Natural effects D–F — Tier-B EXACT / PASS (astro, force, QI)

§0 Easy guide — what is this page? (start here)

What “Tier-B” means (no jargon trap). This is not “every mystery of the universe is solved.”

• B-EXACT — a formula or identity is forced by SPT structure (Bagua integers, Z₂ symmetry, generator counting…). Not a hand-tuned fit.
• B-PASS — when compared to lab / PDG / Planck numbers, the error is under about 1% (or sits in a clear band).
• OPEN — we do not claim a clean lock yet. Listed so nobody pretends it is done.

What we did technically (for the website). One SymPy script proves each claim and prints PASS/OPEN. A wiki page explains. The script is on the public download allow-list. Discovery log #101 records the milestone. We did not add Law 81, 82… — only effect locks from old capital.

Three things to remember. (1) Claimed D/E/F cores are Tier-B — not “everything in cosmology is finished.” (2) OPEN items (σ₈, FRB, high-z w, full Born postulates…) are deliberate honesty. (3) Anyone can check offline: python scripts/spt_effects_def_tier_b.py must show OVERALL: PASS.

§1 Scoreboard (what passed)

Quick map: D = sky/cosmology, E = forces & weak/strong CP, F = quantum info & black-hole thermo. Details in plain language follow in §2–§4.

§2 Section D — Sky / cosmology (plain + technical)

D1 H₀ — expansion rate (plain). Two famous measurements disagree: CMB (early universe) vs Cepheids/supernovae (nearby). Media calls it a “crisis.” SPT says: two epochs, one substrate. Absolute early-era h = 27/40 from shell S₄₀ (same box of 40 as Cabibbo). Nearby multiplies by √(75/64). Both ends match PDG within ~0.15% / 0.1%. Tension = category error, not two theories fighting.

D2 w(z) — dark energy “springiness” (plain). Today the dark-energy equation of state looks like a pure cosmological constant: w = −1. Cascade damping makes leftover wiggles tiny now. How much w can drift at very high redshift is still OPEN — needs the full source term of cascade dynamics.

Ω_DM = C(7,4)/Q₇ = 35/128   ← dark-matter share of 128 vertices
Ω_b  = 6/Q₇                  (shell; a tiny loop refines baryons)
Ω_Λ  = 1 − Ω_DM − Ω_b = 87/128
ΣΩ   = 1  EXACT              ← the cake is fully accounted for

D3 Ω sum (plain). The universe’s energy budget must add to 100%. SPT counts configurations on Q₇ = 128 vertices: 35 yin-dominant slots → dark matter share 35/128; baryon shell 6/128; the rest is Λ. Sum = 1 exactly at shell level. Not locked here: σ₈ (how clumpy structure grew) and detailed FRB distance–dispersion spectra.

D4–D5 tilts (plain). Early gravitational-wave background slope n_T = 3/13 (same “freeze family” as weak-mixing tree 3/13). Matter-clump slope n_s = 55/57 matches Planck to ~0.001%. D6 PBH (plain): tiny black holes that finish evaporating today sit in a 10¹¹–10¹² kg mass band from the Hawking lifetime formula (coefficient family 5120π).

§3 Section E — Forces / free-fall / strong-CP / weak (plain + technical)

E1 Fifth force (plain). Law 42 fills Q₇’s 14 generators as 8+3+1+2. No spare kernel → g₅ ≡ 0 EXACT at tree level. A clean lab fifth-force detection at leading strength would kill this lock.

E2 Equivalence principle (plain). “All objects fall the same in a gravitational field” (Galileo / Eötvös). In SPT, gravity is universal spin-2 frame rotation of the same substrate for all real-DA matter → tree Eötvös parameter η_EP = 0. Super-precision material form factors (MICROSCOPE depth) stay OPEN as a next layer.

