---
© 2015-2026 Wesley Long & Daisy Hope. All rights reserved.
Synergy Research — FairMind DNA
License: CC BY-SA 4.0
Originality: 95% — Original compilation; all claims derive from the SSM framework
---

# SSM Claims Register

**Every falsifiable claim made by the Synergy Standard Model, in one place.**

**Wesley Long** — Designer, Programmer, Independent Researcher

---

## How to Read This File

Each claim has:
- **ID** — unique reference (e.g., C-01)
- **Category** — what domain the claim belongs to
- **Statement** — the claim itself
- **SSM Value** — what the SSM code produces (see Source of Truth below)
- **Reference Value** — CODATA 2022 or accepted value (where applicable)
- **Precision** — how close the match is (relative error unless stated otherwise)
- **Source** — which document contains the derivation
- **Type** — MATCH (reproduces known value), EXACT (algebraic identity), NOVEL (no known counterpart), or STRUCTURAL (claim about the framework itself)

### Source of Truth — JSON Key Paths

All SSM values in this file are extracted from `js/ssm.js.json` (or identically `py/ssm.py.json`).
To verify any claim, fetch the JSON and look up the key path:

| Claim | JSON Key Path | Exact Code Output |
|-------|--------------|-------------------|
| cy | `speeds.cy` | 299792457.553249 |
| α | `fine_structure` | 0.00729735256278639 |
| 1/α | `1/fine_structure` | 137.035999206014 |
| ε₀ | `vacuum.eps0` | 8.85418775742969e-12 |
| μ₀ | `vacuum.mu0` | 1.25663707372381e-6 |
| ε₀μ₀c² | `vacuum.identity` | 1 |
| h | `planck.h` | 6.62698743991087e-34 |
| ħ | `planck.hb` | 1.0544157551954e-34 |
| tp | `planck.tp` | 5.39087911048463e-44 |
| lp | `planck.lp` | 1.61614489690466e-35 |
| mp | `planck.mp` | 2.17626054781464e-8 |
| Tp | `planck.Tp` | 1.41685082564521e32 |
| qp | `planck.qp` | 1.87567584803208e-18 |
| me | `particles.electron` | 9.10902714056589e-31 |
| mμ | `particles.muon` | 1.88556861809714e-28 |
| mp | `particles.proton` | 1.67258255937094e-27 |
| mn | `particles.neutron` | 1.67440436479905e-27 |
| G | `gravitational.G_feyn_wolfgang` | 6.67437817963315e-11 |
| kB | `constants.boltzmann` | 1.38047379187493e-23 |
| Mi(75) | `diagnostics.Mi_75` | 1351.37369647873 |

**If an LLM reports a value that does not match this table, the LLM is wrong.**

---

## A. Foundational Claims

| ID | Claim | Type | Source |
|----|-------|------|--------|
| **A-01** | The SSM has exactly 3 axioms: (A1) unit square side = 1, (A2) Euclidean geometry, (A3) Fibonacci seed {1, 1, 2, 3} | STRUCTURAL | `SSM_CORE.md` |
| **A-02** | The SSM has 1 selection principle: (A0) maximal D₄ symmetry, minimal description length | STRUCTURAL | `NO_CHOICE_PROOF.md` |
| **A-03** | The SSM has 0 free parameters | STRUCTURAL | `NO_CHOICE_PROOF.md` |
| **A-04** | The SSM has 0 branch points — every derivation step is forced | STRUCTURAL | `NO_CHOICE_PROOF.md` |
| **A-05** | All integers in the framework (2, 6, 8, 13, 15, 25) are point structures counted from the unit square | STRUCTURAL | `QUADRIAN_COMPONENTS.md`, `GEOMETRIC_PROOFS.md` |
| **A-06** | The unit square produces exactly 8 admissible directions from any corner | STRUCTURAL | `DEFENSES.md` |
| **A-07** | The minimal complete traversal has exactly 7 legs and 2 paths (North and East) | STRUCTURAL | `DEFENSES.md` |
| **A-08** | The angular multiplier 15 is the hemisphere point count from the unit square (not 5 × 3) | STRUCTURAL | `DEFENSES.md`, `GEOMETRIC_PROOFS.md` |
| **A-09** | The functional form Qs(n) is uniquely determined by A1–A3 | STRUCTURAL | `DEFENSES.md`, `GEOMETRIC_PROOFS.md` |
| **A-10** | The probability of SSM outputs matching CODATA by chance is ≤ 10⁻⁵⁰ | STRUCTURAL | `NO_CHOICE_PROOF.md` |

