The theorem began as a practical alignment problem.

A decade of watching

We had spent ten years scanning for sundogs and circumzenithal arcs without ever catching one in the wild. The literature was easy to find. The geometry was easy to read. The phenomenon itself stayed out of reach. That long, unrewarded watching turned out to matter — it primed us to recognize the geometry later, in a place we were not looking for it.

The job was environmental controls

The discovery happened on the clock. We were installing environment controls for a quantum computing stress test — Quantinuum and DARPA's program — with the computational cloud below and our HVAC equipment to be suspended above it. The work meant aligning acoustic ceiling anchors at tight tolerance, with limited shared language on site, and a plumb laser as the most reliable common reference between us and the help.

The accidental tutorial

We were trying to teach the procedure to a crew member who did not share our first language. The only way to make the steps unambiguous was to describe what the plumb laser was doing at every moment of fastener insertion. The construction sequence had a specific shape worth preserving in detail, because it later became the model for our v1 experiment.

1. The plumb laser projected a vertical reference from a marked point on the floor up to the structural deck, identifying the precise install location for the ceiling anchor.
2. As the fastener was brought into position over that point, the head of the fastener intercepted the laser beam. The reference signal disappeared.
3. As the fastener seated into the substrate, the head moved through the beam's path on a known geometry.
4. At the moment the seat was correct, the laser reappeared on the far side of the head at the expected position and angle.

Loss and return of signal were not noise to work around; they were the procedure. To explain to the crew member why this was fine — why the geometry of the obstruction itself, plus the timing and position of the signal's return, was enough to confirm alignment without ever directly inspecting the seated fastener — we wrote the procedure down as a formula.

That same construction sequence, with the fastener head playing the role of the occluder and the laser playing the role of the refracted source, became the model for our v1 photometric experiment. The v1 had its own flaws and we are honest about that on the claims and scope page, but the geometry it preserved was honest enough to be a useful first test.

The formula was a sundog

When we cleaned it up, the geometry was the geometry we had been chasing in the sky for a decade: the angles, the way an obstruction sits in front of a refracted source, the structure that produces the parhelion. We had described, by accident and from the wrong side, the optical phenomenon we had failed to find in the wild. The applications felt immediately gravity-like — generally applicable in shape, not just to the alignment task in front of us.

Discovery-era publications

The first public versions were rough, fast, and emotionally overloaded. They were written while the real job was still being finished: anchors still had to be set, equipment still had to hang safely, and the environmental-control project still had to land. In parallel, we started testing the idea in conversation with other people. We spoke with computer science researchers at Saint Mary’s University and with Dr. Robin Rise, a clinician who works with AI-related psychosis, because the exciting version of an idea is not automatically the trustworthy version. Those conversations did not finish the work for us, but they helped us keep going.

The early publications still matter because they preserve the moment of discovery: the field procedure, the first H(x) notation, the torque-shadow framing, and the first attempt to turn the construction method into a MuJoCo experiment.

The point of linking these is not to freeze the first version as the final one. It is to make the provenance inspectable. The current project has deliberately moved from broad theorem language toward measurable tasks, baselines, and failure boundaries.

What we have shipped

After that first public trail, we kept building. Four application surfaces now sit downstream of the theorem. We list them by evidence tier rather than by enthusiasm. Each one used the theorem as a triage layer when something — data, expertise, time, a clear line of sight — was missing.

• Photometric mirror alignment A controller aligns a mirrored end-effector without target coordinates, using sparse photometric feedback. Terminal accuracy is statistically indistinguishable from a target-aware oracle in the tested MuJoCo setup (U=526, p=0.264 on terminal target intensity). The cost is convergence time, not accuracy. Research result · the narrow defensible claim Repository · Paper draft · Researcher guide
• EyesOnly / Gone Rogue Procedural roguelike agents act from compressed perception in stop-conditioned action batches. Sundog turn envelopes against a real game engine, where partial information is treated as a design feature rather than a degraded backup. Instrumented prototype Repository · Runners documentation
• Dungeon Gleaner Physical-feeling simulation in a raycast dungeon crawler. Glass-and-window approximations and pressure-washing mechanics that keep player-readable coherence at a fraction of conventional cost. Same indirect-measurement pattern, applied to visual simulation. Product expression Repository
• Money Bags Softbody graph telemetry. Torsion, deformation, symmetry, and recovery become readable signals rather than per-frame noise. Here the theorem extends past optics into graph interpretation. Instrumented prototype Repository

Rough and electric

We are publishing this trail while it is still rough. There is no version of intellectual honesty in which we hide the awkward parts, so we link them too.

• The original theorem materials live in the repo as sundog_alignment_theorem_final_fixed/, with the filename you’d expect from a project that has been “finally fixed” more than once. We keep them for historical readability, not as the current statement of the theorem.
• SundogMujoco2.0/ is the earlier leisure-environment artifact — the less defensible MuJoCo stack that preceded the experiment we now defend. It records the path, including the dead ends.
• The paper draft is a draft. It is not a paper, and the difference matters. We link it because doing the work in public seems better than doing it in private and arriving polished.
• Wikipedia outreach is a plan, not a contribution. The proposal exists. The edits do not yet.

The trail is electric because the geometry was right often enough to keep testing it, and the work became sturdier whenever we forced the claim into smaller, more inspectable pieces. We will keep the awkward parts visible.

Where we are going

The plan is to keep pointing the writing at the proven applications rather than the metaphysics. The temptation runs the other way. During the years leading up to this discovery, senior people in computer science were warning publicly that misaligned software could become catastrophic. We know that “sidestepping Goodhart” is exactly the kind of phrase that should be earned in small, demonstrable pieces rather than declared. So: small, real, demonstrable. Keep building. Keep watching the sky.