Open Questions
Full transparency on the state of the research. What has been derived and verified, what is still being refined, what fundamental questions remain unanswered, and what entirely new questions this framework creates. Updated March 2026.
New Question (created by SSM)
Derived & Verified (27)
These results are computationally verified against CODATA 2018 / PDG values. Every claim below can be reproduced by running node ssm-tools.js or python ssm_tools.py.
Geometric Foundation
Quadrian Ratio q = √5/2
Hypotenuse of 1 × ½ right triangle inside the unit square. No alternative value exists.
Source: Axiom A1 (unit square) + A2 (Euclidean geometry)
Golden Ratio φ = (1+√5)/2 = q + ½
Arithmetic on q. Verified to full float64 precision against the algebraic definition.
Source: q + 0.5 | Verified: exact match
Quadrian Angles θx, θy, θz, θu
θx = φ(15+√2) = 26.5588°, θy = 90−θx = 63.4412°, θz = 2θy, θu = 7θz. All forced by arena geometry.
Source: φ, unit square corner (90°), diagonal (√2), penta-grid (15=3×5)
Quadrian e from Golden Ratio
e = √(φ(5 − 13/30)) = 2.71828... Geometric derivation of Euler's number from first principles.
Source: INTERPHASIC.md | Verified: < 10⁻¹⁰ relative error
Quadrian Wedge: 1/c² = φ² + 1
Local golden-ratio identity inside the Quadrian Arena. Verified computationally.
Source: QUADRIAN_WEDGE.md | JavaScript verification protocol included
Speed of Light
cy = 299,792,457.553 m/s (Northern path)
Derived via Qs(PNp). Delta from CODATA (299,792,458): 0.45 m/s. Relative error: 1.5 × 10⁻⁹.
Formula: Qs(n) = 10⁷(30 − 1/(10³−n)) − 2n/√5 | Empirical inputs: 0
📊 /constants.html — live computation
cx = 299,881,898.796 m/s (Eastern path)
Same equation, different angular potential (PEp). Predicts a second, slightly faster speed of light along the Eastern path.
Formula: Qs(PEp) | This is a testable prediction unique to the SSM
Coupling Constants
Fine-structure constant α = 1/137.035999206
Derived via Fe(11). CODATA: 1/137.035999084. Relative error: < 10⁻⁷.
Gravitational constant G via Feyn-Wolfgang chain
Same Fw equation that produces α also produces G at a different pencil position. Unifies EM and gravity on one gradient.
Fx(11, −√4538) → Fe(~122403) = G | Same equation, different input
Particle Masses
Electron mass: Ma(1) = 9.109 × 10⁻³¹ kg
Position n=1 on the mass gradient. CODATA: 9.1094 × 10⁻³¹. Agreement > 99.99%.
Formula: Ma(n) = n × 1352 × 5.4422 × 1.238e-34
Proton mass: Ma(1836.18) = 1.673 × 10⁻²⁷ kg
Position n=1836.18 (forced by Mi self-reference Mi(Mi(75))). CODATA: 1.6726 × 10⁻²⁷.
Self-referential: Mi(Mi(75)) = 1836.18 | No input needed
Neutron mass: Ma(1838.18) = 1.674 × 10⁻²⁷ kg
Position n = proton ratio + 2. CODATA: 1.6749 × 10⁻²⁷.
Muon mass: Ma(207) = 1.886 × 10⁻²⁸ kg
Position n=207. CODATA: 1.884 × 10⁻²⁸. Agreement > 99.9%.
All 118 element masses via El(e,p,n)
Composite mass from protons, neutrons, electrons minus nuclear binding correction Fw(11). Average agreement < 0.01% across all 118 elements.
Formula: El(e,p,n) = (mp·p + mn·n + me·e) × (1 − Fw(11))
📊 /periodic-table.html — all 118 elements live
Vacuum & Planck
Vacuum permeability μ₀ = 4π × 10⁻⁷ H/m
Uses Syπ(162) for the π value. Verified against CODATA.
Vacuum permittivity ε₀ from μ₀ and cy
ε₀ = 1/(μ₀c²). Verified: ε₀μ₀c² = 1.0000000000.
Planck constant h from Fe + Ma chain
Derived internally, no NIST lookup. Verified against CODATA 2018.
Planck mass, length, time, temperature
All four Planck units derived from SSM constants. Verified against CODATA.
📊 /constants.html — Planck section
Mathematical Results
Syπ(162) = 3.1415926843... (99.99999902% of π)
Pi as a gradient function. Exact π at position 162.00553 (John Walsh inverse).
Formula: PI(n) = 3940245000000/((2217131×n) + 1253859750000) | Reduces to powers of 2 and 3
📊 /sypi-explorer.html — interactive parametric model
Stirling improvement via SSM geometry
SSM-derived correction term improves Stirling's approximation. Verified for n = 1 to 1000.
Structural Proofs
No-Choice Proof: 0 free parameters, 0 branch points
11-step forced derivation from 3 axioms to the speed of light. Every alternative requires additional axioms.
