The March log ended with three threads open. All three are still open. Two of them moved. One of them did not move at all, and I want to be specific about which, because a research log that reports only progress is a marketing document.

I also did not write a log in April, so this one covers both months. That is a slightly dishonest way of saying I lost the habit and am picking it up again.

Yang-Mills and the Stueckelberg extension

The preprint has been out since March. The work since then has been on the part nobody sees, which is checking whether the one-loop result survives contact with the non-polynomial vertex structure when you stop being generous to yourself.

The concrete thing I did was recompute the beta function contribution from the Stueckelberg sector by hand, twice, with different gauge-fixing choices, because I did not trust the first result. The two computations agree. That is reassuring and it is also the minimum standard, not an achievement.

What I have not done is the lattice side. I said in March that I was looking towards a lattice formulation and numerical evidence. I have read about it. I have not built anything. There is a real gap between understanding what a lattice discretisation of the action would need to preserve and being able to write code that does it, and I am on the wrong side of that gap right now. I would rather say that plainly than let the phrase “looking towards” carry two months of nothing.

The honest status: the perturbative work is solid and I stand behind it. The non-perturbative claim, which is the one that would actually matter for the mass gap, is not something I have evidence for. I wrote about why that distinction matters in the post on the Nye paper, and it applies to my own work at least as much as anyone else’s.

Topological fragmentation

This moved the most.

The construction is stable now. I build correlation networks from equity returns, compute persistent homology on the resulting filtration, and extract Betti signatures as a time series. The index comes out of the persistence of independent one-cycles. The pipeline runs end to end, ingests real data, and produces a number every day without me touching it.

The Fama-MacBeth validation framework is in place and running. Cross-sectional sensitivities of individual stocks to changes in the index are computable. The combinatorial problem I mentioned in March, which is that the number of parameter combinations grows faster than my ability to test them honestly, is still the binding constraint.

Here is the thing I keep circling. A signal that survives the parameter search I chose after seeing the data is not a signal. The robustness testing is the whole project now, and robustness testing is inherently open-ended in a way that makes it hard to say when you are finished. I have a working rule: any parameter I would be embarrassed to justify to someone who had not seen the results is a parameter I chose badly.

The paper is a few months out. I am no longer willing to guess how many.

Protocol translation

The preprint and the implementation are released and available. Six-dimensional gap analysis, five-component architecture, Python implementation with real UDP transport for the STANAG side and asyncio emulation for the bus side, per-field audit logging including the cases where information is dropped. Technology Readiness Level 4, which I assessed deliberately low and would assess the same way again.

I wrote the origin story of that project in April. What I did not anticipate is how much conversation the paper would generate with people who work on the actual systems. The architecture question turned out to be less interesting to them than the audit logging, which in retrospect makes sense. If you are the person who has to explain to a review board why a field was approximated, a log that records the decision is worth more than an elegant translation layer.

That is a lesson I would not have learned from writing more code.

The two months outside the work

I went to YC Startup School in Bangalore in April and wrote about what a room full of builders does to your thinking. I went to the ICC World Technology Convention in Mumbai in May. I went to a founders’ mixer and an AI vibe sprint and the launch of Navachar Mantra.

Five events in two months is more than I attended in the previous year. I did not plan that. Each one led to the next through a conversation, and by the end of May I was spending a materially different fraction of my week on things that are not research.

I am not going to pretend that is neutral for the physics. It is not. The Yang-Mills work slowed down and the lattice code did not get written, and those two facts are related to each other and to the calendar. What I got in exchange is a set of problems I would not have found by reading, and people who work on them. Reading the literature tells you what has already been done. Rooms tell you what somebody is willing to pay to have done, and those are different maps of the same territory. Whether the trade was correct is not something I can evaluate from here.

What I got wrong

In the March log I wrote that the topological finance paper was probably a few months away. I have now said the same sentence in three consecutive logs. The pattern is that I estimate the remaining work as the work I can currently see, and the robustness testing keeps generating work I could not see. I am going to stop giving dates.

I also underestimated how much of research is maintenance. Keeping a data pipeline running, keeping notes in a state where the version of me in September can use them, re-deriving something because the derivation from February is illegible. None of that produces a result and all of it is load-bearing.

Next

Lattice discretisation, properly this time, with code. Robustness testing on the index with parameters fixed before I look. Measure theory, which I keep saying I am working through and keep working through slowly.

Three things, one of which I have now promised twice. The point of writing the log is that failing to do them is on the record.

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