ORT · Sing Boundaries · The Sing Constant 𝓢
ORT · Sing Boundaries by SK

ORT: Sing Boundaries

𝓚₊ = Singₘₐₓ (ρₘₐₓ)
≈ 3 × 10⁶⁶ kg/m³
𝓚₋ = Singₘᵢₙ (pₘᵢₙ)
≈ 1 × 10⁻⁵⁷ kg/m³
𝓢 = ρₘₐₓ / pₘᵢₙ
≈ 2⁴¹⁰ ≈ 2.64 × 10¹²³

The Sing Constant

Qₘₐₓ / Qₘᵢₙ = 𝓢^γ(Q),   𝓢 ≈ 10¹²³

where

  • Q is any physical quantity,
  • γ(Q) is the scaling exponent:
  • γ(Q) = 1 → Density
  • γ(Q) = 1/2 → Length, Time, Mass, Energy, Temperature, Velocity
  • γ(Q) = 1/4 → Quantum length/energy scales

ORT: The Sing Constant — General Law

Qₘₐₓ / Qₘᵢₙ = 𝓢^γ(Q) · N_eff^δ(Q),   𝓢 ≈ 10¹²³

Exponents

  • γ(Q)= 1 → Density
  • γ(Q)= 1/2 → Length, Time, Mass, Energy, Temperature, Velocity
  • γ(Q)= 1/4 → Quantum length / energy (single)
  • δ(Q) ≈ 1/2 → Collective states

Where

  • N_eff = 1 → single particle
  • N_eff > 1 → effective number of coherent particles (collective states: BECs, superconductors, etc.)

Pure ORT Derivations — 𝓢, 𝓚₊, 𝓚₋, alongside c and mₑ

ORT locks the minimum and maximum scales of physics: density, length, time, mass, energy, temperature, velocity and quantum object size.

  • Density: pₘᵢₙ ≈ 1 × 10⁻⁵⁷ kg/m³; ρₘₐₓ ≈ 3×10⁶⁶ kg/m³
  • Length: ℓₘᵢₙ ≈ 6.7×10⁻³³ m; ℓₘₐₓ ≈ 3.5×10²⁹ m
  • Time: tₘᵢₙ ≈ 2.2×10⁻⁴¹ s; tₘₐₓ ≈ 1.15×10²¹ s
  • Mass: Mₘᵢₙ ≈ 1.3×10⁻⁶¹ kg; Mₘₐₓ ≈ 6.5 kg
  • Energy: Eₘᵢₙ ≈ 1.1×10⁻⁴⁴ J; Eₘₐₓ ≈ 5.9×10¹⁷ J
  • Temperature: Tₘᵢₙ ≈ 8.3×10⁻²² K; Tₘₐₓ ≈ 4.3×10⁴⁰ K
  • Velocity: vₘᵢₙ ≈ 5.8×10⁻⁵⁴ m/s; vₘₐₓ = 3.0×10⁸ m/s
  • Quantum (single-object) scales: ℓ_Q ≈ 1.8×10⁻⁵ m (~18 μm); E_Q ≈ 1.8×10⁻³ eV

𝓢 locks all boundaries — no infinities, no zeros

English

The Sing Constant

There is only one true scale in the universe. None other can exist.

Through this scale the universe is designed — a single, absolute measure that governs all things, from the tiniest quanta to the vastest cosmic reaches. It is the universal scaffold built into the foundation of existence. All physics, all constants, and all boundaries arise from it.

𝓢 ≈ 2⁴¹⁰ ≈ 2.64 × 10¹²³

Sing Constant — timeless, exact, and absolute. It is the Key that unlocks every mystery and locks all truths into place. To make it understandable, we anchor it to the electron; in that translation, familiar constants c and h appear. Any civilization may choose a different anchor; the scale itself remains universal.