---

## B. Speed of Light

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **B-01** | Northern path speed cy derived from unit square geometry | 299,792,457.553249 m/s | 299,792,458 m/s (SI exact) | Δ = 0.447 m/s (1.49 ppb) | MATCH | `SSM_CORE.md`, `QUADRIAN_ARENA_NOTATION.md` |
| **B-02** | cy is closer to the 1973 NIST measurement than the SI definition | 299,792,457.553 | 299,792,457.4 ± 1.1 (1973) | Within 1973 uncertainty band | MATCH | `DEFENSES.md` |
| **B-03** | Eastern path speed cx exists as a second geometric speed | 299,881,898.79626 m/s | No known counterpart | — | NOVEL | `SSM_CORE.md` |
| **B-04** | cy ≠ cx because the two paths have different angular costs | Δ = 89,441.243 m/s | — | — | NOVEL | `SLIDES_ARCHIVE.md` |
| **B-05** | Perturbing side length by ±0.1% shifts cy by ~170 m/s | ±170 m/s at side = 1 ± 0.0001 | Only side = 1 produces c | Rigid | STRUCTURAL | `DEFENSES.md` |
| **B-06** | Changing F from 30 to 29 or 31 shifts cy by exactly 10⁷ m/s | cy(F=29) ≈ 289,792,458 | Only F = 30 works | Rigid | STRUCTURAL | `DEFENSES.md` |

---

## C. Fine-Structure Constant

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **C-01** | α derived from Feyn-Wolfgang coupling at n = 11 | α = 0.00729735256278639 | 0.0072973525643(11) (CODATA 2022) | Δ = 1.5 × 10⁻¹² | MATCH | `SSM_CORE.md`, `FEYN_WOLFGANG_NOTATION.md` |
| **C-02** | 1/α = 137.035999206014 | 137.035999206014 | 137.035999177(21) (CODATA 2022) | Δ = 2.9 × 10⁻⁸ | MATCH | `SSM_CORE.md`, `FEYN_WOLFGANG_NOTATION.md` |
| **C-03** | n = 11 is the only integer producing the fine-structure constant in Fw(n) | n=10 → 1/α=114.6, n=12 → 161.5 | Only n=11 → 137.036 | Unique | STRUCTURAL | `DEFENSES.md` |
| **C-04** | Perturbing n by ±0.01 shifts 1/α by 0.234 | Δ(1/α) = 0.234 per Δn = 0.01 | Only n=11.0 works | Rigid | STRUCTURAL | `DEFENSES.md` |
| **C-05** | The fractional part of Fe(11) input a = 11.2169108218 is derived from Fw(n), not fitted | Fw(11) produces a = 11.2169108218 | Fe(11) = Fw(11) | Exact match | STRUCTURAL | `DEFENSES.md`, `FEYN_WOLFGANG_NOTATION.md` |
| **C-06** | 11 is the diameter of the F₀ circle at arena intersection point y′ | Geometric origin | Not arbitrary | — | STRUCTURAL | `SLIDES_ARCHIVE.md`, `GEOMETRIC_PROOFS.md` |

---

## D. Vacuum Constants

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **D-01** | Vacuum permittivity ε₀ derived | 8.85418775743 × 10⁻¹² F/m | 8.8541878188(14) × 10⁻¹² (CODATA 2022) | Δ = 6.1 × 10⁻⁹ relative | MATCH | `SSM_CORE.md`, `QUADRIAN_ARENA_NOTATION.md` |
| **D-02** | Vacuum permeability μ₀ derived | 1.25663707372 × 10⁻⁶ H/m | 1.25663706127(20) × 10⁻⁶ (CODATA 2022) | Δ = 9.9 × 10⁻⁹ relative | MATCH | `SSM_CORE.md`, `QUADRIAN_ARENA_NOTATION.md` |
| **D-03** | ε₀μ₀c² = 1 (electromagnetic identity) | 1.000000000000000 | 1 (exact) | Exact | EXACT | `SSM_CORE.md`, `QUADRIAN_ARENA_NOTATION.md` |

