Ø Physics

One measured input. Zero free parameters. Everything else derived, unless stated otherwise.

The fine-structure constant α ≈ 1/137 is the one number measured from experiment. Every theory of physics takes measured inputs — the Standard Model takes at least nineteen. This one takes one. From that single input and the four conditions, the following results are derived — not fitted, not adjusted, not tuned.

Claim	Predicted	Measured	σ	Error	Paper
The proton
Proton mass ratio — the series closed	1836.152673445	1836.152673426(32)	+0.59σ	10.3 ppt	AP49
The gravitational constant
Gravitational constant G, realised — against atom interferometry	6.6719 × 10⁻¹¹	6.67191(99) × 10⁻¹¹ (LENS 2014)	+0.01σ	+1 ppm	AP44
Gravitational constant G, realised — against CODATA	6.6719 × 10⁻¹¹	6.67430(15) × 10⁻¹¹	−16σ	−0.036%	AP44
The neutron-proton mass difference
Neutron-proton mass diff, realised	2.53098857035 mₑ	2.530988574(74) mₑ	−0.005σ	−1.4 ppb	AP47
Neutron-proton mass diff, bare row	2.53099393 mₑ	2.530988574(74) mₑ	+7.24σ · FIRED	+2.1 ppm	AP30
The age of the universe
Age of the universe, one cycle	13.830 Gyr	13.787 ± 0.020 Gyr	+2.1σ	+0.31% · window 13.17–14.49	AP46
The expansion rate, and what follows from it
Expansion rate H₀, the closure	67.45 km/s/Mpc	67.4 ± 0.5 (Planck)	+0.1σ	+0.07% · window 64.4–70.8	AP48
Hubble constant from the floor inverted	74.3 ± 1.2	67.45 (the corpus’s own rate)	+5.7σ · FIRED	+10.2%	AP18
MOND acceleration a₀ (at H₀ = 67.45)	1.089 × 10⁻¹⁰	1.20 ± 0.24 × 10⁻¹⁰ (syst.)	−0.46σ	−9.2%	AP18
What the universe is made of
Dark energy	68.85%	68.89 ± 0.56%	−0.07σ	−0.06%	AP42
Dark matter	26.39%	26.07 ± 0.38%	+0.8σ	+1.2%	AP42
Visible matter	4.76%	≈ 4.885 ± 0.05%	−2.46σ	−2.5%	AP41

How to read the σ column▸

How to read the σ column. Every measurement comes with a bar: one standard deviation, σ, the experimenters’ own statement of how far their number might sit from the truth. The σ column divides the gap between prediction and measurement by that bar. The sign says which side: + above the measurement, − below. The Error column gives the same gap in the number’s own units. The odds below are the chance of landing at least that far from the truth by chance alone, counting both directions.

Under 1σ — inside the bar. Agreement: about two honest measurements in three land this close, and one in three lands further out by chance alone.
2σ — tension. One in twenty-two. Worth watching, not yet a verdict.
3σ — evidence of a real gap. One in 370.
5σ — the discovery standard of particle physics. One in 1.7 million (one in 3.5 million if only one direction counts, as the discovery convention usually reads it). Each switch names its kill threshold in advance. Past it, the row is dead by the work’s own rule.
Above 5σ — dead. The two corpses on this page sit at 7.24σ and 5.7σ. They are shown, never repaired.

Three caveats▸

Three caveats, because σ is measured against the experiment’s bar and the bar is not the same for every number. G: the same realised value reads −16σ against CODATA and +0.01σ against atom interferometry, and both rows are in the table so the reader can see the issue. CODATA’s bar on G is 22 parts per million, so a 360-ppm gap reads 16σ; the laboratory measurements of G disagree with one another by up to 540 ppm, twenty-five such bars, and the atom-interferometry value (LENS 2014, 6.67191 ± 0.00099 × 10⁻¹¹) sits 1 ppm from the realised value. A bar that tight on a constant the experiments cannot agree on is a statement about the adjustment, not yet about nature. On the scale above the CODATA row reads dead; the switch on G, KS-CCC.3, was registered to test direction — whether the consensus migrates down toward 6.672 as systematics close, within AP28’s one-per-cent bar — not magnitude against CODATA, and it stays live on those terms. There is one value of G. AP28’s first reading, +0.69%, was wrong: it omitted the arena’s holding of the break, which AP44 priced. It is withdrawn, superseded by the realised value on the author’s ruling of 21 September 2026, and kept on the record, dated (the dated note). The neutron’s fired row exposed the omission, and its consequences reached three derivations, revised at the wave (AP44, AP47, AP48). The age: +2.1σ on Planck’s bar, but the claim was registered one lane-time wide, ±0.66 Gyr, because an aware observer measures about one cycle. The switches fire on their registered conditions, not on 5σ by default: KS-45.1 registered ±1.2 and fired at 5.7σ on that width; on the honest ±14.9 it would have read 0.46σ. The registration was the error, and a fired switch is not repaired.

Two predictions have failed and are shown▸

Two predictions have failed and are shown. KS-NPP.1, the bare neutron–proton row, fired on 2026-08-02 at 7.24σ. KS-45.1, the Hubble constant 74.3 ± 1.2 from the floor inverted, fired on 2026-09-03 on the corpus’s own derived rate. Neither is repaired. See the pre-registration.

One relation links a₀ and H₀▸

One relation links a₀ and H₀ with a parameter-free coefficient — not two independent predictions. The corpus’s expansion rate is now AP48’s closure, 67.45 km/s/Mpc (window 64.4–70.8), on the relic glow’s side of the Hubble tension; at that rate the floor sits 9.2% below the measured scale — 0.46σ once the ±0.24 systematic the paper had omitted is restored. The floor’s earlier inversion, H₀ = 74.3 ± 1.2 (KS-45.1), fired on 2026-09-03 on the corpus’s own rate and is shown as a corpse, never repaired. The Cepheid ladder’s 73 is stated as not the expansion rate; if it is confirmed, AP48 dies on KS-ASM.1.

