Explainer

What this is

Projective Process Monism (PPM) is a unification program. From a single geometric arena and one measured input, it derives the structure of the Standard Model, gravity, and cosmology — and, the framework further argues, extends the same structure to the geometry of conscious experience.

Most current programs are scoped to one regime: string theory and loop quantum gravity target quantum gravity; integrated information theory targets consciousness. PPM is unusual in working from one arena across all of them — quantum measurement, the Standard Model, gravity, cosmology, and the geometry of experience. Whether that breadth holds up is what its predictions put at risk. For how the framework measures against the conditions any total theory must satisfy — and where today’s alternatives fall short — see the case.

The claim is that the smallest mathematical structure able to hold the geometry of quantum possibility, of measurement, and of conscious experience at once is enough to fix everything else. One measured number from experiment — the pion mass, 140 MeV — sets the scale; the geometry does the rest. The exact ledger behind that claim — what is assumed, what is derived, and what is still owed — is further down this page.

Where it starts

Two facts you might not have noticed are connected.

The first is from quantum mechanics. The space of possible states for any quantum system is a complex projective space. For a four-state system (the simplest one rich enough to support the Standard Model’s structure), this space is called CP³, complex projective 3-space. Wavefunctions live here. Every measurement we can in principle perform corresponds to a direction in this space.

The second is from perceptual phenomenology — the systematic study of the structure of conscious experience, treated as an empirical science. In 2017, David Rudrauf and colleagues published a model whose geometric structure is real projective 3-space, RP³. They derived this from properties of perception (depth, perspective, the relation between viewpoint and viewed) and validated it against psychophysical data on how humans perceive geometric scenes.

Here’s the connection. If you take CP³ — the complex space where quantum possibilities live — and ask which subset of it is “real” in the sense of being unchanged when you replace every complex number with its conjugate (the operation called complex conjugation, which the framework labels τ), the answer is exactly RP³. The “real points” of CP³, fixed under conjugation, form RP³.

The same RP³.

The structural move

PPM treats this as a fact about the world, not a coincidence. The framework’s single axiom:

• Possibility space is CP³.
• Actuality space — the realm of facts — is RP³.
• The projection from one to the other (taking complex possibilities and selecting the real outcomes) is the operation we call “measurement.”
• Conscious experience is what it is like to be on the actuality side of that projection. An observer’s standpoint and actuality are one geometry, RP³. That identification is the framework’s monism. Which systems have an inside, and at what scales, is fixed by stated physical conditions rather than asserted — experience is placed as the interior of the same event measurement describes from outside, not produced by the dynamics as an add-on.

This is one structural choice. Everything else in the framework unfolds from it — the derivations, the debts, and the two further load-bearing choices the accounting keeps on the books.

What comes out

With one measured number from experiment to set the dimensionful scales, the framework derives the following — each entry checked against measurement, with the misses as visible as the hits:

The Standard Model spectrum. Particle masses, coupling constants, mixing angles. The framework reproduces nineteen of these measured quantities to about 2.6% mean error (1.1% median). None postulated; all derived from the geometric energy ladder the structure produces.

The Born rule. The quantum-mechanical rule that probability equals the squared amplitude of the wavefunction is forced as the unique probability law compatible with τ-projection — a uniqueness theorem about Z₂-invariant probability on the arena, derived rather than postulated.

Newton’s gravitational constant and the cosmological constant. Both turn out to be topological invariants of the framework’s structure — quantities determined by the global shape of the arena, not by dynamics. Λ is static, and it is small because the boundary capacity is exponentially large — not because the universe is old or because anything has been spent.

The Hubble rate and the JWST early galaxies. The expansion rate follows from the geometric identity H₀ = 1/T, where the boundary capacity fixes the cosmic age; it comes out to 70.9 km/s/Mpc and reproduces the observed age to about 1%. Separately, the gravitational constant that sets nucleosynthesis and the CMB stays fixed over cosmic history, while a separate effective coupling inside collapsed structures was stronger at high redshift, G(z) ∝ (1+z)^(3/2) — a candidate account of the unexpectedly massive early-universe galaxies the James Webb Space Telescope reports, with the quantitative match still open. The framework does not claim to settle the early-vs-late H₀ disagreement.

