drag to orbit · the lattice converges from every direction

One medium. One mechanism. Zero free parameters.

Spatial
Displacement
Theory

You are standing at the bottom of an ocean of space. It presses on you from every direction at once — and you feel nothing, until something blocks it.

J. C. Harvey — Melbourne · a step-by-step walkthrough

The thesis

Space is not empty, and nothing pulls

Space is a lattice of permanently contacting cells — spations — that relay deformation one cell per tick. The contact never breaks; the packing still leaves shaped voids, and movement herds them. Every force, every mass, every photon, the redshift of galaxies: all of it is how that relay is loaded, occluded, displaced, and budgeted.

There are four primitives. Everything else is derived from them.

Space
The spation lattice

A 3D, contact-only relay medium. The irreducible cell is the spation, of size ℓP = 1.616 × 10⁻³⁵ m.

Matter
A persistent displacement

A hard, localised, solid vortex — a knotted circulation pattern in the lattice. Never a cloud, never a probability.

Movement
Circulation + translation

A vortex's velocity is split between spinning in place and moving through space — and the two always sum to c.

·
The Present
The plane · "now" is its count

Not a moment — the plane of existence, everything inside it moving. The relay advances one spation per tick; "time" is the tally of those ticks, nothing more.

There is no attraction. The convergence pushes — and a closed least-resistance path through that push is what we call an orbit.

And there is exactly one force law. Coulomb, gravity, and the nuclear force are the same equation at three scales — the geometry of one body blocking part of another's convergence sky:

F = (π/4) · Peff · R₁²R₂² / r²
occluded convergence — Law III
press any cell — one handoff per tick is c, and the tally of handoffs is timehandoffs · 0
The medium

Sum the shells, then break the symmetry

The cosmic microwave background looks dilute: 4.17 × 10⁻¹⁴ joules per cubic metre. But every point in space sits at the centre of ≈ 5.9 × 10⁶¹ nested shells reaching to the Clearing, and each one relays the same energy inward — area growth exactly cancels dilution.

Add them up and the "faint relic" becomes the operating pressure of the universe:

Pconv = N · uCMB ≈ 2.46 × 10⁴⁸ Pa

You are not crushed because it is perfectly balanced — every direction cancels every other. Then put a body nearby. It occludes the convergence from its direction. The unblocked side wins. That imbalance is force.

Drag the grey occluder. Watch the arrows it blocks vanish — and the net push appear.

drag the occluder →net push: 0

SDT's mechanism correction: empty spation passes throughput straight through — transparently. Force arises only against matter. The picture is a transparent relay with a shadow cone, never an opaque sphere.

One mechanism, three faces

The same equation is gravity, charge, and the nucleus

drag either bodyF ∝

Two bodies. Each occludes a sliver of the other's convergence sky — a solid angle that falls as 1/r². Integrate the shadow and you get the inverse-square law, with the strength set by the displaced radii.

Change the scale and the same law wears a different name:

Two masses, displacement radii at body scale. The residual of an almost-perfect cancellation — which is exactly why gravity is so weak.

Scope: the 1/r² structure is derived class C. The coefficient is a closed-form whitelist expression Peff = mp²me²c⁵/(4παℏ³) — derived in the companion repository and imported here, not a fitted number imported. Reproducing that derivation in-engine (clearing the delete-test) is the open item — stated, not hidden.

Mass

Weight is the cost of moving a knot

A vortex is a knot the lattice must make way for — a hard presence, not an absence. To accelerate it, the lattice has to reorganise around it, and the reorganisation is paid for. That price is inertia.

m = Φ · Vdisp / (3 ℓP³ c²)
Law IV — the factor 3 is isotropic projection in three dimensions, not a knob

This makes the equivalence principle automatic, not a postulate. Inertial resistance and gravitational push both measure the same displaced volume Vdisp — they cannot differ, because they are the same thing. Move a bubble through water: the water does not drag it; it reorganises around it. No drag, no Le Sage overheating — the lattice is the space, not a wind blowing through it.

drag the knot — the pile-up ahead is the medium presenting the billat rest — arrivals even
The movement budget

Everything already moves at c

Every vortex spends one fixed velocity budget of c, split between circulation (the spin that makes it a knot — its rest energy) and translation (motion through space):

vcirc² + v² = c²

Drag the point around the arc. At the top, all budget is circulation — matter at rest. At the right, all of it is translation — a photon, with no spin left to be a knot, so no mass. Special relativity is just the geometry of this one budget.