Burmese

The Sing Constant

စကြဝဠာတွင် မှန်သော အတိုင်းအတာ (Scale) တစ်ခုတည်းသာရှိသည်။ အခြားနောက်တစ်ခု မရှိနိုင်ပါ။

ဤတစ်ခုတည်းသော ပကတိအတိုင်းအတာ (Scale) အားဖြင့်သာ — အသေးငယ်ဆုံးကွမ်တာမှ စကြာဝဠာအာကာသကြီးအထိ အရာခပ်သိမ်းကို ပုံစံထုတ် တည်ဆောက် ထိန်းချုပ်ထားခြင်း ဖြစ်သည်။ ယင်းသည် ဖြစ်တည်မှု၏ အခြေခံအုတ်မြစ်တွင် ရေးထားသော စကြာဝဠာ ငြမ်း ဖြစ်သည်။ ရူပဗေဒအားလုံး၊ ကိန်းသေအားလုံးနှင့် ဘောင်အားလုံးသည် ၎င်းမှ ဖြစ်ပေါ်လာသည်။

𝓢 ≈ 2⁴¹⁰ ≈ 2.64 × 10¹²³

Sing Constant သည် ပကတိဖြစ်ပြီး အာကာသအချိန် တို့၏ အတိုင်းအတာအားလုံး၊ ဘောင်အားလုံးကို ကန့်သတ် ထိန်းချုပ် ထားသည်။ ၎င်းသည် လျှို့ဝှက်ဆန်းကြယ်မှုတိုင်းကို ဖွင့်ထုတ်သည့် သော့ ဖြစ်ပြီး အမှန်တရားအားလုံးကိုလဲ တည်မြဲအောင် သူ့နေရာနှင့်သူ ဘောင်ခတ်ပေးသော သော့လဲ ဖြစ်သည်။ လူသားများ နားလည်နိုင်စေရန် ဤအတိုင်းအတာကို လူသားယူနစ် အသွင်အဆောင်များဖြင့် ဖော်ပြထားသည်။ ဤနေရာတွင် ကျွန်ုပ်သည် ၎င်းအား အီလက်ထရွန်တွင် ချိတ်ဆွဲထားပြီး၊ ထိုဘာသာပြန်ဆိုမှုတွင်မှ ရင်းနှီးသော ကိန်းသေများ c နှင့် h ပါဝင်လာသည်။ အခြားနေရာများတွင် အခြားအသိစိတ်ရှိသက်ရှိများ ရှိပါက ၎င်းတို့သည် ကိုယ်ပိုင်အကိုးအကားများဖြင့် Sing Constant ကို ချိတ်ဆွဲနိုင်သော်လည်း၊ အတိုင်းအတာ၌ ပြောင်းလဲမှု မရှိပါ။

The Constant 𝓢 — Manifesto

  • No zeros. No infinities. Only real limits.
  • Locks all boundaries — nothing smaller, nothing greater.
  • Turns chaos into order by fixing every scale.
  • Makes the universe finite, calculable, complete.
  • The anchor of reality — the scale nothing escapes.
  • With 𝓢, physics has edges instead of paradoxes.
  • The constant that closes gaps and ends infinities.
  • Gives meaning to size, time, mass, and energy — all bounded.
  • The true scaffold of the universe.
  • 𝓢 doesn’t just forbid infinities — it builds the corridor of existence itself.

The Gradient Constant κ

κ(γ) = 2^(γ√3)

κ = 2^(√3) ≈ 3.314

  • γ = 1 → Density
  • γ = 1/2 → Length, Time, Mass, Energy, Temperature, Velocity
  • γ = 1/4 → Quantum single-object

Effective law

κ_eff = κ(γ) · (1 + Σ εᵢ)

Where κ(γ) = 2^(γ√3) is the straight slope; Σ εᵢ are tiny cross-corridor contributions (time, length, mass, energy, temperature, velocity, density, quantum).

Approximate values

  • k(1) ≈ 2^1.732 ≈ 3.314
  • k(1/2) ≈ 2^0.866 ≈ 1.825
  • k(1/4) ≈ 2^0.433 ≈ 1.351
  • k(0) ≈ 2^0 ≈ 1

Proton Lifetime

ORT

τₚ = K_d · S^(1/2) · ħ / (mₚ c²) S = 2^410 ≈ 2.64×10^123,   S^(1/2) ≈ 5.13×10^61 ħ / (mₚ c²) ≈ 7.0×10^-25 s K_d ≈ η_B^(-1/2),   η_B ≈ 6×10^-10 → K_d ≈ 4.1×10^4 ⇒ τₚ ≈ (4.1×10^4)(5.13×10^61)(7.0×10^-25) s ≈ 4.7×10^34 yr

Physics

τₚ ≈ M_X^4 / (α² mₚ^5) If M_X ≈ 10^15–10^16 GeV, α ≈ 10^-2 – 10^-1 ⇒ τₚ ≈ 10^34–10^36 yr

Observed

  • No proton decay detected
  • Experimental bound τₚ > 10^34 yr
Summary

ORT: τₚ ≈ 4.7×10^34 → effectively stable.
Physics: model-dependent 10^34–10^36 yr.
Observed: τₚ > 10^34 yr.

