Common ground · one engine, four products
Reality is a
consensus protocol
running on a 2D screen.
Observer-Patch Holography replaces "fundamental fields in 3+1D space" with three axioms and two closure equations. Finite observer patches carry the state, agreement on overlaps turns it public, and nothing beyond that agreement is written into the world. The 3D space you feel, gravity included, is the bookkeeping of that protocol. Every OMEGA product edits the bookkeeping at the screen layer instead of fighting the bulk.
Patch network · live consensus
Interactive stage-by-stage visualisations of the full stack (carrier, federation, overlaps, repair, S² chart, gravity, gauge, matter) live at simulation.floatingpragma.io.
01 · The basis
Three axioms. Nothing else is postulated.
Release r2000 cut the framework down to three statements. A1 says what the hardware is. A2 says what the observers owe each other. A3 says what the world is allowed to contain beyond that. Everything further down this page, and every product OMEGA builds, is a consequence of these three plus the two closure equations in §02. If a claim on this site does not trace back to them, it is marked as a branch assumption or a design hypothesis.
A1 · Carriers and federation
There exists a finite or regulated observer-patch net built from local twelve-port echosahedral carriers with icosahedral (A₅) symmetry, sewn into a federation whose observer-facing support is an oriented S². This fixes the hardware: incidence (V,E,F) = (12,30,20), the proper A₅ action, and the support screen the geometry gets read off. A cube would be a different axiom.
A2 · Overlap agreement
When observers share, translate, or coarse-grain observer-accessible data, they agree on its meaning. That single requirement generates the local-fit contract on collars, the repair moves that resolve mismatches, and the quotient normal form that survives them. Public facts are the fixed points of A2, not a separate postulate.
A3 · No structure beyond the receipts
Among all states compatible with the observer-visible constraints generated by A1 and A2, the realised state contains no additional structure. Unconstrained state is maximally random. This is the axiom that pays for Born weights, Lüders conditioning, the Tsirelson bound, and the statistical shape of the dark sector.
A3 · no structure beyond the receipts
pinned 32 / 140 cells · rest drawn uniformly, 0 redraws
A3 is the one people skip. It is doing the heaviest lifting. Once A1 and A2 have pinned everything the observers can compare, the remaining freedom is not filled in by a hidden mechanism. It is drawn flat. Probability in OPH is what maximal ignorance looks like from inside a patch net, which is why the quantum record algebra falls out instead of being assumed.
Source paper
Observers Are All You Need · r2000 ↗Mueller and Osika (2026), release r2000. The synthesis paper owns the observer interpretation, the three-axiom basis, and the two quantitative closures. The bounded observer patch is the primitive object. Its physical size and carrier realisation stay branch data, and spacetime, fields, and particles enter through additional physical readout maps.
02 · The two closures
Two equations the universe has to solve about itself.
The axioms describe a protocol. The closures ask that protocol to be self-consistent, and that is where the numbers come from. The local closure fixes the pixel constant P. The global closure asks a trial universe to reproduce its own logarithmic correctable-record capacity. Neither carries a free parameter.
Local closure · pixel constant
The stronger of the two. A fixed-point uniqueness schema plus outward-rounded interval certificates give one root for each declared map on the full analytic domain. Two values circulate and they are not interchangeable: the CODATA-derived comparison pixel P = 1.630968209403959 and the source-side forward closure root P = 1.630972095858897, which takes zero measured input. The source-derived physical hadronic transport for P is work in progress.
Global closure · record capacity
A trial universe 𝔘N has to reproduce its own logarithmic correctable-record capacity. The finite consensus and capacity algebra behind M₀ is established separately. The physical public-record producer and the unique finite-size selector for N are work in progress, so treat this closure as the weaker of the pair and read the N-dependent numbers on this site as branch results.
