The Cohesion UFT is mechanics. Its constants are derived in closed form from a single axiom with no fitted parameters, its causal order is fixed, and one rule applies at every scale. This page states what the framework derives in the form applied work uses: what each quantity bounds, at what scale, with what value, at what standing, and where it is computed. No application is prescribed. A mechanical reader sees the uses the moment the constraint is on the page. For the doctrine, see Universal Mechanics; for what makes the framework executable, see Computable Mechanics; for the framework taught as a course, with the parameter sheet as Chapter 21 and the executed record, the derivation index and the open quantities as Appendices A–C, see the textbook, Cohesion Unified Field Theory: A Course in Computable Mechanics; to evaluate any quantity below, use the Calculator page.
The standard
Every quantity in the framework carries one of five standings, the standings the textbook assigns and this site uses. Derived: it follows by calculation from the axiom and established machinery with no input, and is reported with its residual against measurement. Closure: an identity evaluated with a measured input and returning it, exactly or to rounding, as E = pr at the electron and the MOND scale a₀ at the galactic transition. Identified: its numbers come from the standard account's own calculation with the framework supplying the reading, as the unification scale and coupling and the proton lifetime that follows from them. Stated: a relation the series states and uses whose derivation from the field equations is pending; the textbook indexes these in Appendix B. Open: named as open and left blank until it is derived; indexed in Appendix C. None is fitted. An applied reader who needs a value the framework has not yet derived will find it marked at its standing rather than supplied by adjustment, and can judge the framework by that.
The executed record
Each result below is computed live in the Research Calculator (the link resolves to the latest version) from a closed-form expression, with source paper, residual against observation, and standing. No entry was adjusted to match its observed value.
| Quantity | Computed | Observed | Standing | Source |
|---|---|---|---|---|
| Fine-structure constant, forward geometric chain | 1/α = 137.029 | 137.035999 | Derived; the +0.007 residual is identified as containing-scale pressure, not computed | Complete derivation; Photon–electron coupling |
| MOND acceleration scale a₀ = cH₀R(1+2R⁴)/6 | 1.379 × 10⁻¹⁰ m/s² (H₀ = 70) | 1.380 × 10⁻¹⁰ | Closure: R_trans = 0.748 is fixed by a₀ itself; the scale cH₀/6 and the transition location D_trans/D_GUT = 0.439 are the derived content | Identifying Dgal; Exact R(Dst); Calculator |
| Weinberg angle, SO(10) closure geometry | sin²θ_W = 3/8 at D_GUT; 0.2314 at m_Z from the standard relation with the measured couplings | 0.2312 (m_Z) | Derived at D_GUT; the low-energy value is the standard account's relation evaluated with measured inputs, not a running the framework performs | Weinberg angle |
| Muon mass, λ₁ = 3/(2α) | 105.04 MeV (−0.59%) | 105.66 MeV | Derived | Torsion interval scaling |
| Electron energy identity pr = m_e c² | exact (machine precision) | exact | Closure with unit coefficient | E = pr |
| Toggle threshold Φ_t = 32/(3π² − 4) | 1.249570 | — | Derived | Binary recursion toggle |
| Proton lifetime, p → e⁺π⁰ | τ_p ≈ 6 × 10³⁴ yr | > 1.6 × 10³⁴ yr (Super-K); Hyper-K reaches ~10³⁵ | Identified prediction, falsifiable: M_GUT ≈ 2 × 10¹⁶ GeV and α_GUT ≈ 1/25 come from the standard account's running with the framework's partner set | GUT scale and proton decay |
Derived quantities as design constraints
The same quantities, restated as constraints. Each row gives what the quantity bounds, its standing, and where it is derived and computed. The textbook's Chapter 21 carries the full parameter sheet.