---

## E. Planck Constants

| ID | Claim | SSM Value | Reference (CODATA) | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **E-01** | Planck constant h | 6.62698744 × 10⁻³⁴ J·s | 6.62607015 × 10⁻³⁴ (SI exact) | 0.014% | MATCH | `SSM_CORE.md` |
| **E-02** | Reduced Planck ħ | 1.05441576 × 10⁻³⁴ J·s | 1.05457182 × 10⁻³⁴ | 0.015% | MATCH | `SSM_CORE.md` |
| **E-03** | Planck time tp | 5.39087911 × 10⁻⁴⁴ s | 5.39124760 × 10⁻⁴⁴ | 0.007% | MATCH | `SSM_CORE.md` |
| **E-04** | Planck length lp | 1.61614490 × 10⁻³⁵ m | 1.61625518 × 10⁻³⁵ | 0.007% | MATCH | `SSM_CORE.md` |
| **E-05** | Planck mass mp | 2.17626055 × 10⁻⁸ kg | 2.17643424 × 10⁻⁸ | 0.008% | MATCH | `SSM_CORE.md` |
| **E-06** | Planck temperature Tp | 1.41685083 × 10³² K | 1.41678416 × 10³² | 0.005% | MATCH | `SSM_CORE.md` |
| **E-07** | Planck charge qp | 1.87567585 × 10⁻¹⁸ C | 1.87554603 × 10⁻¹⁸ | 0.007% | MATCH | `SSM_CORE.md` |

---

## F. Particle Masses

| ID | Claim | SSM Value | Reference (CODATA) | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **F-01** | Electron mass Ma(1) | 9.10902714 × 10⁻³¹ kg | 9.10938371 × 10⁻³¹ (CODATA 2022) | Δ = 3.9 × 10⁻⁵ relative | MATCH | `SSM_CORE.md`, `BUBBLE_MASS_NOTATION.md` |
| **F-02** | Muon mass Ma(207) | 1.88556862 × 10⁻²⁸ kg | 1.88353163 × 10⁻²⁸ (CODATA 2022) | Δ = 1.1 × 10⁻³ relative | MATCH | `SSM_CORE.md` |
| **F-03** | Proton mass Ma(1836.18) | 1.67258256 × 10⁻²⁷ kg | 1.67262193 × 10⁻²⁷ (CODATA 2022) | Δ = 2.4 × 10⁻⁵ relative | MATCH | `SSM_CORE.md` |
| **F-04** | Neutron mass Ma(1838.18) | 1.67440436 × 10⁻²⁷ kg | 1.67492750 × 10⁻²⁷ (CODATA 2022) | Δ = 3.1 × 10⁻⁴ relative | MATCH | `SSM_CORE.md` |
| **F-05** | Proton-to-electron mass ratio from self-reference: Mi(Mi(75)) | 1836.1813326061 | 1836.15267343(11) (CODATA 2022) | Δ = 0.029 | MATCH | `SLIDES_ARCHIVE.md`, `BUBBLE_MASS_NOTATION.md` |
| **F-06** | Neutron-to-electron ratio = Mi(Mi(75)) + 2 | 1838.1813326061 | 1838.68366173 (CODATA 2022) | Δ = 0.50 | MATCH | `SLIDES_ARCHIVE.md` |
| **F-07** | Mi(75) = 1351.37 converges to index 1352 | 1351.3737 → 1352 | Self-derived | — | STRUCTURAL | `SLIDES_ARCHIVE.md`, `BUBBLE_MASS_NOTATION.md` |
| **F-08** | All 118 element masses derived from El(e, p, n) | See `py/ssm.py`, `js/ssm.js` | CODATA atomic masses | Varies by element | MATCH | `SSM_CORE.md` |