What the closures buy downstream
P is the number the rest of the site keeps spending. The canonical susceptibility on the co-registered presence branch is 1 − Pχ/24 = 0.9320429912748350 (Pχ = P_C, the CODATA-derived comparison pixel), which sets the ceiling on the anti-gravity channel. The same closure pins the OPH certified fixed point α⁻¹ = 137.035660136946577, against CODATA 137.035999177. The relative residual is 2.5 × 10⁻⁶, which is a real gap and stated as one.
03 · The patch lattice
Finitely many observers, each with a bounded view.
This section is A1 and A2 written out in working form. An observer is a finite agent that can only see a bounded chunk of the world. We call that chunk its patch. Two observers whose patches overlap share a collar: the boundary slab where their data has to agree, which is exactly what A2 demands. The patches form a graph. The collars are the edges. There is no continuous spacetime underneath. There is the finite graph, the labels on each patch, and the overlap-agreement rule on the edges. That's the whole substrate.
Patch (vertex)
A finite-dimensional state σ on a region. Sigma can be a wavefunction chunk, a thermodynamic profile, a record register, whatever the substrate happens to be.
Collar (edge)
A thin slab where two patches both have visibility. The local-fit contract says the two patches' restrictions to the collar must match, up to a declared gauge.
Mismatch score Φ
Total disagreement summed over every collar. Accepted repair moves drive Φ strictly down. Φ is a Lyapunov functional and the dynamics terminates on the patch net.
Holonomy obstruction
Even when every collar agrees pairwise, the loop around a cycle can fail to close. That residual is the topological / gauge charge of the configuration. It's what we usually call "field strength" in the smooth picture.
Source paper
Reality as a Consensus Protocol · r2000 ↗Mueller (2026), release r2000. Defines the patches, the local-fit contract, the Lyapunov descent of Φ, and the cycle obstruction (holonomy). The fixed-cutoff consensus theorem in this release supplies a finite observer-like self-reading system on the declared recovery, record, feedback, selected-fiber, and implementation-invariance packet.
04 · The repair loop
How a candidate world becomes real.
A2 does not say how disagreement gets resolved, only that it must. The repair loop is the mechanism. Each step, every patch looks at its collars, picks the local repair move that lowers Φ the most without violating the local-fit contract, and applies it. The dynamics is schedule-independent: any order of moves that respects the contract converges to the same normal form. That normal form is what we call physical reality on this region of the network.
Repair loop · Φ Lyapunov descent
schedule-independent · Theorem 3.13
1 · propose
Each patch proposes a local repair move from a finite menu (flip a link, rotate a sector, splice a record).
2 · accept
A move is accepted iff it strictly lowers Φ on every touched collar and respects orientation and gauge.
3 · commit
Accepted moves rewrite the patch state. Records get written into central projectors so other patches can read them later.
Most candidate worlds die from disagreement, not from energy. The survivors are exactly the schedules whose Φ converges to zero, modulo the unavoidable holonomy obstructions. Energy and momentum drop out as conserved bookkeeping quantities along those schedules. They are emergent, not postulated.
05 · Screen microphysics
The actual computation runs on a 2D screen.
A1 names the hardware, and this is what it looks like. The federated implementation surface is not 3D space. Each local carrier is a twelve-port oriented interface with incidence (V,E,F) = (12,30,20) and a proper icosahedral A₅ action. Many such carriers get routed together into a federation screen of interfaces, records, repairs, and checkpoints. The 3D world we experience is the support screen A1 ends on: an oriented S², the observer-facing geometric chart reconstructed from that federation's records. There is no bulk substrate to push against. The bulk is a printout.
Echosahedral A₅ carrier · twelve-port screen substrate
(V, E, F) = (12, 30, 20)
One carrier · 12 ports, A₅ symmetry
Bulk · what observers experience
Local carrier boundary
The twelve-port oriented interface of one Echosahedral carrier. Ports, oriented incidence, accessible algebra, response law, repair interface, clock, and refinement lineage form its observer-visible signature. Change any of these and it is a different carrier contract.