Derivation of the Speed of Light in ORT Flawless High Precision

In ORT, the speed of light is not assumed — it emerges from the Sing Constant S, the density corridor ρ, a particle anchor m, and the unity slope law κ. 1) Corridor Locks • Sing Constant: S = 2⁴¹⁰ = 2.6442238752 × 10¹²³ • Span law (γ = 1/2 corridor; equal L/T split): ℓₘₐₓ / ℓₘᵢₙ = tₘₐₓ / tₘᵢₙ = S¹ᐟ² = 5.1422017416 × 10⁶¹ • Electron anchor (for concreteness): mₑ = 9.1093837015 × 10⁻³¹ kg 2) Density Ceiling (two honest tracks) — Track A (SI-calibrated; uses vₘₐₓ): ρₘₐₓ = ( m⁴ (vₘₐₓ)³ / h³ ) · S¹ᐟ² ≈ 3.2794356547 × 10⁶⁶ kg/m³ (m = mₑ) — Track B (OPS primitive; speed-free): ρₘₐₓ = ( m / ℓ₀³ ) · S¹ᐟ² (no speeds) → vₘₐₓ = ℓ₀ / t₀ 3) Floors (independent primitives) • ℓₘᵢₙ = (mₑ / ρₘₐₓ)¹ᐟ³ = 6.5247412529 × 10⁻³³ m • tₘᵢₙ = ( mₑ⁵ᐟ³ / ( h · ρₘₐₓ²ᐟ³ ) ) · S¹ᐟ⁶ = 2.1764194124 × 10⁻⁴¹ s 4) Ceilings (by span) • ℓₘₐₓ = ℓₘᵢₙ · S¹ᐟ² = 3.3551535835 × 10²⁹ m • tₘₐₓ = tₘᵢₙ · S¹ᐟ² = 1.1191587693 × 10²¹ s (≈ 3.5464001360 × 10¹³ yr) 5) Geometric Means (span midpoint) • ℓ* = √(ℓₘᵢₙ · ℓₘₐₓ) = 4.6788362843 × 10⁻² m • t* = √(tₘᵢₙ · tₘₐₓ) = 1.5606917938 × 10⁻¹⁰ s • ℓ* / t* = 2.9979245800 × 10⁸ m/s ← emergent invariant slope vₘₐₓ 6) Direct Ratios (consistency checks) • ℓₘᵢₙ / tₘᵢₙ = 2.9979245800 × 10⁸ m/s • ℓₘₐₓ / tₘₐₓ = 2.9979245800 × 10⁸ m/s ⇒ floors = means = ceilings = vₘₐₓ 7) Span Consistency (γ = 1/2) ℓₘₐₓ / ℓₘᵢₙ = K_d,L · S¹ᐟ²; tₘₐₓ / tₘᵢₙ = K_d,T · S¹ᐟ² K_d,L = K_d,T = 1.0000000000 ⇒ √(K_d,L / K_d,T) = 1 8) κ-Law (unity corridor) L / T = κ(γ) · vₘₐₓ, κ(γ) = 2^(γ√3) At γ = 0 → κ(0) = 1 ⇒ L / T = vₘₐₓ 9) Results (one number, three ways) From means, floors, ceilings → vₘₐₓ = 2.9979245800 × 10⁸ m/s 10) SI Comparison (what “c” is here) c_SI = 299,792,458.0000000000 m/s (definition) vₘₐₓ (ORT numerics in SI) = 299,792,458.0000000000 m/s → exact closure 11) Anchor Invariance (mass cancels) Using Track B: ℓₘᵢₙ = ℓ₀, tₘᵢₙ = t₀, ρₘₐₓ = (m/ℓ₀³)·S¹ᐟ² → ℓ₀/t₀ = vₘₐₓ (independent of m) 12) What to remember • ORT fixes a unique invariant slope vₘₐₓ by corridor structure. • Floors, means, ceilings, κ-law all return the same value. • In SI, identify vₘₐₓ ≡ c. No tuning. No infinities. Pure ORT.

Anchor Invariance in ORT

Universal Speed of Light (vₘₐₓ) from Any Stable Anchor — electron, proton, neutrino, photon all reproduce the same invariant slope.

