Observer Patch Holography

Physics from the records observers can share.

Main paper · Book · Notebook · Lean library · Reproduce · Pragma Research · Français

Mission

The mission of Observer Patch Holography (OPH) is to create a consistent and complete, formal and rigorous theory of reality. That theory has no starting point: it is a closed loop, and it has to meet four conditions.

1. Consistent. The loop closes. Its fixed point exists, constructed explicitly and machine-checked, and a theory with a model contains no contradiction.
2. Rigid. Every dimensionless quantity is forced. One measured value sets the units and nothing else.
3. Complete, in the sense Einstein, Podolsky and Rosen gave the word in 1935. Every element of physical reality has a counterpart in the theory, and every measured quantity is derived.
4. Correct. Derived values agree with measurement, and new predictions are frozen before they are tested.

OPH does not claim to be the only theory with these properties.

The idea

OPH proposes that physics is what bounded observers can establish together. Finite observers compare records on shared boundaries, repair their disagreements, and treat as real whatever survives every comparison. Three problems that resist a classical account motivate the programme: quantum measurement, correlations that no local classical model reproduces, and the origin of an apparent spacetime. OPH seeks one explanation for all three in the consistency of observers' records and operations, and it pursues that explanation as an executable observer, machine-checked mathematics and predictions fixed in advance.

The Universe reads itself into existence. OPH has one hypothesis, the closure hypothesis: the Universe is a timeless, self-referential structure whose observers recover the specification of their own world from their records and build hardware that realizes that same history, including its builders. Nothing lies outside this loop, so the recovered specification owes no further justification. It has to run and reproduce what observers measure. Space, time and matter are effective descriptions of the records, and "our Universe" is the public record, what survives every comparison between observers. The basis states the hypothesis, the no-outside rule, the agreement condition and the executable specification; the working terms explain the timeless view and the clocks inside it.

The executable hypothesis

The concrete bet is a program. One simple local repair and memory law, running on a network of twelve-port carriers, should produce observers whose shared records look like our world: interacting quantum fields in 3+1 dimensions, and gravity on large scales. Particles are the knots in that network: protected defects that local repairs cannot undo.

The hypothesis says what would count as success, and the completion program splits the work into gates with stopping rules. Either the pieces join up on one running process, or a proof shows that the whole class of laws cannot work.