Federation screen
The routed system of many carriers at finite cutoff. Identical local carriers can be wired as a path, a cycle, a higher-genus complex, or a spherical complex. Local incidence does not determine federation topology.
Support screen
The observer-facing geometric chart. On the spherical branch, a refined conformal S² used for caps, collars, modular flow, and Lorentz reconstruction. The map from routed carriers to a support-visible nerve is a physical bridge, not a change of notation.
Structure-sensitive, presentation-invariant
OPH is invariant under changes of presentation that preserve the full carrier signature. Hidden coordinates, worker partitions, materials, and wiring are silent. A cube and an icosahedron are different contracts even in the same material.
Source paper
Federated Echosahedral Screen Microphysics · r2000 ↗Müller, Osika, Xue, Cassie, Matscheko and Visser (2026), release r2000. Owns the finite carrier and its public interfaces: the twelve-port Echosahedral carrier boundary with incidence (V,E,F)=(12,30,20), the proper A₅ action and rank-three six-axis frame, the federation screen, the support screen, Born–Lüders and CHSH records, and checkpoint restoration after repair. Companion to Reality as a Consensus Protocol (which owns accepted repair and the quotient public normal form) and the compact SM/GR paper (which owns conditional maps into support geometry, gravity, and matter).
06 · Bulk laws are emergent
Gravity, mass, inertia: printout, not substrate.
Once the screen has settled on a consensus fixed point you can read off a 3D effective geometry. The chain runs from repaired normal forms through the receipt-selected round S² and the modular flow to a four-dimensional event manifold, and the Einstein relation follows from the typed modular, null-stress, entropy, and small-ball premises. Both the event manifold and the Einstein step stay conditional on those named receipts: the celestial S² does not populate a spacetime by itself. On top of the recovered geometry sits a non-baryonic gravitating sector sourced by an interpolation function ν(x). On Earth ν → 1 and there is no anomaly to see.
Dark-sector source · OPH-canonical
This equation is a bookkeeping rule extracted from the screen's repair statistics. It is not the fundamental law. The fundamental law is the consensus loop on the screen. That distinction is the reason we can hope to bend the equation without breaking the framework.
07 · How OMEGA bypasses bulk laws
We don't fight gravity. We edit the screen.
Every emergent bulk law is a printout of some statistic on the screen. A device that biases the repair statistics on its section of the screen, without violating the local-fit contract, changes what the bulk reports back. The bulk obeys what the screen says. Coherent matter is the lever.
Anti-gravity
Computing
AGI
08 · Claim boundary
What is derived, modeled, and hypothesised.
- Axioms, not results. A1 (twelve-port echosahedral carriers federated onto an oriented S²), A2 (observers agree on the meaning of shared, translated, or coarse-grained data), and A3 (no structure beyond the observer-visible constraints). These are assumed. Judge them by what they generate.
- Derived from OPH. Patch consensus, Φ Lyapunov descent, the cycle obstruction, the gauge quotient, the P closure and its interval certificates, the ν coupling, the dark-sector source equation, the Echosahedral A₅ calibration suite. Theorems with proofs in the paper trail.
- Conditional. The four-dimensional event manifold, the Einstein relation, the Standard-Model matter image, and the N closure. Each carries named receipts or an unfinished selector, and the site marks them wherever they carry a number.
- Modeled. The OMEGA computing dataset (pre-hardware, computed, schema v1) and the χν vehicle auto-trim simulation on the Anti-Gravity page.
- Branch theorem (Mueller, Osika & Matscheko). On the co-registered presence branch, the canonical χν is pinned to 0.9320 ≤ χνcan ≤ 1, with exact presence-branch value 1 − Pχ/24 = 0.9320429912748350…. The hoverboard question is engineering a substrate that holds the required vertical coherence contrast ΔScoh, not the value of χν. See Theoretical Bounds on χν (PDF).
- Not claimed. Built hardware, or a measured ΔScoh on a controlled torsion-pendulum protocol. Work in progress.
Full derivation chain on the Pragma learning portal.