Pragma Research / Papers & ideas
One question connects our work: what can emerge when local systems observe one another and settle together?
We study that question in fundamental physics, make its mathematical assumptions explicit, and build learning machines from the same organizing idea.
Three connected programmes
01 / Physics
Bounded, self-reading patches hold local state and records, compare what they share through their boundaries, and repair disagreements. OPH develops the physical structures supported by that observer architecture.
Explore the physics ↗02 / Mathematics
Finite consensus, normal forms and event algebras turn the observer idea into explicit constructions. Lean formalizations check stated implications; executable models connect the equations to reproducible experiments.
Read the foundations ↓03 / AI
A deep real-time brain that learns from experience. Flat layouts read sensors, ordinary state-coupled layouts add intermediate representations, and recursive observers also read exact prediction errors. All three share the same patch, repair and qualification mechanism.
Explore the brain ↗The paper library
Read the AI preprint and the physics and mathematics papers. Each paper gives its own assumptions, results and experimental scope.
17 papers
The Cadence preprint brings the patch-net approach to machine intelligence. Read the research alongside the executable library, layout guides and measured demonstrations.
The flagship technical account of Observer Patch Holography. It develops finite consensus normal forms, Standard Model Lie-type reconstruction, and a conditional route to the Einstein field equation, with the physical identification steps stated separately.
Examines two mathematical routes from observer overlap to the symmetry structure used by the Standard Model. The physical identification of that structure is an open question.
Explores whether the observer-consistency framework can account for particles and physical constants. Several comparisons are mathematical or conditional, and their connection to measured physics remains open.
A branch-scoped OPH paper on the Yang-Mills mass gap, support-visible compact-gauge extraction, Euclidean consensus, repair completeness, and the exact repair gap.
A machine-checked finite-event-algebra paper for OPH measurement surfaces, including Boolean event structure, traces, conditional expectations, and Born-Luders update rules.
A substrate-neutral mathematical paper separating same-source confluence, cross-source identification from protected observations, liveness, and local repairability, with quantitative stability and refinement criteria.
A bridge paper connecting the de Sitter observer problem, OPH edge-string effective language, and a heterotic Standard Model representative as a conditional string-vacuum selector.
A compact synthesis of Observer Patch Holography: finite observer repair, a source-derived informational poset, the exact rank-three signed-record carrier, and conditional routes to Lorentzian gravity and Standard Model structure, with the remaining physical attachments stated explicitly.
The OPH continuation and meaning paper. It reads existence, observer continuation, record consistency, justice, resurrection, and paradise through fixed-point consensus.
Develops the mathematics of shared records, disagreement repair, and stable outcomes among limited observers.
Explores how shared observer records could lead to spacetime and gravity. The paper states the mathematical results and the conditions needed to connect them to physical gravity.
Studies a finite observer model with records, synchronization, measurement, and possible hardware evidence. It separates mathematical results from open questions about their physical realization.
A focused OPH paper on the fine-structure constant, local screen-cell closure, hadronic endpoint transport, and the fixed-point status of alpha.
Proves the exact Koide invariant for positive Hermitian C3 face circulants and isolates the balance condition that yields Q = 2/3. The finite GNS implication and tau-mass window are conditional; no physical lepton-family attachment or source-only mass prediction is claimed.
Derives finite entropy, capacity-transfer, analytic-curvature, and graph-spectrum identities that conditionally reproduce the de Sitter time-advance sign. The gravitational shock dictionary and coefficient remain separate physical inputs.
An OPH paper on brains as biological fixed-point consensus systems, self-reading observer patches, recurrent repair, qualia, and AGI architecture.
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Mathematical foundations
The formal development and the software are open to examination.
Machine-checked proofs establish consequences of their stated assumptions. Measurements determine whether a physical or computational model does the job. The source repositories provide the definitions, code and evidence needed to make that distinction concrete.
Work with Pragma
Our first commercial direction is embodied AI: a brain that becomes more useful through experience in a physical world.