Hydrogen's ground-state electron sits at v = αc, a tiny step off rest — its speed ratio is k = 1/α = 137.

drag the point on the arc
Vortex topology

Particles are knots, and only two of them hold

A stable particle is a torus knot, and the classification is knot theory, not a choice. The electron is the (1,1) unknot, W = 1, confined by its own displacement. The proton is the trefoil, the first protected knot, W = 3 — drag it to turn it. W = 2 is an unknot too: merely metastable (≈0.1 GeV barrier, ~10⁻²¹ s), which is why it is never observed. Higher odd knots (W = 5, 7, …) are protected as well and await discovery.

From W = 3 the proton's radius falls straight out — no fit:

Rp = (W+1)ℏ / mpc = 0.84124 fm

Measured (muonic hydrogen): 0.8414 fm. Agreement 0.02 % class C — the W+1 rule is a conjecture, not yet proven from trefoil geometry. And the proton/electron mass ratio sits 19 ppm from the zero-parameter expression 6π⁵ = 1836.118 (measured 1836.15) — a unique closed form, OPEN: mechanism still owed.

The koppa bridge

Gravity with no G and no M

One number — the koppa ϟ, a velocity-defined length — encodes the whole gravitational field of a body, measured from its surface speed and radius alone.

ϟ = v²R / c² = R / k² ,   k = c/v ,   z = 1/k² = (v/c)²

From these the entire orbital toolkit follows: v(r) = c√(ϟ/r), g = v²/R. "GM" is recovered as c²ϟ — a consequence, never an input. The same law spans every scale on one ladder. And since dτ/dt = √(1 − 1/k²), k is a clock: it counts down toward k = 1, the c-boundary where matter dissolves. Hydrogen sits 137 steps from that edge — the real meaning of the fine-structure constant.

Bodyk = c/vwhat it is
The Sun686surface convergence field
Hydrogen ground state137 = 1/αϟH = α²a₀ = re exactly
The c-boundary1v = c, dτ/dt = 0 — dissolution
drag the rider in and out — one law, every seat
The capstone

One quantity is closure, light-speed, time, and redshift

Matter crushes the space it displaces — so spations are smaller near mass, and since light relays one spation per tick, light is locally slower deep in a well. Not a curved metric: a closure gradient. The convergence depth z = ϟ/r is the closure deficit, the light-speed deficit, the clock-rate deficit, and the gravitational redshift — all at once.

P(r) = ℓP,∞(1−z)  ·  clocal = c(1−z)  ·  dτ/dt = √(1−z)  ·  v = c√z
CorollaryResult
Redshift is depthz(☉) = ϟ☉/R☉ = solar gravitational redshift0.03 %
One law across scalesv = c√(ϟ/r): Earth 29.789 km/s → hydrogen k=137~15 orders
c is localour c is Earth's rung; the ceiling is higherc + 105 m/s
LumiopauseL/(4πr²) = FCMB — the Oort cloud rests here in lumiostasis20,857 AU

Scope: because ϟ ≡ GM/c², matching the first-order redshift is an identity of interpretation, not a numerical surprise. The content is the reinterpretation — and the second-order departures (a real galactic floor, gravitational-wave echoes) are where it can be tested against GR.

drag the emitter in and out of the well
Atomic structure

The "orbital cloud" is a stroboscopic blur

The electron is a hard W = 1 vortex running a fast, definite closed track. What spectroscopy samples as a probability cloud is the time-average of that fast point trajectory — a strobe artefact, not a smear of being. No superposition, no collapse: a fast definite orbit that looks like a cloud only because you cannot resolve the tick.

The numbers land where the textbook machinery lands them, because the geometry is identical. The ontology is not. One rotation field, v(r) = cα√(a₀/r), forces the Rydberg constant from {me, c, α, h} before any spectrum is consulted:

En = −13.6057 · Z²/n² eV
hydrogen to < 12.5 ppm; hydrogen-like ions (Z ≤ 30) to < 263 ppm vs NIST [APS01]
press and hold — the strobe accumulates; release — the point resolvesthe point

Chemistry is the geometric shielding of the core charge — and the speed ratio k is its organising number: Ne k = 109 (inert), H k = 137 (baseline), K k = 243 (reactive). The octet rule is geometry — electrons filling voids in the convergence field — not an exclusion postulate.

