Is the universe elegant — or just weird?
The building blocks
Every result on this site is anchored on two groups of building blocks: three fundamental axioms — the deep roots the whole framework bottoms out in — and a named set of measured observables. Nothing here is derived from nothing. The three axioms are not deduced; they are honestly arrived at — one selected by constraints, one anchored to measurement, one posited as a primitive — and their credibility is that they turn out to be load-bearing, at full precision, across many gates at once.
The board these blocks carry — in one glance
Verify each column yourself: The Gates (ledger + per-gate dossiers, the closure-of-record) · The observables (all 362) · What “paying” means · the three roots: Shape · Scale · Granularity · the screen above them: The Second-Layer Roots.
Axiom 1 — The Shape (selected by constraints)
The Shape is the exact frozen object the theory computes from: a specific, hash-pinned object in three levels — a Stage (the metric carrier), a Rulebook (which configurations are admissible), and a set of Actors (the matter, gauge, and Higgs content plus the maps that read off observables). Only the Stage sets the dimension count, D = 4 + 6 + 2 + 1 = 13 (a 4D arena times a 6D color space K₆ = SU(3)/T², a 2D weak sphere, and a folded 1D hypercharge circle); the other two levels carry no dimensions but are just as load-bearing — read the Shape as “just the geometry” and it fails for that reason alone.
The Shape was selected by constraints, not deduced: two of its carriers are forced by theorems that close off entire classes of alternatives, and the color space is the unique clean survivor once a cheaper-looking rival is actually built end-to-end and breaks. Inside the declared search space it is the most economical complete candidate — the most economical, not the provably unique one. “No simpler shape exists anywhere” is a claim no theory can settle, and this one does not pretend to. See The Shape, the full Foundational Constraints register, a worked example, and the complete but long construction on the GUT page.
Axiom 2 — The Scale (anchored to measurement)
The Shape gives structure — ratios, indices, mixings — but never a magnitude in GeV. The Scale axiom supplies the one absolute ruler that turns structure into numbers. That an absolute scale must exist is a theorem: change the units and any bare dimensionful number changes with them, so only ratios, or values measured against a fixed anchor, carry real content. But the value of that anchor is read from experiment, never derived. The master ruler is the Planck scale, MPl = 1.2209 × 1019 GeV, with the electroweak scale as the second ruler the scheme conversions run on — a two-ruler floor. Existence is proven; the numbers are measured; the two are never merged. See The Scale.
Axiom 3 — The Granularity (posited as a primitive)
Granularity is the discipline that reality bottoms out in a smallest distinguishable step of cost — an action, not a length; it names no smallest length and does not claim space is pixelated. It lives on the full Shape, across all 13 dimensions including time, and rests on a single named, value-free posit: a uniform positive cost-floor, with ħ (Planck's constant) as its measured size. Why a posit and not a proof? Because it is credentialed by negative controls: two worked counter-models show that merely having finite resources does not force a uniform floor — you can have finitely many stable records with arbitrarily fine grain. Finiteness alone is provably not enough, which is exactly why the uniform floor has to be named as its own axiom rather than assumed for free. See The Granularity.
The measured observables
Paired with the three axioms is the second group of building blocks: the measured values the framework is anchored on. No framework derives its measured inputs from nothing — the honest questions are only how many, which ones, and whether they are all named. Both counts are published.
The calibration set (4–5)
The values read before any comparison, used only to set the dials: MPl (the Planck scale ruler), αi (the three gauge couplings at MZ), yt (the top Yukawa), |Vus| (the Cabibbo entry), and Nν = 3 (the LEP light-neutrino count — an integer, not a magnitude). The question this set answers: which measured values fix the dials?
The full consumed set (~12–14)
Every measured or charged input the machinery actually spends: the calibration set plus the electroweak scale, the fitted flavor normalizations Nd, Ne, Nν, the seesaw scale MR, the cosmological constant Λ, ħ (folded into the Planck ruler through G), and the observed matter content E as a charged, non-numeric input. Each is measured or paid — none is claimed as a result. The question this set answers: what does the whole machinery run on?
The full honest ledger of the consumed inputs, row by row, is on the Anchors register; what it costs to “pay” an input — and why a paid scale is never dressed up as a prediction — is defined on What “paying” means. The complete second layer — all 362 observable phenomena across 11 domains the framework is anchored to and tested against — is catalogued on The observables.
The full-precision rule
Every mention of an axiom means the complete axiom at full precision, not a shorthand. “The Shape” means all three levels at sixteen significant figures on the named, frozen branch; “the Scale” means the anchor at full precision applied over that complete Shape. A calculation may consume exactly the precision its anchors are charged for — no more, and no less. Use a rounded anchor or a stripped-down geometry and the result can fail, or appear to succeed, for that reason alone — with nothing right or wrong in the physics itself.
Why load-bearing lends credence
The case for these axioms is not that they were conjured from nothing — it is that, once fixed, the same three axioms and the same handful of measured anchors carry a much larger body of results at full precision. From just two measured flavor anchors, nineteen or more independent flavor observables come back (and a second two-anchor calibration returns six to eight more) — counted strictly, only the genuine within-sector predictions against effective inputs, that is still roughly twenty-two outputs from about five or six inputs — a fourfold over-determination. That is the honest evidence: not derivation, but over-determination. The genuine predictions are the within-sector ratios and the mixing angles, not the overall scales, which the fitted normalizations inject as anchors — over-determination is destroyed, not strengthened, by dressing paid scales up as predictions.
This remains a complete, gate-verified, reviewable candidate — not proven truth. The board stands at all 33 gates closed at honest endpoints — 33 resolved at +0 and 0 anchored at +1. The formerly standing up-quark falsifier is resolved (a published, symmetry-derived 1/√6 moves it from a ~4.4σ miss to +0.058σ — kept as a sharp falsifiable prediction), and the two former structural frontiers are now both closed terminals: the global-anomaly leg is resolved outright — the degree-five host class vanishes in the target ring (y²·x³ = 0), so there is no class to carry a nonzero residue — while the black-hole horizon leg reproduces the Bekenstein–Hawking area law and rests only on a single named external quantum-gravity dependency, certified irreducible and stated openly rather than asserted away. See how each of the 33 gates is graded on The Gates.