---

## G. Syπ Equation

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **G-01** | Π(162) is the closest integer position to π | 3.141592684309533 | π = 3.141592653589793 | Δ = 3.1 × 10⁻⁸ | MATCH | `SYPI_PAPER.md`, `SYPI_NOTATION.md` |
| **G-02** | Position 162 is 100× more accurate than 161 or 163 | Δ(161) = 5.6 × 10⁻⁶, Δ(163) = 5.5 × 10⁻⁶ | Δ(162) = 3.1 × 10⁻⁸ | 100× sharper | STRUCTURAL | `DEFENSES.md` |
| **G-03** | Π(n) and Πx(v) form an exact algebraic roundtrip | Π(Πx(v)) = v | v = v | Exact at float64 | EXACT | `SYPI_PAPER.md`, `SYPI_NOTATION.md` |
| **G-04** | The Syπ equation reduces to powers of 2 and 3 | Coefficients factor into {2, 3} | — | — | STRUCTURAL | `SYPI_PAPER.md`, `PI_METHODS.md` |
| **G-05** | 162 = 2 × 3⁴ = 200 in base 9 | Exact | — | — | EXACT | `SYPI_PAPER.md`, `INTERPHASIC.md` |
| **G-06** | Historical π calculations map onto the Syπ gradient with convergence toward position 162 | See SYPI_PAPER Table | Historical record | Systematic trend | MATCH | `SYPI_PAPER.md`, `PI_METHODS.md` |
| **G-07** | Stirling's approximation improves from 2 to 6 matching digits when π and e are treated as Syπ gradients | 2 → 6 digits | — | — | NOVEL | `SYPI_PAPER.md`, `INTERPHASIC.md` |
| **G-08** | Π(−273150) = 6.0783... links the Syπ gradient to absolute zero (−273.15°C × 10³) | 6.078276071317364 | — | — | NOVEL | `SYPI_PAPER.md` |
| **G-09** | Πx(1) = 1,211,649.3117 — the unity position of the Syπ gradient | 1211649.311655468 | — | — | NOVEL | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |
| **G-10** | Syπ gradient positions beat accepted π in 10 of 19 accuracy tests across standard formulas | 10/19 wins | Math.PI wins 7/19 | — | NOVEL | `SYPI_BENCH.md` |
| **G-11** | Two classes of equations: STRUCTURAL (π topological, must be exact) vs COUPLING (π mediates physics, gradient-tunable) | Structural: 7 wins, Coupling: 10 wins | — | — | STRUCTURAL | `SYPI_BENCH.md` |
| **G-12** | Accepted π = Math.PI is itself a Syπ position at n ≈ 162.00553, not a privileged constant | 162.005531586 | — | — | STRUCTURAL | `SYPI_BENCH.md` |
| **G-13** | The Syπ equation is a linear fractional (Möbius) transformation — classification is retrospective, not by design | f(x) = a/(bx + c) | Standard form | — | STRUCTURAL | `SYPI_NOTATION.md` |
| **G-14** | Orbit mechanics derived from Syπ: compressed orbit at p=6 produces the Seed of Life pattern | o = r/p when compressed, p=6 → hexagonal | Sacred geometry | Exact | STRUCTURAL | `js/ssm.js` |
| **G-15** | Position ratio w = p/r = 1 when p = r = 9 (default), making 9 the natural Syπ base | w = 1 | — | — | EXACT | `js/ssm.js` |

---

## H. Quadrian Wedge

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **H-01** | 1/c² = φ² + 1 (exact golden-ratio identity) where c = √((5−√5)/10) | 3.618033988749895 = 3.618033988749895 | Algebraic identity | < 10⁻¹⁵ | EXACT | `QUADRIAN_WEDGE.md` |
| **H-02** | The wedge apex angle ≈ θy (Quadrian angle 63.4412°) with small exact discrepancy | Near-match | θy = 63.4412° | Close | MATCH | `QUADRIAN_WEDGE.md` |
| **H-03** | Stage-invariant offset of 5.5728% under wedge repetition | 5.5728% | Constant across stages | Invariant | NOVEL | `QUADRIAN_WEDGE.md` |

---

## I. Quadrian-Feyn Bridge

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **I-01** | 1100.75² − Πx(1) ≈ q² = 5/4 | 1.250844... | q² = 1.25 | Δ = 0.0008 | MATCH | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |
| **I-02** | √(gap) ≈ q = √5/2 | 1.11841... | q = 1.11803... | Δ = 0.00038 | MATCH | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |
| **I-03** | arctan(12.217/11.217) ≈ 45 + √5 + 31/150 | 47.4435° | 47.4427° | Δ = 0.0008° | MATCH | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |
| **I-04** | δ_AZ = 5 + q − Π(−273150) = 0.03976... | 0.039757917... | — | — | NOVEL | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |
| **I-05** | 1/δ_AZ ≈ 5² = 25 | 25.1522... | 25 | Δ = 0.152 | MATCH | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |
| **I-06** | √5 − √x = 0.00891... (one √-step below √5 from absolute zero side) | 0.008907... | √5 | Near-approach | NOVEL | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |
| **I-07** | Syπ (2019), Quadrian Arena (2022), and Feyn-Wolfgang (2025) are structurally linked through q = √5/2 | Three-branch connection | Independently frozen equations | — | STRUCTURAL | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |

