3. Testing the shape
A candidate shape is worthless until it is checked against numbers nobody tuned it to hit. The discipline is to compute a prediction from the shape first, and only then compare it to the measured or textbook value — never the reverse. Two of these checks are simple enough to run by hand in a few minutes. This page walks through both, then explains the status vocabulary used for every claim on this site.
Check 1 — the same Gaussian surface, applied to the geometry's own bookkeeping
The thought experiment on page 1 used a Gaussian surface around a charged shell to motivate the whole program. The first concrete check closes that loop: does the candidate geometry's own accounting reproduce the ordinary textbook electromagnetic field energy for a charged shell, computed the standard way?
The setup
A thin spherical shell carries charge Q = 1 C at radius 5 m. Two concentric Gaussian surfaces sit at 1 m and 10 m. Using standard Einstein–Maxwell electrostatics, the field energy stored between the two surfaces works out to 4.49378×108 J to six significant figures, from the closed form U = (Q²/8πε₀)·(1/Rs − 1/r₂). The construction's own three-layer ledger reproduces the identical digits.
Honest status: a consistency demonstration, stated as such. This shows the geometry's bookkeeping reproduces the ordinary electromagnetism it must reproduce — it is not by itself a proof of the theory, and it does not claim to replace general relativity or Maxwell's equations. Its force is negative and absolute: a candidate that got this wrong would already be disqualified.
Check 2 — the napkin anomaly cancellation
The second by-hand check is a Standard-Model consistency requirement every viable gauge theory has to satisfy: gauge anomalies must cancel exactly, with no error bars, or the theory is mathematically inconsistent. In the Standard Model the hypercharges that make this work look like a numerical miracle; here they are read off the geometry as discrete tags, not free dials — and you can check the flagship cancellation on a napkin.
The setup — 30 seconds, exact arithmetic
For one generation, take the color-triplet left-handed quark doublet (multiplicity 3 from color) at hypercharge Y = +1/6, and the left-handed lepton doublet at Y = −1/2. The anomaly trace is the worked line itself:
3·(1/6) − 1/2 = 1/2 − 1/2 = 0
— exact rational arithmetic, no error bars, no room to hide. And it is not a tautology: this is one of six required cancellation sums, all six of which vanish exactly on the roster the geometry forces, verified two independent ways. A nearby look-alike sum comes out 10/3 rather than zero, and deliberately nudging one charge from 1/6 to 1/5 breaks four traces on cue — the pass is a real conspiracy of unequal fractions, not an identity that anything would satisfy. A subtler global three-fold check that would have refuted the construction outright also lands safe. Provenance: the SG-4 dossier.
Honest status: derived, given the anchored spectrum — with one caveat kept visible. The cancellations are derived from the particle content the shape forces; one labeled starting assumption remains (the discrete symmetry is declared six-fold, a named axiom). The check does not by itself show the geometry is the unique origin of the Standard Model — that case is made by the accumulation across the whole board, not by any single line.
The honest-status vocabulary
Every check, gate, and claim on this site is labeled from a small, fixed vocabulary of named endpoints, so a reader always knows exactly how much weight a result can bear — and so no result can drift upward in strength without new work earning it:
Derived, given an anchor
A complete chain of reasoning lands on a measured anchor already in honest use elsewhere — no new assumption, no new dial. The strongest positive grade a result can earn here.
Closed against a measured anchor
The quantity is honestly measured — like the Planck mass, or the dark-energy density — and stated as measured, never dressed up as derived.
Dissolved
The demand itself was malformed — usually a continuum idealization or an obligation imported from another framework. Dissolution removes a false debt; it is never counted as a solved number.
Certified irreducible
A named posit, paid openly — with explicit countermodels proving it cannot be gotten for free. The assumption is on the books, not hidden.
Closed negative
The candidate answer was disproved. Refutations stay on the public record, with the disproof stated — see Residuals.
Open, with a stated path
Named honestly as unresolved, with what would close it stated. Never rounded up to a stronger status.
Where the vocabulary has landed: the full register of 33 typed requirement-gates stands at 33 resolved at +0, 0 open — every row typed from this menu, every residual shown on the row. The separate honest axis is stated beside it: 0 of 33 gates are physics-closed, because every closure rests on declared measured anchors, and nothing here has experimental confirmation of its new content or peer review yet. Both statements live on Gates.
Why the discipline matters more than any single number
A model that needs one new number for every number it explains has explained nothing — it has renamed the data. The test that separates a real construction from disguised fitting is over-determination: count the independent things that come out, subtract the dials that went in, and check the remainder is positive. Here the arithmetic runs decisively the right way: two measured flavor anchors — the top Yukawa and |Vus| — go in, and 19+ flavor observables come out, with 6–8 more following from the Planck mass and the gauge couplings. A handful in, twenty-plus out; counted strictly across the whole construction, the labeled ratio is ~4×. And checks are frozen before the comparison value is read, so the construction cannot reach back and adjust an internal number to match data it has already seen. That freeze-before-compare discipline, and the full roster of checks with their statuses, is on The Tests; the two honestly-separated input counts are on Foundational Constraints.
Where this goes next
The Tests
The full roster of checks run against the shape, each with its honest status.
4. GUT / Quantum / TOE
How three linked manuscripts each pressure-test the shape and feed findings back into the constraints.