Highlights

• The particle families are identified. Every protected defect carries a six-valued flux class, and it is exactly the class the Standard Model gives its particles: left- and right-handed quarks, leptons with the Higgs, and neutral fields. Quarks and leptons come out as fermions, and no colour charge ever sits alone. Particle paper.
• The charged-lepton mass ratios. A generation register in the same repair law gives muon/electron 206.770 and tau/electron 3477.47 (measured 206.768 and 3477.37), with no measured mass as input.
• An early universe like ours. The runs create every particle class in pairs, quark pairs annihilate, colour stays confined, and matter and antimatter come out equal, as before baryogenesis.
• The gauge group with equal couplings. Phases on the carrier's ports give (SU(3)×SU(2)×U(1))/Z6 with equal strengths at the cell scale, and neutrinos come out as Dirac particles.
• An observer that runs. A twelve-port observer keeps its records and uses them to choose its next repair. Overlapping observers read a common reference and its clock, a finite quantum process joins electric flux, charged matter and a scalar field, and refining screens give Gaussian field limits and waves of finite speed.
• A Lorentzian scalar field from the observers' records. On a declared radial extension of the refining screen, one action fixes correlations, response and a modular clock, and a smooth (1+3)-dimensional scalar field theory reproduces any finite set of joint readouts. The radial direction and the physical units are inputs. Integrated verdict.
• Standard physics from finite agreement. Under stated premises, finite theorems give public records that do not depend on the order of repairs, the Born rule and the Tsirelson bound, a carrier that is three-dimensional in its slow response, the Standard Model gauge Lie algebra with an anomaly-free matter representation, a (1+3)-dimensional causal order and the Einstein equation from null balance.
• Energy readouts. Complete interacting quantum sources give gauge-constrained energy records, including preparation failures, and a finite electric/magnetic field has a certified charged ground. Charged-field attachment.
• Continuum fields and their measurements. The ordered-spin construction has three continuous spatial dimensions, time, positive energy and finite propagation. Its position observable is conjugate to the same spatial momentum, with complete finite detectors and ordered source limits. Spectral measurements retain all outcomes. Proving Lorentz symmetry and surviving interactions on that same state is the central field requirement. A separate scaling gives free massless Weyl fields and the matter stress response used by the conditional gravity derivation. Field constructions, spectral readout, ten common-theory requirements.
• Interacting fields and actual position records. A declared gauge-field construction has controlled local detector records and a causal bound uniform in physical refinement, including quantum links and all fermion occupations. A joint field/reference instrument supplies conserved crystal momentum, position backaction and finite uncertainty. Physical chiral refinement and particle mass identification require their own same-state derivations. The illustrated atlas explains these finite measurements and the remaining physical connections.
• Thermal records, work and pressure. One interacting quantum-flux control has a certified thermal preparation and complete two-time records, with every occupation and reference retained. Its spatial strain response calculates work and pressure from a declared geometry coupling on the same state and clock. The proper geometric interpretation and regional entropy and area premises required for Einstein dynamics are separate physical requirements.
• One source, state, reference and clock. The selected Wilson construction has a common observable algebra, a stationary limiting state, positive energy and convergent finite detector histories on one subsequence. Its energy currents obey exact finite conservation. A controlled energy pulse produces a nonzero original current response and positive cyclic work; its Ward identity includes the work supplied by the pulse. Selected energy moments obey a bound of 4000000/a, independent of link degree, where a is the source spacing. The positive finite-window probability deteriorates with capacity. An equal-work control on the same source has an elastic limit, so mean work alone cannot prove particle survival. The native chirality audit identifies a paired response that a physical chiral assignment must resolve. Lorentz covariance, surviving interacting particles and proper geometric stress remain requirements on this same source and state. The ten-step dependency map records the precise remaining physical requirements.
• Mathematics you can check. The Lean library contains more than 12800 public theorems and lemmas with no admitted proofs. Computational receipts bind their source inputs and include replay checks.
• Tests fixed in advance. Predictions and their rejection rules enter the frozen-prediction ladder before the eligible comparison data, with OpenTimestamps proofs, most of them anchored in Bitcoin; the dispersion prediction for the primitive port orbit is one of them. The postdiction ledger, the falsification programme and the cross-scale audit keep comparisons with measurements apart from tests of the mathematics.

Agreement with the full range of observed measurement statistics has not been established. The theorems hold under stated premises, and the executable observer is a candidate judged by declared acceptance criteria.

Run the observer

From the repository root, with Python 3.11 or newer:

python3 -m model.observer run --trials 10000 --seed 42

This runs the minimal record-and-feedback experiment and prints forecast scores and a result hash. The model guide covers the rest.

Mathematical results

• Agreement and stable records. Under explicit termination and consistency conditions, local repairs reach one shared public result whatever their order. Consensus paper.
• Quantum observations. Within the stated finite quantum algebra, verified results cover repeatable measurements, classical records that later operations cannot disturb, uncertainty and the Bell correlation bound, with a state that attains it. Native repair histories reconstruct a positive functional on the full 66-state matrix algebra, where the Born trace rule holds; native evolution does not prepare that state. Finite quantum event algebras, native reconstruction.
• Three spatial directions. Optimal readout of a supplied three-dimensional response selects the twelve-port incidence, and the carrier's mean repair rule gives an exact three-dimensional slow response with Euclidean geometry, which an observer's current records recover. Carrier construction.
• Gauge symmetry. Under stated premises on complete reversible response and observer transport, the twelve-port response algebra has the Standard Model gauge Lie type, and a specified matter representation gives an anomaly-free generation. Port phases realize the global group, and six of its central elements form the flux alphabet of the particle defects. Gauge derivation.
• Thermodynamics. Finite repair theorems give a Clausius inequality, fluctuation relations and an information Landauer inequality under a stated reference and energy calibration. Fair-coin seam repair is exact conditional resampling, so entropy never falls on binary populations while the complete tape keeps every bit. A native memory refresh realizes the machine-checked finite four-law core in internal cost units. Thermodynamics account.
• Information capacity. Exact results count which records stay distinguishable after the allowed operations, bound that count by the available carrier, and follow it through refinement. Record capacity.
• Entangled-pair coupling candidate. Alex Wissner-Gross derives a finite spectral expression with inverse 137.035999189566. The independent OPH reconstruction credits that construction and tests its complete-outcome and normalization assumptions. Its identification with the physical electromagnetic coupling and its proposed attachment to the screen-grain equation are conditional.
• Matter and fields. A supplied charged-scalar and Maxwell action with its geometry and quantization give an interacting Hamiltonian after gauge reduction, and controlled scalar refinement connects classical detector readouts to a nonlinear field equation. Gauge invariance, face locality and carrier rotations select the Maxwell action on the seams. A common metric dictionary is constructed. Matter continuum.