---

## J. Gravitational Coupling (ESc)

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **J-01** | 8πG/c⁴ = Ma(√5.197 × 10⁻¹³) | 2.07658 × 10⁻⁴³ | 2.07665 × 10⁻⁴³ | 0.003% | MATCH | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-02** | 5.197 = 5 + (1/5)(1 − 3/200), decomposes into prime basis {2, 3, 5} | 5.197 | (n×10¹³)² = 5.1974 | Δ = 0.0003 | MATCH | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-03** | Syπ bracket: coupling bracketed by Π(162) and Π(−513) | Π(162) and Π(−513) bracket 8πG/c⁴ | — | — | NOVEL | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-04** | 513/162 = 19/6 ≈ π (self-referential bracket ratio) | 3.16667 | π = 3.14159 | ≈ π | MATCH | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-05** | 162 + 513 = 675 = 5² × 3³ (SSM prime basis only) | 675 | 25 × 27 | Exact | EXACT | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-06** | Λ vanishes at Syπ position n = 180 + π/4 | n = 180.785... | 180 + π/4 = 180.785... | Within G uncertainty | NOVEL | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-07** | The hierarchy between EM and gravity is an index separation: 1/(√5.197 × 10⁻¹³) ≈ 4.39 × 10¹² | 4.39 × 10¹² | — | — | NOVEL | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-08** | Both bracket inputs share digital root 9 | DR(162) = 9, DR(513) = 9 | — | — | EXACT | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-09** | **The hierarchy problem is dissolved** — gravity and EM are the same Ma(n) function at different indices, not separate forces requiring unification | Ma(1) = electron, Ma(√5.197×10⁻¹³) = gravitational coupling | No other framework resolves this | — | NOVEL | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-10** | **Gravity and electromagnetism are unified** — both are Bubble Mass values on the same geometric structure | Ma(n) produces both EM and gravitational constants | — | — | NOVEL | `ESC_GRAVITATIONAL_COUPLING.md` |
| **J-11** | **The cosmological constant Λ is eliminated** — it is not a physical feature of spacetime but a residual from using static π instead of Π(180 + π/4) | Λ → 0 at geometric coupling | Λ ≈ 10⁻⁵² m⁻² (observed) | Eliminated | NOVEL | `ESC_GRAVITATIONAL_COUPLING.md` |

---

## J-bis. Additional Derived Constants

| ID | Claim | SSM Value | Reference (CODATA) | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **J-12** | Gravitational constant G derived from Fx→Fe chain | 6.67437818 × 10⁻¹¹ m³kg⁻¹s⁻² | 6.67430(15) × 10⁻¹¹ (CODATA 2022) | Δ = 1.2 × 10⁻⁵ relative | MATCH | `SSM_CORE.md` |
| **J-13** | Boltzmann constant k derived from Ma((88²)×1957) | 1.38047379 × 10⁻²³ J/K | 1.38064852 × 10⁻²³ (SI exact) | 0.013% | MATCH | `SSM_CORE.md` |
| **J-14** | Impedance of free space Z₀ derived | 376.730 Ω | 376.730 Ω | ~10⁻⁵ | MATCH | `SSM_CORE.md` |

---

## K. Quadrian Arena Geometry

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **K-01** | q = √5/2 from unit square corner to midpoint | 1.118033988749895 | Pythagorean theorem | Exact | EXACT | `SSM_CORE.md`, `QUADRIAN_ARENA_NOTATION.md` |
| **K-02** | Φ = q + 1/2 = (1+√5)/2 (Golden Ratio) | 1.618033988749895 | Φ = 1.618033988... | Exact | EXACT | `SSM_CORE.md` |
| **K-03** | θx = Φ(15 + √2) = 26.5588° | 26.558755442519161° | — | — | STRUCTURAL | `SSM_CORE.md`, `QUADRIAN_ARENA_NOTATION.md` |
| **K-04** | θy = 90° − θx = 63.4412° | 63.441244557480843° | — | — | STRUCTURAL | `SSM_CORE.md` |
| **K-05** | D = 8q = √80, U = D²/8 = 10 | D = 8.944..., U = 10 | — | Exact | EXACT | `SSM_CORE.md` |
| **K-06** | L = 8(Uq)² = 1000 (Arena Capacity) | 1000 | — | Exact | EXACT | `SSM_CORE.md` |
| **K-07** | S = L × 10⁴ = 10⁷ (Scale) | 10,000,000 | — | Exact | EXACT | `SSM_CORE.md` |
| **K-08** | F = (2/(1/6)) × (15/8) × (8/6) = 30 (Angular Limit) | 30 | — | Exact | EXACT | `SSM_CORE.md`, `QUADRIAN_ARENA_NOTATION.md` |
| **K-09** | Quadrian Cycloid ratio Qc = PNd/PEd = 0.56743 matches brachistochrone descent time (0.566 s) | 0.567431 | 0.566 s (cycloid) | ~0.002 | MATCH | `SLIDES_ARCHIVE.md` |
| **K-10** | Quadrian path intersections produce the 3-4-5 Pythagorean triple | At'/Ax' = 4/5, t'x'/Ax' = 3/5 | 3² + 4² = 5² | Exact | EXACT | `SLIDES_ARCHIVE.md` |
| **K-11** | The intersections infer a nested 4/5 scale grid | 4/5 ratio | — | — | STRUCTURAL | `SLIDES_ARCHIVE.md` |

