Testable Hypotheses

What would count as evidence?

Important: AI-Generated Content

These hypotheses were generated through extended conversation between a human (Will Goldstein) and an AI (Claude). The mathematical formulations, experimental protocols, and statistical frameworks are AI-generated extrapolations from pattern observations.

This is not peer-reviewed science. These are speculative hypotheses that would require rigorous empirical testing by domain experts before any claims could be considered validated.

The value here (if any) is in the testable predictions themselves — not in the theoretical framework that generated them. If the predictions fail, the framework is wrong.

If RSM describes real structure, it should make predictions. Below are hypotheses extracted and "steelmanned" — stated in their strongest defensible form with clear falsification criteria.

Organized by confidence level, from most testable to most speculative.

Primary Hypothesis

Highest confidence — specific, quantitative, testable with current technology

Perpendicular Branching in Morphogenesis

Core Claim

In developing biological systems where new structure emerges from existing structure under influence of chemical gradients, branching events correlate with geometric configurations where gradient direction meets existing boundary approximately perpendicularly.

Mathematical Formulation

At branching point p:

θ(p) = arccos(∇G(p) · ∇B(p) / |∇G(p)||∇B(p)|)

Prediction: P(branch | θ ≈ 90°) > P(branch | θ ≠ 90°)

Where: ∇G = chemical gradient, ∇B = boundary surface normal

Why This Might Be True

At perpendicular intersection:

  • Gradient cannot reinforce existing boundary (no parallel component)
  • Gradient cannot directly oppose boundary (no antiparallel component)
  • Force balance requires structural response orthogonal to both
  • New growth direction naturally perpendicular to plane of gradient-boundary

This is mechanical optimization, not mysticism.

Test Protocol

For N≥30 branching events in developing tissue:

  1. Image morphogen distribution (fluorescence microscopy) → Compute ∇G
  2. Reconstruct boundary geometry (3D segmentation) → Compute ∇B
  3. At observed branching locations → Measure θᵢ for each event
  4. Statistical test: H₀ (θ uniform) vs H₁ (θ clustered at 90°)

Use Rayleigh test for circular data. Reject H₀ if p < 0.01.

Falsification Criteria

Hypothesis is false if:

  • Branching angles uniformly distributed (no clustering)
  • Angles cluster elsewhere (e.g., 45°, 0°, 180°)
  • Mean angle significantly different from 90° (μ < 75° or μ > 105°)

Valid Domain

This hypothesis applies to:

  • Biological morphogenesis (plant development, neural arborization)
  • Systems with identifiable chemical gradients
  • Contexts where new structure extends from existing structure

Excluded: Quantum systems, abiotic processes (unless analogous geometry)

Status: Untested hypothesis with plausible mechanism

Supporting (circumstantial): Phyllotaxis patterns, Murray's law for vascular branching, root gravitropism. No systematic study measuring ∇G and ∇B simultaneously at branching events.

Secondary Hypotheses

Pattern observations — valid in specific contexts, not universal

Hollow Centers in Peripheral-Growth Systems

Observation (Properly Scoped)

Many stable systems exhibiting radial growth or circulation around a center have that center physically unoccupied or minimally occupied relative to surrounding structure.

Physical Mechanisms (Not Mysticism)

  • Trees: Growing layer (cambium) is peripheral by definition; interior is dead structural support
  • Hurricanes: Conservation of angular momentum creates low-pressure core
  • Atoms: |ψ|²r² maximum at Bohr radius due to kinetic/potential energy balance

Steelmanned Claim

In systems where structure circulates around or radiates from a center, the center tends to be less dense than surrounding regions. This is optimization (put structure where action is), not paradox.

Falsification: Many systems have maximum density at center:

  • Solid spheres under gravity (Earth's core is densest)
  • Stars (nuclear fusion in core)
  • Fermi gas (electrons fill states from center outward)

Status: Pattern exists but not universal — specific to peripheral-growth systems

Boundary-Centric Activity

Observation

In many growing or evolving systems, active processes occur at boundaries/interfaces while interior regions are relatively inactive.

Why This Occurs

Thermodynamic: Gradients drive processes. Gradients strongest at interface. Therefore activity concentrates at boundary.

Examples: Plant cambium, neural growth cones, cell membranes, crystal growth surfaces, flame fronts.

Falsification: Many systems have interior activity:

  • Stars (fusion in core)
  • Brain (activity distributed, not just cortical surface)

Status: Valid pattern in specific contexts (growth, exchange) — not universal

Mathematical Structures

Valid mathematics — potential applications, properly scoped

Hyperbola-Line Perpendicularity

Valid Mathematical Result

For rectangular hyperbola xy = k and diagonal line y = x:

  • They intersect at (√k, √k)
  • At intersection, curves are perpendicular
  • This is the unique point where x = y on the hyperbola

Potential Application

Could model systems where two quantities multiply to constant (resource tradeoffs) and optimal balance is sought (equal weighting). Transition occurs at perpendicular configuration.

Status: Correct mathematics — application to optimization problems is speculative

Unitary Evolution Structure

Valid Observation

Any physical theory with linearity, norm preservation, and continuous evolution will have evolution operator of form U(t) = exp(iGt) where G is Hermitian.

What This Actually Shows

This is general structure for norm-preserving linear evolution — not specific to quantum mechanics or RSM. Appears in classical wave equations, Hamiltonian mechanics, probability currents.

Status: Valid mathematical structure — not unique to any particular framework

Speculative Claims

Interesting patterns — weak evidence, hard to test

Perpendicularity as Optimization Criterion

In systems where multiple constraints must be simultaneously satisfied, optimal configurations often exhibit orthogonality between constraint gradients.

Examples: Planetary orbits (F_g ⊥ v), fluid vortices (∇P ⊥ v), electrostatic equilibrium (E ⊥ surface)

Status: Valid in optimization — biological application is the testable part (see Primary Hypothesis)

Transformation Without Collapse

No physical system exhibits true "collapse to origin" — all apparent collapses are transformations into other structures.

Partial support: QM "collapse" increasingly interpreted as decoherence (continuous)

Open question: Black hole singularities — genuine discontinuity or limitation of current theory?

Status: Speculative — depends on unresolved physics

What We're Not Claiming

The following were considered and rejected as untestable, overclaimed, or invalid:

  • Deriving physics from "reality is infinite" axiom
  • Claiming Euler's identity "encodes existence"
  • Asserting 3D space is "necessary" (vs. empirical fact)
  • Isomorphism claims with quantum mechanics or gauge theory
  • Reading the Schrödinger equation into the Dao De Jing

Pattern recognition is not derivation. If we can't test it, we can't claim it.

Test These Hypotheses

If you have domain expertise and can actually test any of these — especially the perpendicular branching hypothesis — we want to hear about it.

Contact via r/ourinfinitereality or the email on the About page.

Negative results are valuable. If the primary hypothesis fails, that's important information.