| Quantity | Constrains | Standing | Source |
|---|---|---|---|
| E = pr — energy as pressure times recursion volume | Energy budget of any recursion structure at a stated volume; exact at the electron scale | Derived identity; its electron evaluation is a closure | E = pr; Calculator |
| I = p — inertia as local pressure | Resistance to displacement of a recursion volume; F = ma recovered as a limit | Derived | Inertia = Pressure |
| Torsion slope g = 6κ₆Ī^(3/2) and slip operator Δθ = 2g | Rate of torsion accumulation and angular release per cycle at the electron scale: g = 0.0041775 (ω = 1), Δθ = 0.478711° | Derived | Complete derivation; Calculator |
| Slip cadence t_coh = 2/g | Timing of recursion restart; propagation bound at the electron scale | Derived at the electron scale; open at fluid and macroscopic scales | Slip Acceleration; Calculator |
| Toggle threshold Φ_t = 1.249570 | Stability criterion between the n = 6 and n = 2 states | Derived | Binary recursion toggle; Calculator |
| R(D_st) — exact implicit solution | Propagation as a function of density ratio; no free parameters | Derived | Exact R(Dst); Calculator |
| a₀ = cH₀R(1+2R⁴)/6 | Acceleration floor below which inertial response saturates | Closure; the scale cH₀/6 and the transition location are derived, R_trans is fixed by a₀ | Identifying Dgal; Calculator |
| Displacement fraction δ = V_probe / V_target | Fraction of a target's field engaged by any measurement; equals the fine-structure constant for the photon–electron pair | Derived | The Measurement Problem |
| Switching energy of a torsion-phase bit | 2ħg at the slope and rate of the lattice that holds the bit; at the electron's rate, 2g m_e c² = 4.27 keV, it is the free recursion's gear-shift and not a device figure | Form derived; lattice slope open (the free-electron bound withdrawn) | The c-bit; Research Calculator, Version 6.5 |
| Rotation-curve law constants C_I, α, ρ₀, p | Galactic rotation profile | Open: not yet derived, and not fitted | Rotation-curve law |
The constraints by domain
The same record indexed by domain, so that a reader who works in one of them finds its quantities in its own vocabulary, with the applied-register results of the textbook's Chapters 19 and 22 added. Grouping by domain prescribes no application. Each entry carries its standing in the terms of the standard above, and the numbers are the ones the executed record and the parameter sheet carry.
| Domain | Quantities, with standings | Source |
|---|---|---|
| Devices and computing | Switching energy of a torsion-phase bit (the c-bit): 2ħg at the slope and rate of the lattice that holds the bit, held against the exchange energy per spin of a ferromagnet (0.01 to 1 eV; 90 meV at iron's Curie point); the form is derived and the lattice slope is open. The free-electron bound the c-bit paper first stated is withdrawn, since a single electron's spin flips at the millielectronvolt scale set by the field that holds it. Graphene lattice at the Dirac point: coherence interval ≈ 0.49 fs (2a/vF) and natural clock ≈ 647 THz (vF/2πa) from a = 0.246 nm and vF ≈ 10⁶ m/s, identified. Toggle threshold Φt = 1.249570 as the switching criterion between the n = 6 and n = 2 states, derived. | The c-bit; Graphene at the Dirac Point; Cohesion Computing; Binary recursion toggle |
| Fluids and turbulence | Reynolds number Re = UL/ν read as tν/tc, the ratio of the viscous diffusion time to the coherence time, with the onset of turbulence as the onset of slip and not of singularity, identified. Re-closure of a tightening vortex core at the slip cadence, with the cascade as the restart, derived. The cascade cutoff radius, which waits on the slip cadence at the fluid scale, open. | Vortex Closure |
| Environmental systems | Structural-coherence index Ψs(t) of a tropical cyclone: a constructed diagnostic with weights set by construction, recorded as such; applied to the Katrina best-track record at six-hourly resolution it placed the onset of cascade collapse at 29 August 00Z, six hours before landfall and before the collapse appeared in the wind record. | Tropical Cyclone Structural Integrity |
| Pulsing systems and timing | The toggle surface Φ = Φt of a pulsing object: the light cylinder RLC = cP/2π of a pulsar, the innermost stable orbit of a black hole, the convective envelope of a variable star, with the pulse as the toggle there and one toggle per rotation, identified; sub-pulse structure from cascade levels, stated; timing beyond the period waits on the slip cadence at that scale, open. | Pulsars and Pulsing Objects |
| Orbital mechanics | Lagrange points as coherence nodes at 60°, one hexapolar sector, with the stability ratio m₂/(m₁ + m₂) below about 1/25 read as the node-depth condition Φnode < Φt, identified; the ratio from Φt, open. Perihelion coefficient from the toggle condition (nκ)eff = 3 with two torque injections per orbit: Mercury 42.98″ per century against the measured 42.98″, derived; earlier records carried 42.92″ from a rounded input. A three-body stability classification, constructed. | Unipolar State, Lagrange Points, Tidal Locking; Perihelion Precession; Three-Body Stability Classification; Calculator (Module 19) |