The strong-CP angle. The QCD parameter θ that should be measurable but stubbornly looks zero is forced to zero by the τ-symmetry of the arena. No axion required.

The quark CKM CP phase. δ_CP = π/φ² = π(1 − 1/φ) ≈ 1.200 rad, where φ is the golden ratio (the icosahedral A₅ character). The PDG 2024 CKM phase is 1.137 ± 0.022 rad — the geometry lands within about 5.5% of the measured value, a ≈2.9σ separation at current precision, and a few-percent residual remains open.

A consciousness window. The framework’s resolvability function — comparing per-event quantum information to ambient thermal noise — has a transition zone where individual quantum events are neither dominantly informative nor dominantly thermal. At biological temperature, this transition lands at the energy scales where neural processes operate. The framework also predicts a binding-window timescale of ~60 ms for distributed neural content to integrate consciously, within the range of measured psychophysical integration times.

What is not yet settled

The same honesty runs the other way, and the framework states its debts in the same place as its results. Some quantities are not yet computed from the geometry — a few particle masses still need inputs the derivation does not yet supply. Inflation is treated as an external input, not a prediction. The primordial fluctuation spectrum is not yet derived. A small residual in the gravitational constant is unexplained. And the framework’s simplest model of dark energy is in tension with recent survey data — a place it can be shown wrong. None of these is a domain the framework goes silent on; each is a located, quantitative debt inside a domain it already addresses, and a place the account puts itself at risk rather than a gap it papers over.

Why this is unusual

The parameter economy is worth stating, then setting in its place. The Standard Model alone requires 26 free parameters (νSM, Dirac convention) that have to be measured rather than predicted; add cosmology and the count grows. PPM works instead from a small, fully declared base: the geometric structure (CP³ with τ) and one measured mass scale, with two load-bearing choices kept openly on the books — the restriction to compact projective spaces, and the tiling behind the boundary-capacity number. The framework does not claim zero free parameters; it claims a base small enough that every input it uses is visible and countable, so the derivations are checkable rather than adjustable.

The parameter count is not the deepest thing here, though, and it is not what the framework rests on. What is unusual is structural. PPM is a single account that places its own observer inside the physics it describes, keeps one rule across quantum measurement and conscious experience with no special exemption for either, and pins what it means by “actual” inside its own geometry — while still reaching across quantum measurement, the Standard Model, gravity, cosmology, and the geometry of experience. Most programs manage one of these regimes; carrying a principled position across all of them under one uniform structure is the framework’s distinctive bet, and its predictions are where the bet can fail.

What is testable

Several quantitative predictions are open to confirmation or falsification by experiment.

Forward tests, not yet settled:

• The redshift dependence of gravity inside collapsed structures (CMB analysis, JWST follow-up)
• The 3.5 keV X-ray line as a sterile-neutrino dark-matter signature

Comparisons against already-measured values:

• The Hubble rate (independent ladder measurements)
• Specific particle mass ratios (laboratory experiments)

The Predictions chapter has the full list with measured values, predicted values, and the experimental status of each.

Where to go from here

To watch the whole framework run as one process — the arena, the projection, the cascade, and the synchronization that emerges as it crosses the critical zone — open the Model.

For how the framework measures against what any total theory must address — and the two papers that set that standard before any candidate is named — read the case.

For the framework’s account of reality and what its structures derive, read the ontology.

For the rigorous mathematical treatment — derivations, spectral calculations, proofs — read the technical reference.

For the mathematical vocabulary the framework uses (manifolds, projective spaces, fiber bundles, Kähler structure, and so on), the math primer has short, self-contained entries on each concept.

To verify the numerical claims yourself, run the notebooks. Every result is reproducible from open code.

To test or extend the framework, clone the Python package. A self-consistency suite runs in CI on every commit.

To ask questions in natural language, the NotebookLM workspace has the entire framework loaded.

The work is open. The math is open. The predictions are specific. What is asked of the reader is engagement on those terms.