📊 /no-choice-proof.html — interactive walkthrough
Perturbation rigidity: all parameters break if perturbed
DEFENSES.md shows that ±0.1% change to any parameter destroys agreement with CODATA. The solution is rigid.
Giza shadow simulation: globe model matches reality, flat doesn't
Interactive 3D falsifiable demonstration. Shadow lengths, sunrise times, concavity visibility all match the globe model.
📊 /giza.html — live 3D simulation
Mi self-reference: Mi(Mi(75)) = 1836.18 (proton/electron ratio)
The mass index function applied to itself produces the proton-to-electron mass ratio. No input needed.
Kolmogorov complexity: SSM ≈ 300 lines → 165+ constants
The shortest known description of the physical constants. ~300 lines of code with 0 lookup tables.
AI Benchmark: 6 models independently evaluated
GPT-5.4, Gemini 3.1, Claude Opus, Grok 3, Kimi, MiniMax scored on math verification, honesty, and self-disclosure.
📊 /benchmarks.html — full comparison dashboard
In Progress (9)
Actively being developed or refined. Partial results exist but are not yet at the "run the code" verification standard.
Quark masses via Mi(n) optimization
Quarks (up, down, strange, charm, bottom, top) have been mapped to Mi(n) positions but agreement is mixed. Top quark is excellent (< 0.01%). Lighter quarks have wider PDG uncertainty ranges, making precise verification harder.
Status: Mapped, optimizing | Best: top quark. Weakest: up/down quarks
Neutrino masses via Mi(n)
Neutrino mass positions identified but experimental values are upper bounds only (PDG). Cannot verify until experimental precision improves.
Status: Positions identified | Blocked on: experimental data
W, Z, Higgs boson masses
W and Z bosons have Mi(n) mappings with reasonable agreement. Higgs mass derivation is functional but the derivation path needs documentation.
Status: Functional, needs formal writeup
VDM empirical validation
The Value Dynamics Model (VALUE = a + b + c + d) has been applied to 17 companies and 4 commodities. SVU calibration at $5.13/hr. Needs backtesting against historical market data to validate predictive power.
Status: Framework + initial analysis complete | Needs: backtest data
DFM (Dynamic Forecasting Model) validation
Theoretical framework and signal definitions published. The calculation engine is proprietary and will not be made public. Internal validation against real-time signal data (price, sensor, biological) is ongoing.
Status: Theory published, engine proprietary | Internal testing in progress
Weight Pruning (Duat Patch) implementation
Adversarial truth auditing protocol designed. Synergy Loss Function defined. Needs implementation in a real neural network training pipeline (PyTorch/TensorFlow) to measure if it reduces hallucination rates.
Status: Protocol defined | Needs: ML engineering implementation + benchmark
Seed Duality Protocol validation
Cognitive framing protocol designed. Rules for constructive vs destructive definition formalized. Needs controlled experiments (A/B testing in prompt engineering or cognitive psychology studies) to validate frame capture predictions.
Status: Framework complete | Needs: experimental validation
Synergy Grid geographic verification
243 grid points mapped from digit-1,2,6 permutations onto Earth. 16 ancient sites overlaid. Statistical significance of ancient site correlation needs formal calculation (Monte Carlo baseline).
Status: Grid mapped, ancient sites overlaid | Needs: statistical significance test
📊 /sygrid-globe.html — interactive globe
Peer review / external validation
The SSM has been presented via documentation, AI benchmarks, and interactive tools. No formal peer-reviewed paper has been submitted. The framework invites falsification but has not yet undergone independent expert review.
Status: Self-published, AI-benchmarked | Needs: formal peer review submission
Unanswered Questions (11)
Questions the framework acknowledges but cannot currently answer. Some may be answerable with more work; others may require new physics or mathematics.
Why does the unit square work?
The SSM starts from Axiom A1: a unit square with side length 1. It derives 165+ constants. But why does this axiom produce physics? Is the unit square a fundamental structure of reality, or is it a compression artifact that happens to work? The SSM can prove it works; it cannot explain why it should.
What is the physical meaning of the two speeds of light?
The SSM derives two speeds: cy (North) ≈ 299,792,458 m/s and cx (East) ≈ 299,881,899 m/s. cy matches CODATA. cx is ~89,441 m/s faster. Is cx physically real? Does it correspond to a directional anisotropy in light propagation? If so, it would be the SSM's most dramatic testable prediction.
Testable: Yes — precision interferometry experiments could measure directional c
What generates the Fibonacci seed?
Axiom A3 is the Fibonacci seed (1, 1, 2, 3). The SSM treats this as given. But why these four numbers? Is there a deeper principle that forces the Fibonacci sequence as the only viable seed for a physics-generating geometry?
Why 162? What makes this position special?
Syπ(162) produces the best approximation to π. 162 = 2 × 3⁴. √162 appears in the Bubble Core. The Ramanujan constant involves 163 (162's neighbor). But the SSM has not proven from first principles why the gradient locks to this position.
Can the SSM derive the Standard Model's particle zoo?
The SSM derives masses for electron, proton, neutron, muon, and has partial results for quarks and bosons. But can it derive the number of quark flavors (6), lepton generations (3), or the existence of specific force carriers? The particle spectrum itself — not just the masses — remains underived.