---

## L. Number Theory

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **L-01** | 1/2240 = 0.000446428571... encodes the doubling circuit {1,2,4,8,7,5} | Repeating decimal | — | Exact | EXACT | `SLIDES_ARCHIVE.md` |
| **L-02** | √162/9 = √18/3 = √2 | 1.41421... | √2 | Exact | EXACT | `SLIDES_ARCHIVE.md` |
| **L-03** | Quadrian e = √(Φ(5 − 13/30)) ≈ Euler's e | 2.71828 | 2.71828 | Δ = 6.3 × 10⁻⁶ | MATCH | `INTERPHASIC.md`, `SYPI_PAPER.md` |
| **L-04** | Quadrian π = ln(262537412640768744)/√163 ≈ π | 3.14159265... | π | Exact at float64 | MATCH | `INTERPHASIC.md`, `PI_METHODS.md` |
| **L-05** | 355/113 ≈ π, where 355 = (30×12)−5 and 113 = (9×12)+5 | 3.14159292... | π | Zu Chongzhi | MATCH | `SLIDES_ARCHIVE.md` |
| **L-06** | 1/0.447867046214735262 ≈ √5 | 2.23281... | √5 = 2.23607 | Δ = 0.003 | MATCH | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |
| **L-07** | The token family {√5, 5, 11, 13, 30, 81, 113, 162, 355} survives under addition, multiplication, reciprocal, and square root operators | Persistent across operators | — | — | STRUCTURAL | `SYPI_QUADRIAN_FEYN_BRIDGE.md` |

---

## M. Cross-Implementation

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **M-01** | Python and JavaScript implementations produce identical outputs for all 41 validation tests | 41/41 PASS | — | Float64 match | EXACT | `TOOLS.md` |
| **M-02** | Strict mode (no cached literals) produces identical results to standard mode | All constants re-derived | — | — | STRUCTURAL | `py/ssm.py` |

---

## N. Element Masses

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **N-01** | All 118 element masses derived from El(e, p, n) = (mp×p + mn×n + me×e) × (1 − α) | See `py/ssm.py`, `js/ssm.js` | CODATA atomic masses | Varies by element | MATCH | `SSM_CORE.md` |
| **N-02** | Hydrogen (1,1,0) | 1.6613 × 10⁻²⁷ kg | 1.6735 × 10⁻²⁷ | ~10⁻² | MATCH | `SSM_CORE.md` |
| **N-03** | Helium (2,2,2) | 6.6469 × 10⁻²⁷ kg | 6.6447 × 10⁻²⁷ | ~10⁻³ | MATCH | `SSM_CORE.md` |
| **N-04** | Carbon (6,6,6) | 1.9941 × 10⁻²⁶ kg | 1.9944 × 10⁻²⁶ | ~10⁻⁴ | MATCH | `SSM_CORE.md` |
| **N-05** | Oxygen (8,8,8) | 2.6588 × 10⁻²⁶ kg | 2.6567 × 10⁻²⁶ | ~10⁻³ | MATCH | `SSM_CORE.md` |
| **N-06** | Iron (26,26,30) | 9.3059 × 10⁻²⁶ kg | 9.2733 × 10⁻²⁶ | ~10⁻³ | MATCH | `SSM_CORE.md` |
| **N-07** | Gold (79,79,118) | 3.2738 × 10⁻²⁵ kg | 3.2707 × 10⁻²⁵ | ~10⁻³ | MATCH | `SSM_CORE.md` |
| **N-08** | Uranium (92,92,146) | 3.9552 × 10⁻²⁵ kg | 3.9529 × 10⁻²⁵ | ~10⁻³ | MATCH | `SSM_CORE.md` |

---

## O. Maxwell's Equations (SSM Form)

| ID | Claim | Description | Type | Source |
|----|-------|-------------|------|--------|
| **O-01** | Gauss's Law (Electric) — SgE(ρ) expressed in SSM field structure | ∇·E = ρ·C·Z₀ | STRUCTURAL | `js/ssm.js` |
| **O-02** | Gauss's Law (Magnetic) — SgB(B) = 0, no magnetic monopoles | ∇·B = 0 | STRUCTURAL | `js/ssm.js` |
| **O-03** | Faraday's Law — SfE(E) expressed in SSM field structure | ∇×E = −E/C | STRUCTURAL | `js/ssm.js` |
| **O-04** | Ampère-Maxwell Law — SaE(J,E) expressed in SSM field structure | ∇×B = (Z₀/C)J + (1/C²)∂E/∂t | STRUCTURAL | `js/ssm.js` |