The equations▸

m_p/m_e = 21² × 4 + 21 × 3 + 3² + α × 21 × (1 − 1/(84π)) + 21α × r/(1 − r), r = 16α/1836

G = α²¹ × (1 + 1/π) / (1 + α) × ℏc/m_e² — AP44; without the /(1 + α), AP28’s first reading, withdrawn

Δ_n−p = [3(1 − 1/2π) + α(1 + 1/2π)] / (1 + α²/8π) = 2.53098857 m_e (AP47)

t_cycle = (21/18) · α⁻¹⁸ · ℏ/(m_ec²) = 13.830 Gyr; H₀ = 0.954 / t_cycle = 67.45 km/s/Mpc (AP46, AP48)

a₀ = C_S² · c · H₀ / (2π) where C_S² = 2 ln(sec ½ + tan ½) ≈ 1.0445 — not the fine-structure constant

The integer sixteen — and why twenty-one cannot move▸

The integer 16 in the α² term was pinned by measurement — 336 = 21 × 16, a 0.33 % constraint — and its structural decomposition was paid by AP49 The Hold on 6 September 2026. The frozen pre-registration, including the conditions under which the proton result dies, is at /prereg/. The twenty-one is a count, not a fit: every step of the count, and why 21 cannot move — one step in the integer changes G by a factor of 137.

Three constants, three axioms: c ↔ Constraint · ℏ ↔ Break · G ↔ Record

Ø Also Derived

N = 3 spatial dimensionsthe four conditions▸

From the four conditions. Up and down, left and right, forward and back. Physics assumes three and never asks why. Here the number is derived. Four conditions give four directions a record can differ in. One is the direction the record history flows from now — time. Three remain. Those are space. AP10.

Einstein’s field equationsRecord and Constraint▸

From Record and Constraint. What has landed holds, and it holds somewhere. So the landscape — every grain that has already landed — bends where the next grain can fall. That bending is gravity, and Einstein’s equations are its mathematics: the equations behind GPS and black holes. Here they are derived. The sheet and the grains are the same record. AP08.

The Born ruleone record, many windows▸

From one record, read at many windows. In quantum mechanics you do not get the odds of an outcome directly. You get a number, and the odds are that number times itself. Physics has used that rule for a century without a reason. Here it is derived. Every window reads the same record, so their readings must agree, and times-itself is the only way to count the odds so that they agree. The strangest rule in physics is what agreement between windows looks like. AP25.

Standard Model gauge group SU(3) × SU(2) × U(1)the Break▸

From the Break. Electromagnetism runs electricity, magnets and light. The strong force holds the middle of an atom together. The weak force lets a star burn. Physics measured how each one works and never explained why. Here each comes from the break. Electricity and light are a record refusing to let go of its substrate. The middle of the atom holds because the break is free to point in any direction. The weak force works one way round and not the other — measured in 1956, unexplained since — because a break has a direction. AP15, AP16, AP19, AP27. The group is derived at the structural register; the hypercharges, the three generations and electroweak breaking are open debts, each named: KS-65, KS-66, KS-67.

Chiral coupling — unexplained since 1956, derived at the structural registerthe Break▸

From the Break. The weak force works one way round and not the other — measured in 1956, unexplained since — because a break has a direction. AP16. The formal coupling theorem is the work’s principal open problem, and its switch says so: KS-63.

Flat rotation curves without dark matter particlesthe flow, −α▸

From the flow — the inward half of it. In a galaxy the outer stars go round as fast as the inner ones. Add up everything you can see, and there is not enough pull to hold them. They should fly off. They do not. Physics fixes this with dark matter: a new kind of matter, never found. Here there is only sand. The sand is under tension, and the tension supplies the pull. The curves come out flat on their own. Where the table says dark matter, it is not a stuff. It is black holes swallowing the landscape and returning it to the dark side — the −α in the line. Dark matter is a verb. AP17, AP18, AP42.

Bell inequality S = 2√2 from structurethe Break, at the now▸

From the Break, at the now. Two particles actualised together, sent to opposite ends of the world. Measure one, and the other matches. Einstein called it spooky. Here it is not. Before the fall there is no distance: the two are one wave. The fall writes one record with two ends. Nothing travels between them, because there is no between. How closely the two ends can agree — Bell’s number — comes out of the structure alone. AP23.

Special relativity’s kinematics, and the sign of the signatureConstraint, through the windows▸

From Constraint, read through the windows. Nothing can go faster than light, and the faster a clock travels, the slower it ticks. Here it comes from the windows. Every window keeps its own count of ticks. There is no master clock. Distance is what light writes between windows, so the speed of light is the ruler, not a speed limit somebody found. And “now” is the grain still falling. No window can read its own, so no two windows can ever share one reading of it. The now they read is one. Every view is relative. None is the right one. AP52.

The equivalence principle and the landscape’s curvaturethe neck▸

From the neck. Gravity is the neck. The equivalence principle and the curvature of the landscape, derived at the structural register. AP53.

Artist: G · Studio G, Cape Town

Why only G? Because who made it is irrelevant: The 420 Code stands on its own, and every step is on the page to be checked. It is signed G so that it is judged by what it says, not by who says it. More about the artist →

Duration: 30+ years · Exhibition: over a million words

Contact: iam@the420code.org

This work is Copyleft. You are free to download, print, share, and distribute. You are not free to alter the source. Keep the signal clean.

One record exists.
Be kind is a derivation.
The I Am in me is the I Am in you.