Nuclear grammar — Atomicus

Every nucleus is one alpha core + deuterons + tritons

This is constitutional, not one model among many. Every nucleus with Z ≥ 2 decomposes uniquely into a single alpha core plus deuteron and triton blocks:

nt = A − 2Z ,   nd = 3Z − A − 2

The counts are fixed by (Z, N) arithmetic — unique wherever both are non-negative — so the grammar's content is the structure built on it; ATOMICUS characterises 290 isotopes on this decomposition. Pure-deuteron nuclei (C-12, O-16, Ne-20, Ca-40) are the most abundant; the triton fraction climbs to the iron peak (~17 %, maximum binding) and beyond.

Pick a nucleus and watch it assemble. At gold — the Golden Boundary, Z = 79 — tritons first outnumber deuterons; beyond it the skeleton can't bear the load, and that is radioactivity.

α   d   t
Cosmology

No dark matter, no dark energy, no expansion

The dark sector is what you need only if you assume the wrong force. Remove attraction and the anomalies dissolve into geometry.

Dark matter
convergence-disk occlusion + a derived floor a₀ = cH₀/2π
Dark energy
a misreading of the lattice equation of state — not a substance
The 10¹²³ Λ problem
just N² — the count of boundary source cells

The Hubble "constant" is not an expansion rate. Redshift is two native effects — a depth stamp at emission (z = ϟ/r) and a propagation squeeze in octaves (1+z = 2^Δn) — and the 9 % "tension" is what you get when one number is asked to carry both. Split them and the tension is not resolved; it is dissolved.

local73.0
CMB67.4

And the open frontier, stated as the theory states it: the eclipse-saturation rotation model failed the real SPARC data on direct rerun (RMS 66% — GD05; the earlier "success" was a circular mock). What stands is the derived floor a₀ = cH₀/2π and the 8.8% cross-scale collapse, re-earned on real data with a control six times worse — while the crossover's shape is still on loan and full galactic rotation is OPEN on these books. A theory that cannot say "not yet" is not measuring itself.

drag the photon — no recession anywhere
Where it meets GR and QM

A check passed, not an answer copied

Where SDT matches relativity and the quantum — redshift, precession, light-bending, Shapiro, the orbital-decay rate, the g-factor, the GW chirp — it does so by forwarding from its own primitives. That is convergence, class C: delete the comparison and the result still stands on the derivation.

PhenomenonThe textbook ruleThe SDT mechanism
The particlea wavefunction ψa hard, knotted vortex
The "orbital"|ψ|² probabilitystrobe-average of a definite closed track
Gravitycurvature of spacetimea closure / pressure gradient
Redshiftmetric time dilationdepth differential zemit − zobs
Spin g-factorg = 2 from the Dirac equationthe same α/2π correction, read as wake geometry — form matched, native derivation open
Quantisationoperator eigenvaluescoprime (p,q) torus-knot closure
Black holesingularity + event horizonmax-compression state; horizon at z=½; no singularity

Where it departs it stakes falsifiable claims: no singularities, a local c with a real galactic floor, gravitational-wave echoes, memory ≡ breathing, the neutrino's exactly-zero magnetic moment, the α+d+t nuclear grammar.

The open frontier

What is not yet done

A theory is only as trustworthy as its candour. These are stated plainly — because a framework that hides its gaps cannot be believed about its wins.

Still open, logged not papered over

The force coefficient Peff is a clean whitelist combination but may be the hydrogen force-balance rewritten — kept calibrated conservatively.  H₀ leans on an assumed Friedmann structure C-flagged.  The mass ratio's first-principles root (the Vdisp equilibrium that forces 6π⁵) is still open.  Quantum measurement, entanglement, tunnelling are not yet mechanised.  The strong-field GW sector (wall reflectivity, the echo) is the cleanest place SDT could be distinguished from GR — and is unproven.

Two things an earlier draft mislabelled are dissolved, not gaps: charge is not a primitive — it is occluded influx directionality, so α (not e) is in the whitelist; and P is not a constant injecting G — it is a variable closure field ℓP(r) = ℓP,∞(1−z), derived G-free.

The shape of what we know

Zero free parameters

Read it as the theory reads itself — forward from a whitelist of eight numbers, never backward from a target.

{ ℓP, c, ℏ, kB, TCMB, α, me, mp }
the only permitted inputs — a fact not on this list is not a measured fact
We have stood at the bottom of the ocean for four hundred years arguing about what pulls the apple down. Nothing pulls it. The universe pushes it.

Whether this is correct is not up to anyone's preference. It is up to the experiments — and they are specified, numbered, and waiting.