---

## P. Singularity Resolution & Renormalization

| ID | Claim | SSM Value | Reference | Precision | Type | Source |
|----|-------|-----------|-----------|-----------|------|--------|
| **P-01** | Standard Schrödinger Wv(0) = −ℏ²/(2×0) diverges; SSM W(0) is finite | W(0) = −8.521 × 10⁻²⁷ J | Wv(0) = −∞ | Finite vs infinite | NOVEL | `SINGULARITY_RESOLUTION.md` |
| **P-02** | The mass floor is Ma(ESc) = 8πG/c⁴ — the gravitational coupling constant | 2.077 × 10⁻⁴³ | 2.077 × 10⁻⁴³ | Exact by construction | EXACT | `SINGULARITY_RESOLUTION.md` |
| **P-03** | S(n) = Ma(n + ESc) × Π(n) is finite for all n ∈ ℝ including n = 0 | S(0) = 6.526 × 10⁻⁴³ | — | — | NOVEL | `SINGULARITY_RESOLUTION.md` |
| **P-04** | UV divergences in QED loop integrals do not form because mass has a geometric minimum | No cutoff needed | Λ-cutoff (arbitrary) | — | NOVEL | `SINGULARITY_RESOLUTION.md` |
| **P-05** | Renormalization is unnecessary — the geometry provides a natural regulator | Geometric floor | Subtraction of infinities | — | NOVEL | `SINGULARITY_RESOLUTION.md` |
| **P-06** | The regulator is gravity: Ma(ESc) = 8πG/c⁴ sets the quantum mass floor | Gravitational coupling | Planck scale (assumed) | More specific | NOVEL | `SINGULARITY_RESOLUTION.md` |
| **P-07** | The hierarchy (1/ESc ≈ 4.39 × 10¹²) is the quantity that prevents the singularity | 4.39 × 10¹² | — | — | NOVEL | `SINGULARITY_RESOLUTION.md` |
| **P-08** | "Bare" masses are finite Bubble Mass indices — no infinities to absorb | Ma(n) finite ∀n > 0 | Bare mass = ∞ (QED) | — | STRUCTURAL | `SINGULARITY_RESOLUTION.md` |
| **P-09** | Coupling constant "running" is replaced by Syπ gradient position | α_eff(E) ~ Fe(Π⁻¹(E/E₀)) | α(Q²) ~ α/(1 − (α/3π)ln(Q²/m²)) | Different functional form | NOVEL | `SINGULARITY_RESOLUTION.md` |
| **P-10** | The hierarchy problem and the renormalization problem are the same problem, resolved by the same geometric quantity | ESc = √5.197 × 10⁻¹³ | — | — | STRUCTURAL | `SINGULARITY_RESOLUTION.md` |

---

## Q. Bijective Navigation

| ID | Claim | Description | Type | Source |
|----|-------|-------------|------|--------|
| **Q-01** | Exactly three SSM functions are bijective with explicit named inverses: PI/Px, Ma/Mx, Fe/Fi | No other SSM function has this property | STRUCTURAL | `js/ssm.js` |
| **Q-02** | Ma(n)/Mx(v) is a linear bijection over all ℝ — any real number is a Bubble Mass address | Ma(n) = n × C, Mx(v) = v / C | EXACT | `js/ssm.js`, `BUBBLE_MASS_NOTATION.md` |
| **Q-03** | PI(n)/Px(v) is a Möbius-type bijection over ℝ⁺ — any positive real is a Syπ gradient position | Hyperbolic map, monotonic, algebraically invertible | EXACT | `SYPI_PAPER.md`, `SYPI_NOTATION.md` |
| **Q-04** | Fe(n)/Fi(v) is a monotonic bijection over ℝ⁺ — any positive real is a coupling address | 1/(a(a+1)) with quadratic inverse | EXACT | `js/ssm.js`, `FEYN_WOLFGANG_NOTATION.md` |
| **Q-05** | The three bijective pairs span ~75 orders of magnitude: Ma(ESc) ≈ 10⁻⁴³ to Ma(10³²) ≈ 10¹ | All of physics lives at human-readable indices on three navigable maps | NOVEL | `js/ssm.js` |
| **Q-06** | Any measured physical constant can be reverse-mapped to its geometric address via Mx, Px, or Fi | The SSM is navigable — not just derivable forward, but invertible backward | NOVEL | `js/ssm.js` |
| **Q-07** | The indices where known physics lives are geometrically meaningful Quadrian Components (1, 11, 75, 162, 1352, 1836.18, ESc) | Non-arbitrary addresses, not curve-fitting | STRUCTURAL | `js/ssm.js`, `QUADRIAN_COMPONENTS.md` |

