Key Results
A curated flagship-result entry surface for readers who want substance before the full ledger.
Curated First Set
This page is the Discover entry into the Results lane’s Landmark Results surface.
This is not the full Results lane. It is a small, high-signal entry surface for readers who want to see landmark consequences before entering the full Results structure: Landmark Results, World Readouts, Challenge Responses, Core Semantics Status, Additional Derived Results, and Progress Against Agenda.
Use AI-Assisted Discovery if you want a structured outside-in assessment of these landmark result surfaces before reading in depth.
Worked example — Hubble tension, in 200 words
Of the cards below, the Hubble tension result is the most accessible to a non-specialist reader. The argument compresses to:
The Hubble constant $h$ measures how fast the universe expands. Two independent measurement methods disagree by ~5σ: the Planck CMB (early-universe) gives $h \approx 0.674$; SH0ES/Cepheid/JWST (late-universe) gives $h \approx 0.730$. This 5σ tension has resisted explanation within ΛCDM and motivated extensive new-physics proposals.
The τ-framework derives $h = \tfrac{2}{3} + \iota_\tau^2 / 17 = 0.6735$ from two structurally fixed components: $\tfrac{2}{3}$ is the matter-dominated Einstein–de Sitter base value, and $\iota_\tau^2 / 17$ is the holonomy correction where $17 = W_3(3)$ is the sum of three consecutive partial quotients of the continued-fraction expansion of $\iota_\tau$ starting at index 3. Both terms are fixed once $\iota_\tau$ is posited — neither is fitted to data.
The result lands at –120 ppm from the SH0ES/JWST measurement and is consistent with Planck CMB. Falsification condition: any joint Planck-and-SH0ES tightening that rules out $h = 0.6735$ at >5σ falsifies the readout. The readout sits in V.T259; the integer divisor $17 = W_3(3)$ is Lean-certified at Tau.CF.w3_at_3 : windowSum cf_head 3 3 = 17 in TauLib.BookV.Astrophysics.H0TensionLCDM (uniqueness wrapper: Tau.BookV.Astrophysics.hubble_uniqueness).
This is the orientation, not the proof. The full derivation, dependencies, and falsification path live in the linked result page below — but the sketch above is enough to know what the claim actually is.
Hubble tension
A zero-continuous-parameter readout for the Hubble constant: h = 2/3 + ιτ²/17 = 0.6735, –120 ppm from SH0ES/JWST.
Theorem: V.T259 · Lean: Tau.CF.w3_at_3 · Falsifier: any joint Planck-and-SH0ES tightening that rules out h = 0.6735 at >5σ.
No dark matter particle
A structural exhaustion claim rather than a new-particle hypothesis: the four primitive sectors plus ω exhaust all positions in Category τ.
Theorem: V.P69 (Sector Exhaustion) · Falsifier: direct detection of a non-baryonic massive particle that requires its own sector position, or rotation curves the V.T85 capacity-gradient mechanism cannot reproduce.
Hinge theorem
A no-knobs route from the formal build to the claimed physical readout: 10 inter-sector couplings as rational functions of ιτ alone.
Theorem: III.T41 (Hinge) + III.T42 (No Knobs) · Falsifier: any inter-sector coupling measured to depend on a continuous free parameter, i.e. not a rational function of ιτ.
Homochirality
A life-sector derivation path tied back to the formal corpus: 12-step chain K0–K6 → ιτ → weak sector → Parity Bridge → universal L-amino-acid chirality.
Theorem: VI.T43 (via VI.T01 Parity Bridge) · Falsifier: discovery of a persistence-sector lineage with the opposite universal chirality, or a chirality-mixed lineage that satisfies SelfDesc closure.
Consciousness as global section
A metaphysical readout surface for mind, binding, and self-model structure — at the E₂ binding layer, not the E₃ Hard Problem.
Theorem: VII.T41 (binding = sheaf gluing; CC1–CC3 from VI.D86) · Falsifier: a system satisfying CC1–CC3 that empirically lacks unified cognitive binding, or a binding-unified system that fails CC1–CC3.
Categorical imperative
An ethics result surface framed as a fixed-point and commitment structure: CI as the unique j-closed fixed point of the τ-digestion operator.
Theorem: VII.T35 + VII.P21 (Stage CI; Knaster–Tarski uniqueness) · Falsifier: exhibition of a second j-closed fixed point of j_dig distinct from CI.
Read Carefully
These cards are orientation, not endorsement. Every result must be read through its status, supporting corpus, verification route, and falsification posture where applicable.
Save or share this page for inspection
Download a portable dossier, copy a reviewer note, or send this page to someone who can inspect it.