ρₘₐₓ(m) ∝ m⁴,   ℓₘᵢₙ(m) ∝ m⁻¹,   tₘᵢₙ(m) ∝ m⁻¹ → ℓₘᵢₙ/tₘᵢₙ = vₘₐₓ

Electron Anchor (baseline)

ρₘₐₓ(e) = 3.2794356547 × 10⁶⁶ kg/m³ ℓₘᵢₙ(e) = 6.5247412529 × 10⁻³³ m tₘᵢₙ(e) = 2.1764194124 × 10⁻⁴¹ s ℓₘₐₓ(e) = 3.3551535835 × 10²⁹ m tₘₐₓ(e) = 1.1191587693 × 10²¹ s ⇒ ℓ/t (floors = means = ceilings) = 2.9979245800 × 10⁸ m/s

Proton Anchor

rₚ = 1836.152673 ρₘₐₓ(p) = 3.7219516362 × 10⁷⁹ kg/m³ ℓₘᵢₙ(p) = 3.5539765173 × 10⁻³⁶ m tₘᵢₙ(p) = 1.1857698749 × 10⁻⁴⁴ s ℓₘₐₓ(p) = 1.8276475973 × 10²⁶ m tₘₐₓ(p) = 6.1014150113 × 10¹⁷ s ⇒ ℓ/t (floors = means = ceilings) = 2.9979245800 × 10⁸ m/s

Neutrino Anchor (Observed Bounds vs ORT Prediction)

(a) Experimental status

  • Oscillations → only mass differences.
  • Cosmology → Σ m_ν ≤ 0.12 eV, each m_ν ≤ 0.8 eV.
  • Absolute neutrino mass unknown.

(b) ORT Prediction

m_ν ≈ mₑ × 2⁻²⁵ × C_ORT
Case A — C_ORT = 0.2626575400 → m_ν ≈ 4 meV
mₑ = 9.1093837015 × 10⁻³¹ kg; 2⁻²⁵ = 2.9802322388 × 10⁻⁸; 1 eV/c² = 1.78266192 × 10⁻³⁶ kg m_ν = 7.1306476413 × 10⁻³⁹ kg → 3.9999999783 × 10⁻³ eV ≈ 4 meV r_ν = 7.8278046846 × 10⁻⁹ ρₘₐₓ(ν) = 1.2312862720 × 10³⁴ kg/m³ ℓₘᵢₙ(ν) = 8.3353398759 × 10⁻²⁵ m; tₘᵢₙ(ν) = 2.7803701039 × 10⁻³³ s ℓₘₐₓ(ν) = 4.2861999227 × 10³⁷ m; tₘₐₓ(ν) = 1.4297223990 × 10²⁹ s Means: ℓ* = 5.9772011119 × 10⁶ m; t* = 1.9937796807 × 10⁻² s Slopes (floors/means/ceilings) = 2.9979245800 × 10⁸ m/s
Case B — C_ORT = 0.0319000000 → m_ν ≈ 0.486 meV
m_ν = 8.6602371954 × 10⁻⁴⁰ kg → 4.8580367922 × 10⁻⁴ eV ≈ 0.486 meV r_ν = 9.5069408417 × 10⁻¹⁰ ρₘₐₓ(ν) = 2.6789356393 × 10³⁰ kg/m³ ℓₘᵢₙ(ν) = 6.8631343789 × 10⁻²⁴ m; tₘᵢₙ(ν) = 2.2892952093 × 10⁻³² s ℓₘₐₓ(ν) = 3.5291621556 × 10³⁸ m; tₘₐₓ(ν) = 1.1772017812 × 10³⁰ s Means: ℓ* = 4.9214951101 × 10⁷ m; t* = 1.6416340634 × 10⁻¹ s Slopes = 2.9979245800 × 10⁸ m/s

(c) Scaling + Triple-Check

ρₘₐₓ(ν) = ρₘₐₓ(e)·r_ν⁴; ℓₘᵢₙ(ν) = ℓₘᵢₙ(e)/r_ν; tₘᵢₙ(ν) = tₘᵢₙ(e)/r_ν → ℓ/t = 2.9979245800 × 10⁸ m/s

Photon Anchor (m = 0)

OPS corridor gives directly L/T = κ(0)·vₘₐₓ = vₘₐₓ. Photon worldlines lie on the null cone; for m = 0 the corridor collapses to that cone — vₘₐₓ is its fixed slope.

Final Result

Both C_ORT cases (0.2626575400 and 0.0319000000) satisfy ℓ/t = 2.9979245800 × 10⁸ m/s — the universal slope vₘₐₓ is invariant.