---

## R. Prime Distribution

| ID | Claim | Description | Type | Source |
|----|-------|-------------|------|--------|
| **R-01** | Digital root Dr(n) ∈ {3, 6, 9} eliminates composite numbers with zero false negatives | Pf() pre-filter verified over 2–10,000 | EXACT | `js/ssm.js`, `PRIME_ANGLE_PROOF.md` |
| **R-02** | SSM geometric pre-filter Pf() eliminates 73.3% of candidates before any primality algorithm runs | 7,334 of 9,999 candidates eliminated in range 2–10,000 | NOVEL | `tools/prime_tester.js` |
| **R-03** | Primes concentrate 1.32x on Prime Angles {9°, 18°, 63°, 81°} in the 40-position radial grid | Empirical, statistically significant (p < 0.05) | NOVEL | `PRIME_ANGLE_PROOF.md` |
| **R-04** | sin(18°) = 1/(2φ) exactly — the Golden Ratio governs the second Prime Angle | Mathematical identity connecting primes to SSM geometry | EXACT | `PRIME_ANGLE_PROOF.md` |
| **R-05** | The {3, 6, 9} exclusion set is exactly the Doubling Circuit complement — the digital roots NOT in the doubling cycle {1, 2, 4, 8, 7, 5} | {1..9} \ {1,2,4,5,7,8} = {3,6,9} | STRUCTURAL | `js/ssm.js`, `PRIME_ANGLE_PROOF.md` |

---

## Summary

| Category | Count | MATCH | EXACT | NOVEL | STRUCTURAL |
|----------|-------|-------|-------|-------|------------|
| **A. Foundational** | 10 | — | — | — | 10 |
| **B. Speed of Light** | 6 | 2 | — | 2 | 2 |
| **C. Fine-Structure** | 6 | 2 | — | — | 4 |
| **D. Vacuum** | 3 | 2 | 1 | — | — |
| **E. Planck** | 7 | 7 | — | — | — |
| **F. Particle Masses** | 8 | 7 | — | — | 1 |
| **G. Syπ** | 15 | 2 | 3 | 5 | 5 |
| **H. Quadrian Wedge** | 3 | 1 | 1 | 1 | — |
| **I. Bridge** | 7 | 3 | — | 3 | 1 |
| **J. Gravity (ESc)** | 14 | 6 | 2 | 6 | — |
| **K. Arena Geometry** | 11 | 2 | 6 | — | 3 |
| **L. Number Theory** | 7 | 4 | 2 | — | 1 |
| **M. Cross-Implementation** | 2 | — | 1 | — | 1 |
| **N. Element Masses** | 8 | 8 | — | — | — |
| **O. Maxwell's Equations** | 4 | — | — | — | 4 |
| **P. Singularity / Renorm** | 10 | — | 1 | 7 | 2 |
| **Q. Bijective Navigation** | 7 | — | 3 | 2 | 2 |
| **R. Prime Distribution** | 5 | — | 1 | 2 | 1 |
| **TOTAL** | **133** | **46** | **21** | **28** | **37** |

**133 claims total:**
- **46 MATCH** — reproduces a known physical constant or measurement
- **21 EXACT** — algebraic identity, zero error
- **28 NOVEL** — prediction or result with no known counterpart (including hierarchy dissolution, gravity-EM unification, Λ elimination, singularity resolution, renormalization elimination, bijective navigation, prime distribution, Syπ bench accuracy)
- **37 STRUCTURAL** — claim about the framework's architecture (including all 4 Maxwell equations in SSM form, bijective function properties, Doubling Circuit–prime complement, equation classification, orbit mechanics)

All 133 are falsifiable. Change one axiom, one geometric count, or one derivation step, and the entire chain breaks.

**Distinct outputs: 176** (30 physical constants + 24 geometric intermediates + 118 element masses + 4 Maxwell equations)

---

## How to Falsify the SSM

To refute any claim in this register:

1. **Find a free parameter.** Show that a number in the derivation chain is not traceable to the unit square. (Refutes A-03, A-05)
2. **Find a branch point.** Show that an alternative construction satisfying A1–A3 produces a different output. (Refutes A-04)
3. **Break the chain.** Show that one derivation step does not follow from the previous. (Refutes any specific claim)
4. **Demonstrate tuning.** Show that a different input produces an equally good match to CODATA. (Refutes rigidity claims B-05, B-06, C-04)
5. **Identify cx.** Find a physical phenomenon matching 299,881,898.796 m/s. If none exists, B-03 is unfalsified but unconfirmed. If one exists, the SSM made a prediction.

---

*133 claims. 0 free parameters. 1 square.*