People often ask me how Fieldflux Biosystems publishes across biology, fluid dynamics, and mathematical physics—and how so much of that work can appear so quickly. The explanation begins with a question we've been pursuing for many years: Can we develop a scale-agnostic formal definition of health? This pursuit has naturally taken us into several seemingly disparate fields and led us to build one of our most valuable assets—our digital scientific research laboratory, where the work of any one investigation remains available to any of the others. The preprints that we publish are some of the results that emerge from that ongoing exploration.
What we mean by health
We usually encounter health at the scale of a person. We see someone recovering from illness, adapting to a life disturbance, or sustaining the activities of daily life. Beneath that experience, cells, tissues, and organs maintain their organization while matter and energy move through them.
Our working definition of health centers on a bounded, invariant, dynamically stabilized state. A living system continuously changes, so making that definition precise requires identifying what remains preserved through its activity, what bounds it must remain within, and how its dynamics sustain that organization. A formal definition specifies these conditions within a particular mathematical setting. A scale-agnostic definition carries an additional burden: explaining how the same underlying concept remains meaningful as we move between scales. A cell and an organism have different boundaries, activities, and needs. We believe that by formally defining one, we give ourselves a place to begin investigating another and formally showing what connects them is naturally a part of the formal process.
Why this takes us into different fields
To investigate a scale-agnostic definition, we have to challenge it above and below the scales where we ordinarily think about health. A cell gives us one setting. A tissue gives us another. A flowing fluid or a mathematical field lets us examine questions of stability and persistence under very different conditions. Across these settings, we keep encountering related questions. What allows organization to persist through change? Can a measurement recover the state we care about? What information disappears when we simplify a description? Each field gives these questions a specific form. In biology, we can investigate how measured states relate to later outcomes and how tissues reorganize through development. In fluid dynamics, we can examine the conditions under which a flow continues smoothly. In mathematical physics, we can study what survives when a physical state is expressed in another representation. Many of our papers arise while exploring, refining, and challenging the proposed structure of health. An investigation can produce a theorem, a counterexample, or an empirical finding whose value extends outside the field where we encountered it. Its contribution to our formal definition may remain unresolved. We publish when the result has a contribution that can be stated, supported, and examined on its own terms.
Two examples, and a possible common principle
In Relational Organization and Directional Stability Across Mouse Organogenesis, we analyzed 4.10 million spatial observations from 37 embryos. We asked how developing tissues relate across stages, and how the answer changes when we alter the neighborhood used to describe each observation. The visible architecture changed substantially with neighborhood size. Changing the comparison rule from tissue identity plus surrounding tissue context to tissue identity alone expanded adjacent-stage relations from 1.70 million to 144.92 million. Yet the aggregate directional score remained negative across the tested descriptions. Individual developmental contrasts were more sensitive to the comparison context. Read the paper.
For developmental biology, this shows that the comparison context helps determine which organization becomes visible. For our health program, it gives us a concrete way to examine invariance: change the observation scale and comparison rule, then determine which features persist.
Paper 5 in our Gaussian series, Source-Aware Weyl-Reduced Celestial Representation, examines what is preserved when we transform a particle-state description. We found that a particular symmetry requires transforming the source together with the output. Accounting for both produces an exact, norm-preserving reduction of the joint representation. A separate calculation shows that the normalized transition with the source held fixed fails norm preservation across an open region of spectral parameters. Read Paper 5. For mathematical physics, this supplies an exact construction and a precise obstruction. For us, it clarifies how to investigate preservation across descriptions: specify the transformation of the whole relevant structure and establish what that transformation preserves.
What interests us is the possibility that these results illuminate a common principle at different scales. In the biological study, a broader feature persists while the visible architecture changes. In the physics study, exact preservation depends on tracking the connected transformations of source and output. This suggests a candidate principle: an organizing relation may remain invariant through substantial changes in its realization or description, under identifiable conditions connecting those changes. Establishing a common law requires further formal work. The biology result demonstrates empirical persistence across tested representations; The mathematical physics work establishes an exact mathematical relationship. Bringing them under one principle means showing precisely which structure they share.
