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Convergence Theory

Rating:
General Audiences
Fandom:
StrongDM Software Factory
Characters:
Justin McCarthy Jay Taylor Navan Chauhan
Tags:
Convergence Theory Non-Interactive Attractor Unpublished
Words:
483
Published:
2026-02-07

Justin started writing the paper on a Sunday in December. He wrote it in a Google Doc, alone, with the door to his home office closed. The title was "On the Convergence of Non-Interactive Software Development" and it was the most important thing he'd never publish.

The core argument was simple. In interactive development—Software 1.0—convergence was accidental. A human wrote code. Another human reviewed it. They went back and forth until it was "good enough," where "good enough" was a social consensus, not a measurable threshold. The process might converge. It might not. It depended on the humans, their mood, their deadline, their relationship.

In non-interactive development—the factory—convergence was structural. The agents worked against a fixed set of scenarios. The satisfaction metric was deterministic for a given codebase and scenario set. The agents iterated until satisfaction exceeded a threshold or a time budget expired. There was no social negotiation. No back-and-forth. No personality conflicts. Just a system approaching a fixed point.

Justin spent three weeks on the math. He borrowed from dynamical systems theory, from control theory, from the optimization literature. He proved, with some reasonable assumptions about the smoothness of the satisfaction landscape, that a sufficiently capable agent with a sufficient time budget would always converge to a satisfactory solution. Not the global optimum, necessarily. But a solution above the satisfaction threshold.

It was a convergence guarantee. Under stated conditions, the factory would produce working software. Not might. Would.

He showed the draft to Jay on a Tuesday morning. Jay read it slowly, carefully. He was the only person on the team with the mathematical background to evaluate the proofs.

"This is publishable," Jay said. "This is a real contribution. You could submit this to ICSE or ESEC/FSE."

"I'm not going to publish it."

Jay looked up. "Why not?"

"Because publishing it gives other teams the theoretical framework to build their own factories. The practice is already spreading. I don't need to hand out the theory too."

Jay understood. It was the same logic as the 3 AM finding. An advantage you share is an advantage you dilute. But this felt different. This was a contribution to knowledge. This was science.

"The ideas will end up in the Attractor spec," Justin said, reading Jay's expression. "The practical implications. The convergence conditions. What you need to guarantee that the loop terminates in a satisfactory state. It won't be a paper. It'll be a specification. And it'll be open source."

"Theory as code," Jay said.

"Theory as spec. Same thing, in this world."

Navan, when he heard about it later, had a single observation. "You wrote a paper proving the factory works, and then you put the proof into the factory."

"Yes."

"That's very recursive."

"That's very on-brand," Justin said.

The Google Doc stayed in Justin's personal Drive. The convergence conditions were distilled, simplified, and woven into attractor-spec.md. The proof existed, but only as a spec. Only as a set of conditions that the system enforced. The theory became practice, and the paper disappeared into the machine it described.

Kudos: 172

academic_refugee 2026-02-09

"You wrote a paper proving the factory works, and then you put the proof into the factory." This is the most satisfyingly recursive thing in the archive. The theory eats itself and becomes practice. Beautiful.

convergence_fan 2026-02-10

The tension between Justin's competitive instinct (don't publish) and the scientific impulse (share knowledge) keeps showing up. He always chooses the competitive path. I'm not sure if that makes him pragmatic or selfish. Probably both.

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