These are conditional mathematical results. Making their premises hold for the observations of one common model is the central construction problem. The premise map records which premises the executable specification supplies and which it takes as inputs.

Papers

• Observers Who Read Their Universe into Existence is the main synthesis: the closure hypothesis, the executable-model hypothesis and the tower of results built on it. Cite its released version, the PhilPapers record.
• An Executable Observer for Observer Patch Holography states the specification, the executed components and the ordered joins that remain.
• The theorem library holds the long proofs, from consensus and observers and records to spacetime and Einstein dynamics and particles. The paper index and the paper set list every paper and its role.
• Companion papers carry focused results. A lepton-mass relation, the Koide relation, holds exactly under a stated balance premise. The capacity programme asks whether the public capacity assigned to the Universe agrees with the one reconstructed from inside. These constant calculations, including the fine-structure root, have diagnostic status.

Where things are

Path	What it holds
model/	The executable observer: implementation, tests, retained receipts and protocol records
flagship/	The synthesis paper
paper/	The construction paper and the theorem library, with archived papers under paper/archive/
extra/, cosmology/	Companion papers
Lean/	The machine-checked library
code/	Exact calculations, lane verifiers and receipts behind the papers
evidence/	Retained evidence packets and custody records
claims/	Established claims and their dependency views
tracking/	Premise, observation, prediction and instrument registers
docs/	The basis, the working terms, policies and registers
book/	The book

Reproduce and verify

The reproduction guide runs the verification suite from a clean clone. The model verifier replays the receipt inventory declared in model/verify.py; the regression suite also checks adversarial cases:

python -m pip install -r model/requirements.txt
python -m model.verify
python -m pytest -q -W error model

The guide also lists the standalone particle and source-field checks used by the observer workflow.

The Lean library builds with Lake, the documentation index lists the registers and policies, and the book gives a longer road in. The textbooks at learn.floatingpragma.ai and the interactive simulation at simulation.floatingpragma.io are the gentlest introductions.

Contributing

The task is to make one observation-and-repair process supply the effective physics: the observer's clock, spatial interpretation and field measurements on the same histories, compared with independent observations. Contributions should resolve a named connection or expose a failure in the shared model; the construction guide, the repair-law guide and the research issues set out that work. Paper releases follow the release policy; main-branch PDFs are source previews, and deposited releases retain their original bytes.

License

Software, including Lean and the model code, uses Apache-2.0. Papers, documentation, figures, data and ledgers use CC BY-NC-SA 4.0, with upstream Particle Data Group terms for the packaged particle values. The license map gives the directory-specific terms.

Related projects and funding

Cadence is the related learning-machine project. Its capability evidence is separate from OPH's physics evidence. Pragma Research brings the projects together.

OPH's official TEO (Theory Of Everything) memecoin was deployed by the Base community and lives on Base at 0xd2a7055317D0c7b316319cDadaE592D0644A0b07 (chart). Its trading fees are routed to Bernhard Mueller to fund the project. The token has no role in the theory. Other tokens using the OPH or TEO name are unrelated. Nothing here is financial advice.