For us we wonder whether this possibility bears directly on health. A cell, a tissue, and an organism each sustain organization through continuous activity. We are investigating whether we can understand their health through a common structure: remaining within appropriate bounds while dynamically preserving the relationships required for continuity.
These papers help illuminate the invariance part of that question. Establishing the bounds and the dynamics that sustain them remains a large portion of our ongoing work.
The laboratory behind the papers
Following a program like this over years requires a way to retain what we learn with precision and impeccable accuracy. To this end, we have built a formal scientific digital research laboratory that holds mathematical definitions, proofs, computational work, research records, and many open questions. Much of its mathematical structure is written in Lean, a system that checks whether a proof establishes its conclusion from the stated assumptions. When a later investigation needs an earlier result, we can inspect its conditions and determine whether they hold in the new setting. When an approach fails, we can preserve the counterexample or obstruction that explains why. Artificial intelligence helps us work within this environment: inspecting code, proposing proofs, examining arguments, and preparing explanations. As models improve, they gain access to the scientific structure already accumulated there. Formal checking establishes what follows from mathematical premises. Experiments and measurements help determine how those premises relate to the physical world. Both contribute to the research we want to do.
How research accumulates
A physical research institute grows through its equipment, datasets, methods, and collective experience. Researchers arrive and leave, while the institution works to preserve what they discovered. Our digital laboratory develops along the same institutional principle. A new investigation can inherit a checked proof, a documented failure, or an unfinished construction. The people and computational tools doing the work can change while more of the research remains available. This helps explain our publication pace. A paper appearing today may draw on years of prior construction. Work developed for one problem can supply a missing piece in another, allowing several investigations to reach publishable conclusions within a relatively short period. Each paper still has to present its argument, explain its methods, and support its claims, but our laboratory's depth gives us a richer starting point.
Why this returns to measurement science
For Fieldflux, this research ultimately returns to a practical question: What would it take to engineer an instrument that measures health? We can describe health through familiar aspirations: well-being, resilience, recovery, and the capacity to function. Turning those ideas into a measurement specification requires us to identify precisely what property the instrument is intended to measure. An engineer needs a defined object. What distinguishes one state from another? Which physical interactions make that distinction observable? What range must the instrument resolve, and what would establish that its readings correspond to the intended property? These questions connect our formal research directly to measurement science. A rigorous definition within one specified system is already a substantial task. A definition that remains meaningful across cells, tissues, and organisms requires us to establish how the property and its measurement change between those settings.
That is why we continue developing the definition and stress-testing it across different objects. Each investigation can reveal another detail of the structure we are pursuing. A discovery may identify a relationship worth preserving. An obstruction may expose information that a proposed measurement cannot recover. A no-go theorem may establish why a particular engineering approach cannot deliver the intended result under its stated conditions. These findings gradually become the foundation for engineering decisions. They help determine which interactions to probe, what observations to combine, how to reconstruct the relevant state, and where ambiguity remains. They also determine what a result can mean. A reading becomes useful only when we can explain its relationship to the defined property, the conditions supporting that interpretation, and the remaining uncertainty.
This is the path we are building at Fieldflux: from a precise account of health, through physical observation and engineering, to measurements whose meaning we can establish.
Our preprints record our discoveries along this path. The laboratory preserves them so that we can continue to explore, investigate, test, and wonder. Our instruments will stand on the details that survive the mathematics, the experiments, and the repeated effort to understand the object itself and any potential laws that govern the exchange across scales.
Explore the broader Research Notebook, the preprint library, the developmental-biology paper Relational Organization and Directional Stability Across Mouse Organogenesis, and Gaussian Paper V, Source-Aware Weyl-Reduced Celestial Representation.