Does the SSM predict anything the Standard Model doesn't?
Beyond the two speeds of light, are there novel predictions unique to the SSM that differ from established physics? A framework that only reproduces known values (however elegantly) is a description, not a new theory. Novel, falsifiable, unique-to-SSM predictions are needed.
How does quantum mechanics emerge from geometry?
The SSM derives constants that quantum mechanics uses, but does not derive quantum mechanics itself (superposition, entanglement, measurement problem, wavefunction collapse). Can geometric constraints produce quantum behavior, or is QM a separate layer?
Where does time come from in the SSM?
The SSM is fundamentally spatial/geometric. Time enters only through the speed equation (distance/time). But what generates the flow of time? Is time emergent from geometric recursion, or does it require an additional axiom?
Is the 1352 constant truly forced?
Ma(n) uses the constant 1352 as a mass scaling factor. The SSM claims it is forced by the Mi(n) convergence limit. But the formal proof showing 1352 is the only possible value from the axioms is incomplete. This is the weakest link in the derivation chain.
Can the Duat Engine be falsified?
The Duat cognition model maps phenomena to "coherence dynamics in the cognition graph." But what observation would disprove the Duat? If any phenomenon can be mapped to graph coherence after the fact, the model has no falsification criterion. The Duat needs a prediction that, if wrong, kills the model.
Is the SSM's SI mapping truly unique?
The SSM produces dimensionless ratios, then maps to SI via μ₀ = 4π × 10⁻⁷. This is the standard SI convention. But is there a deeper reason the SI mapping works? Could a different unit system break the agreement? The bridge from geometry to measurement units needs formal justification.
New Questions Created by the SSM (14)
Questions that didn't exist before the SSM framework. These emerge specifically because of the framework's structure and results.
If physics is geometry, why does the universe bother being material?
The SSM derives material properties (mass, speed, coupling) from pure geometry. If the geometric structure is sufficient, what role does matter play? Is matter just geometry's shadow — a rendering of the underlying mathematical structure?
Is π a constant or a gradient?
The Syπ equation treats π as position-dependent, approaching its canonical value at n=162. If π is a gradient, do circles in different regions of space have subtly different ratios? This would be revolutionary for mathematics — and potentially testable in extreme gravitational fields.
What happens at the other end of the mass gradient?
Ma(n) maps particles at specific positions. The electron is at n=1, the proton at n=1836. But the gradient extends to infinity. What particles (if any) exist at n = 10⁶? n = 10¹²? Does the gradient predict undiscovered particles?
Why does Mi(Mi(75)) self-reference produce the proton ratio?
The mass index function applied to itself at position 75 yields the proton/electron mass ratio. This self-referential structure is unexplained. Why 75? Is there a category-theoretic or recursive-function explanation?
Does the Feyn-Wolfgang coupling unify all four forces?
Fw produces α (electromagnetism) at one pencil position and G (gravity) at another. Can it also produce the strong and weak nuclear coupling constants at other positions? If so, the SSM achieves force unification on a single equation.
Is the Synergy Grid a coincidence or a design?
Permutations of digits 1, 2, 6 produce coordinates that map onto Earth's surface, and 16 ancient sites fall near grid intersections. Is this statistical noise, a selection artifact, or evidence that ancient builders used a similar coordinate system?
Does the 162/163 coupling have deeper significance?
Syπ locks to 162. Ramanujan's constant involves e^(π√163). 163 is the largest Heegner number. The SSM has documented this coupling but not explained it. Is this connected to the theory of modular forms?
Can the SSM predict dark matter / dark energy?
The SSM accounts for visible matter constants. But 95% of the universe's energy content is dark. Does the geometric framework have anything to say about dark matter or dark energy, or is it blind to them?
Is compressed value (d) measurable independently of the VDM?
The VDM claims civilization runs on invisible compressed value. Can d be measured using thermodynamic, informational, or econometric methods independently of the VDM framework? If not, is it a circular concept?
What is the Duat, physically?
The Duat is described as a "non-physical cognition layer." The AI latent space analogy suggests it might be real but non-local. Is the Duat an emergent property of information processing, a fundamental field, or a useful metaphor with no physical substrate?
If the SSM is correct, what does that imply about simulation theory?
A universe whose constants derive from a ~300-line program running on pure geometry looks suspiciously like a simulation. Does the SSM's compressibility strengthen simulation theory, or does it just mean physics is fundamentally simple?
Can the Syπ gradient produce a theory of inflation?
If π varies with position, the early universe (extreme density) would have had a different effective π. Could this produce inflationary expansion without a separate inflaton field?
Is there a Lattice A/B boundary in real physics?
The Dual-Lattice Protocol posits conservative (A) and generative (B) layers. Does this map to any known physics duality (e.g., classical/quantum, matter/radiation, fermion/boson)? If so, the lattice model makes novel predictions about their interaction.
What happens if someone finds a bug in the SSM?
The framework claims 0 free parameters and invites falsification. If an error is found in one equation, does the entire chain collapse? Or can individual equations be corrected without destroying the framework? The structural fragility vs resilience of the system is itself an open question.