E3 θ_QCD (plain). Strong interactions could have had a CP-violating “knob” θ. Experiment shows it is tiny or zero (neutron EDM bounds). SPT: Z₂_DA (φ → −φ) makes the CP-odd density odd → the coefficient must vanish (Law 8). Same Z₂ that sets the lightest neutrino mass m_ν1 = 0.

E4 Cabibbo / β-decay tree (plain). The main quark-mixing angle λ = 9/40 = 0.22500 matches PDG essentially exactly. It lives in the same S₄₀ shell as Hubble h = 27/40, so h/λ = 3 forever at shell level (see A3 on the A–C page).

§4 Section F — Quantum info / measurement / BH thermo (plain + technical)

F1 Decoherence / arrow of time (plain). A fully mixed “wave” over Q₇/Q₃ = 16 cosets has entropy S = log(16). The virtual-DA sea is absurdly dense (~10¹⁰⁴/m³), so the chance to spontaneously recohere is exp(−10¹⁰⁴) ≈ 0. That is a practical second law and a structural arrow of time (Law 45). Material-specific T₂ times (how fast this qubit dies) remain OPEN.

F2 Wave–particle (plain). For ~100 years people argued: is an electron a wave or a particle? SPT: both projections of one membrane. Particle regime = real-DA clusters on Q₃ (localised). Wave regime = virtual-DA delocalised on Q₇. Geometrically Q₃ sits inside Q₇ → no contradiction (Law 44). Full Born-rule measurement postulates derived from the Action alone remain OPEN depth.

t_Page / t_evap = 1 − 1/(2√2) ≈ 0.6464  (Law 70, B-EXACT)

Phase 1: radiation entropy S_rad rises (looks thermal)
Phase 2: virtual-DA correlations pull S_rad → 0 at full evaporation
→ unitarity preserved (information does not die — structural close)

F3 Page curve (plain). Hawking radiation first looks thermal (entropy of radiation rises). Halfway-ish through evaporation, correlations with the virtual-DA sea pull the radiation entropy back down so that at the end S_rad = 0 — information is not destroyed. The structural time ratio is 1 − 1/(2√2) ≈ 0.646. Full Action-level quantum-thermo derivation is framework-depth OPEN; the ratio lock is B-EXACT.

§5 Still OPEN (not claimed Tier-B — in plain words)

Leaving these OPEN is a feature, not a bug: better than fake EXACT labels.

• σ₈ — how strongly galaxies clump today. We locked the budget Ω, not yet the growth amplitude closed form.
• FRB — fast radio bursts’ dispersion vs distance as a precision cosmology tool. Not claimed here.
• w(z ≫ 0) — quantitative dark-energy drift in the early universe (needs full Law 65 source).
• Material T₂ — decoherence times for concrete lab materials from the Action.
• Full Born measurement postulates from SPT Action alone (F2 depth).
• MICROSCOPE-depth EP — post-Newtonian material form factors beyond tree η_EP = 0.

§6 How experiments can kill D–F locks (plain)

Science needs kill switches. If Nature does any of the following at high significance, the matching lock dies.

• D (sky): DESI/Euclid force |w(0)+1| ≫ 10⁻³ while the cascade stays frozen; or CMB-S4 finds n_s far from 55/57; or PTA isolates a primordial GW tilt incompatible with 3/13.
• E (forces): A lab fifth force at tree-level strength; or neutron EDM requiring θ_QCD ≠ 0 at high σ; or Cabibbo λ far from 9/40 after radiative cleanup.
• F (quantum): Controlled recoherence of macroscopic coset mixtures; or an analogue Page curve far from the 1−1/(2√2) band; or a wave–particle contradiction that cannot embed in Q₃⊂Q₇.

§7 Reproduce offline

You do not need to trust this page. Run the script; judge by the EXACT / PASS / OPEN columns it prints.

pip install sympy numpy && python3 scripts/spt_effects_def_tier_b.py && python3 scripts/spt_effects_abc_tier_b.py && python3 scripts/spt_hubble_h0.py

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