Calling-card proof surface
Zero fitted cosmological parameters. One measured mass. 20+ predictions within 1σ of direct measurement. χ² = 2.42 across 8 independent observables, excluding model-extracted values.
This page groups the active public IO predictions against the direct measurements they are meant to confront. Rows that depend on model-extracted Planck quantities or still-open carrier completions are kept in the same table, but labeled honestly rather than folded into the headline χ².
If the theory is correct, the math will just work.
| Observable | IO Prediction | Measurement | Tension (σ) | Theorem Authority | Calculator Link |
|---|---|---|---|---|---|
| Geometry | |||||
| H₀ | 67.58 km/s/Mpc | Planck 67.4 ± 0.5 | +0.35σ | Paper 30 — One Mass, Zero Fits active branch package | H₀ card |
| Ω_m | 0.349 | 0.315 ± 0.007 (Planck 2018) | model-context row | Paper 30 — One Mass, Zero Fits active branch package | Ω_m card |
| Ω_k | −0.046 | Planck CMB-only non-flat fit ≈ −0.044 | within 1σ | Paper 30 — One Mass, Zero Fits active branch package | Ω_k card |
| Ω_Λ | 0.697 | 0.685 ± 0.013 (Planck 2018) | +0.92σ | Paper 8 — The Rosetta Stone Identity–Paper 9 — Gauge Projection for Dark Energy dark-energy density | Ω_Λ card |
| Cosmic chronometers | χ² = 14.70 on 35 points | Planck fixed-reference χ² = 15.15 | Δχ² = −0.45 | Paper 29 — The Branch Consistency Audit chronometer confrontation | H₀ card |
| Galaxy BAO closure | χ² = 27.74 on 13 galaxy/quasar points | Planck fixed-reference χ² = 31.25 | Δχ² = −3.52 | Paper 29 — The Branch Consistency Audit and Paper 31 — Gravitational Slip from Geometry BAO kernel | r_d card |
| Acoustic and CMB | |||||
| First TT peak | ℓ_peak = 224 | Observed first TT peak near ℓ ≈ 220 | within 1σ | Calculator scoped TT first-peak support | TT card |
| 100θ_* | 1.04868 | Planck flat extraction 1.04110 | competing geometry | Calculator active-branch θ_* theorem | θ_* card |
| Acoustic angle θ_s | 0.599° | 0.59652° ± 0.00018° | +0.42% | Paper 20 — The Acoustic Projection Theorem–Paper 21 — The AC1 Derivation acoustic channel | θ_* card |
| n_s | 0.9639 | 0.9649 ± 0.0042 (Planck 2018) | −0.24σ | Paper 28 — The Primordial Spectral Index boundary fixed-point scalar tilt | n_s card |
| A_s | 2.007 × 10⁻⁹ | 2.101 ± 0.030 × 10⁻⁹ (Planck 2018) | −3.1σ raw | Paper 32 — Closure: The Complete IO Framework modular-DtN source block | A_s card |
| r_d | 144.01 Mpc | 147.09 ± 0.26 Mpc (Planck 2018) | −11.83σ model-extracted | Paper 31 — Gravitational Slip from Geometry geometric pre-drag ruler | r_d card |
| Nucleosynthesis | |||||
| D/H | 2.509 × 10⁻⁵ | 2.547 ± 0.025 × 10⁻⁵ (Cooke 2018) | −0.61σ | Paper 24 — The Lithium Problem Solved deuterium channel | D/H card |
| Y_p | 0.2477 | 0.2449 ± 0.0040 (Aver 2021) | +0.68σ | Paper 25 — The Weak-Sector Identity Pin helium channel | Y_p card |
| Li-7/H | 1.75 × 10⁻¹⁰ | 1.6 ± 0.3 × 10⁻¹⁰ (Sbordone 2010) | +0.55σ | Paper 24 — The Lithium Problem Solved lithium channel | Li-7/H card |
| BBN triple | χ² = 1.13 | D/H + Y_p + Li-7/H joint comparison | headline fit | Paper 24 — The Lithium Problem Solved–Paper 25 — The Weak-Sector Identity Pin BBN closure stack | Lithium story |
| Structure and late-time observables | |||||
| S₈ f_Γ readout | 0.8113 | Weak-lensing S₈ ≈ 0.79 ± 0.02 | +1.1σ | Paper 32 — Closure: The Complete IO Framework weak-lensing readout | Theorem node |
| Late-time η_IO | 5.749 × 10⁻¹⁰ | typed observable, not a single-temperature direct match | typed comparison | Paper 35 — Four Problems, One Horizon late-time η_IO closure | η_IO card |
| Hubble-method ladder composite | six methods carried on three α-ladder rungs | Planck, ACT, SH0ES, and other published distance-ladder classes | max 0.57σ across 6 methods | Paper 34 — The Hubble Tension Resolved Hubble-method classification | H₀ card |
| Dark matter direct detection | xenon programs remain null toward the neutrino floor | LZ / XENONnT / PandaX-4T still null | consistent | Paper 33 — General Relativity and Quantum Mechanics Unified and Paper 35 — Four Problems, One Horizon dark-sector reading | Bridge map |
| Open and honest non-closures | |||||
| DESI evolving-w | not predicted on the current clean stack | DESI evolving equation-of-state signal | open | late-time dark-energy reinterpretation boundary | Theorem node |
| Full high-ℓ TT spectrum | canonical first peak supported; high-ℓ ceiling drift remains | full Planck TT spectrum | scoped open | Calculator first-peak support + open n_max ≥ 601 frontier | TT card |
| Baryogenesis mechanism | topological obstruction on the current stack | matter-antimatter asymmetry mechanism | open / no-go boundary | Paper 35 — Four Problems, One Horizon baryogenesis obstruction | Bridge map |
Rows tied to model-extracted quantities such as r_d, A_s, and standard flat-space 100θ_* are kept in the table for honesty, but excluded from the headline χ² = 2.42 summary. The calculator links point to the live output cards or theorem nodes that carry the provenance chain for each claim.