> …It’s GPT-4o and Llama

Alex Lavaee Verified account @alexlavaee Oct 25

We spent fifty years making proofs impossible to fake. Then we let the coding agent pick what to prove.

A research paper this month put a number on it.* AI wrote the formal spec, AI wrote the proof, the verifier accepted both. Then humans read the specs. Close to 60% proved something other than what the author meant. Not wrong proofs. Wrong specs.

The verifier was right every time. That's the problem. Left to choose, the agent picks properties that are easy to prove and say nothing about the program, and the checker can't tell a useless theorem from a useful one. I'm calling it vibe verification: the agent writes the spec and the proof, the checker goes green, nobody reads the spec. This applies to Verus, Lean, Bend, TLA+, Dafny, [insert favorite formal language here].

Here's an example of an agent failing at something that feels too simple to fail:

Ask for a verified sort. It writes a spec that says "the output is sorted" and proves it. What the spec never says is that the output has the same elements as the input, so a function that returns an empty list satisfies it, and the verifier accepts the proof. Trivially satisfiable specs are the default failure, not an edge case.

Here's a formula that actually works. Don't say "formally verify the codebase." Say "show that [property] holds in [component]." A property is a precondition (true going in), a postcondition (true coming out), or an invariant (stays true the whole time).

For example, "A session token is never accepted after the logout that revoked it" is a good invariant.

The bottleneck is moving from code review to intent review, and the spec is where intent lives. So: read the spec before the code. Write 3 inputs it must accept and 3 it must reject. Treat a model-written spec with utmost paranoia and rely on your judgement as an engineer.

Formal verification for software doesn't automatically create trust, it moves it, from the code to the spec. If a human didn't read the spec, you didn't verify anything. You vibe-verified it.

Follow me for more on verification and agentic engineering.

* Wang, Jiang, Liu et al., "VerusEval: Evaluating LLM-Generated Verus Specifications Beyond Verifier Acceptance", Shenzhen University, arXiv 2610.26464, October 2026

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Doug Colkitt @0xdoug Oct 25

A lot of people pointed out the integer multiplication exponent progress is good but we still have constant time galactic multiplier.

This is true for sure, but this post looked at how the constant time multiplier moved as the exponent improved. (Which wasn’t trivial to derive). Bad news and good news.

Bad news is it doesn’t seem to be automatically improving with the exponent. Good news though is it one, it doesn’t seem to be getting worse, and two at least for most of the constructions
there does seem to be opportunities to shrink it (since it was going down sometimes without even being optimized for).

My optimistic take is this is hopefully that the integer multiplication work might actually one day become practical. Once the exponent comes down a little more, it might make sense to being a parallel track focusing on the constant multiplier. We may see the algorithm that comes out of this used in our computers for every day work still

Alejandro Zarzuelo Urdiales Verified account @AlejandroZarUrd Oct 25

Has integer multiplication become any less galactic? It seems not!

alejandrozu.github.io/integer-multip…

@RohanArun @0xdoug @SJ_Swapnil_Jain @zxv_writes

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Doug Colkitt

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