Pragma
Observer Patch Holography
OPH asks a simple physics question: how can limited systems build one shared world from partial views? It starts with bounded systems that have a local state, a boundary, memory, a way to read themselves and nearby systems, and a way to repair disagreement. A shared fact has to be recorded, compared, and able to survive a correction.
The project tests whether those requirements can recover familiar physics, including relativity, gravity, quantum measurement, and parts of Standard Model structure. No measured masses, interaction strengths, or cosmological values are adjusted to make the structure fit. The finite setup and its discrete choices are stated openly. Some links are mathematical theorems. The bridge from those theorems to observed physics has open steps.
OPH works from a small set of rules about limited observers. The technical work derives results from those rules and names the assumptions needed for each physical claim.
One finite version of the model produces the geometry used by relativity. A gravity result follows under further assumptions about entropy and the support of the model. One global part of the spacetime description belongs to a separate open cosmology problem.
A stated twelve-port version of the model has the same mathematical symmetry type used by the Standard Model, physics' map of known particles and forces. A separate finite calculation gives a one-generation charge pattern under specified assumptions. The physical construction of matter and the full global symmetry are open.
A measurement counts as public when its record can be read, compared, and carried across the boundaries allowed by the model. The technical work studies the mathematical rules required for such shared records.
Lean and exact arithmetic verify roots of two proposed local equations. One gives a close numerical comparison with the fine-structure constant, a number that measures the strength of electromagnetism. The proof connecting it to a laboratory measurement is open. A separate cosmology calculation does not derive a single cosmic value.
Each observer patch has a local state, a boundary, and limited access to the world around it. It keeps records of what it can read.
A record becomes a shared fact when other patches can read it, compare it with their own records, and check the overlap.
Conflicting records call for an update, a repeated measurement, or a better explanation. The repair process preserves the evidence needed for others to check the result.
Continuation research examines how a record can retain its role as the system changes, so other observers can use and test it.
Parts of OPH are exact mathematics. The local fixed-point calculation, which looks for a value that reproduces itself, is checked with Lean and exact interval arithmetic. It gives a close numerical comparison with the fine-structure constant. The link to a laboratory measurement is unproved. The result has diagnostic status. It is not a prediction.
The cosmology branch is more tentative. It does not derive a unique value for the universe's information capacity or for the cosmological constant, a number tied to cosmic expansion. Two proposed formulas give after-the-fact comparisons with measured cosmology. They are not predictions. The technical paper and public source contain the assumptions, proofs, and open work.