| Low-acceleration dynamics | Acceleration floor a₀ = cH₀R(1 + 2R⁴)/6 = 1.379 × 10⁻¹⁰ m/s² at H₀ = 70, a closure, with the scale cH₀/6 and the transition location Dtrans/DGUT = 0.439 derived. Rotation-curve constant β = 0.235 pc/(km/s)², β⁻¹ = a₀ = 4.26 (km/s)²/pc, form derived and value stated against the SPARC median; the law's remaining constants CI, α, ρ₀, p, open. | Identifying Dgal; Rotation-curve law; Calculator |
| Energy, inertia and the electron-scale clock | E = pr and I = p, derived, with E = pr exact at the electron as a closure with unit coefficient. Torsion slope g = 0.0041775 and slip operator Δθ = 0.478711° at ω = 1, slip cadence tcoh = 2/g = 478.8 recursion units, mean restart rate ar = g²/ω = 1.745 × 10⁻⁵ per unit: derived at the electron scale, open at every other. Displacement fraction δ = Vprobe/Vtarget engaged by any measurement, equal to the fine-structure constant for the photon–electron pair, derived. | E = pr; Inertia = Pressure; Complete derivation; Slip Acceleration; The Measurement Problem |
| Particle physics | Fine-structure constant 1/α = 137.029 from the forward geometric chain, derived, with the +0.007 residual identified as containing-scale pressure. Weinberg angle sin²θW = 3/8 at DGUT, derived. Proton lifetime τp ≈ 6 × 10³⁴ yr for p → e⁺π⁰, an identified prediction within Hyper-Kamiokande's reach. | Complete derivation; Weinberg angle; GUT scale and proton decay |
Open quantities
The derivations below would extend the record and are named so that the direction is explicit. Each is a derivation to be done, not a value to be adjusted. The textbook's Appendix C indexes the open quantities in full, in four groups: the calibration of D_GUT, the slip cadence beyond the electron, the closure coefficients, and the rest.
- The slip cadence at fluid and macroscopic scales, which would fix the cutoff of the turbulent cascade. See Vortex Closure.
- The torsion slope at the lattice scale, which would fix the switching energy of a torsion-phase bit as 2ħg at the lattice's rate. See The c-bit.
- The rotation-curve law constants, which would open the galactic rotation test on the same no-fitted-parameters footing as the rest of the record. See Rotation-curve law.
- An independent condition of the galactic recursion fixing R_trans, which would make a₀ derived rather than closed. See Identifying Dgal.
- The absolute calibration of D_GUT, which would fix the inflation-onset and late-acceleration thresholds and the minimum propagation function R₀. See Exact R(Dst).
- The structural density of the observable domain at the largest scale, which the exact solution requires to differ between recombination and now by a factor of 1.614 if the two measured expansion rates are two points on R(D_st); the mean matter density over a fixed containing pressure returns 1/33 in place of the measured 1.083. See Exact R(Dst).
Seven of the open quantities — the structural density above, an independent condition fixing R_trans, the three-segment partition behind the closure count, the mode functions that must return the Weinberg angle at the electroweak density, the slip cadence at the fluid scale, the torsion-interval energy fraction, and the rotation-curve constants — are posed in full, with what is given, what is required, the target, what moves in the record, what the rule excludes and where the result is evaluated, in Problems for Derivation, together with the terms of submission, and their current standing is kept on the Open problems page. A derivation that meets the standard enters the series under its author's name.
Using the framework
The framework is a rule system and it executes. The Calculator page evaluates every derived quantity above in a browser, with each module linked to the paper it derives from. The same closed-form expressions run on edge hardware and inside a language model's context as a derivation the model can follow step by step. An extension of the framework to a system the series has not addressed is admitted on one condition, stated in Computable Mechanics and carried by the textbook's Chapter 20: it must be written as a chain from the pressure axiom, through the operator sequence — Tension → Surplus → Torsion → Slip → Acceleration → Maintained Motion — to a quantity the framework computes. Anything that does not end at a computed quantity is not a result of the framework. The calculator carries the standings of the record above on its modules, builds the closure count of one generation (Module 17), computes the targets the framework's own running must meet at the unification sector (Module 18), runs the perihelion chain from the toggle threshold to the figure per century (Module 19), and carries the seven open problems with their targets and the module where each is evaluated (Module 15); the programme the targets belong to is Closure at the Unification Density.
The full catalog is on the Series page. The conceptual map is on the Framework page. Common questions are answered on the FAQ page.