Joint likelihood for correlated observations O-36, O-37 (shared basis: D-9). Step 8 writes the single ## Likelihood block here; the member edges point back via group.
Likelihood
# CG-5 (HC-6) — ONE joint estimate over members E-16 + E-17: both observations are derived from the SAME
# HiRes monocular spectra (source S-60, instrument D-9), so they are one witness, not two (rule 1). The
# pattern judged whole: a 5.3-sigma flux suppression with the break at log10 E = 19.75±0.04 (O-36) AND the
# integral-spectrum E_1/2 = 10^(19.73±0.07) eV landing on the parameter-insensitive proton-GZK prediction
# 10^19.76 eV (O-37). Members in HC-6.hypotheses order [H-9 GZK extragalactic-proton propagation, H-12
# He/CNO source-rigidity-maximum, H-21 heavy-Galactic-to-light-extragalactic transition at the dip, H-37
# residual]. Anchored on H-9 = 1; others priced as ratios to it (rule 7).
lik_supp_H9 = 1.0 # anchor: H-9 is the ONLY member predicting BOTH halves at once — a suppression AND
# its location + E_1/2 at exactly the parameter-free GZK-proton scale. This whole
# pattern is what H-9 forces, so it is maximally expected here.
lik_supp_H12 = 0.35 # 0.35x: a He/CNO account with a narrow source rigidity maximum readily produces a
# steepening (O-36's existence fits), but as a SOURCE property its energy has no
# reason to land on the GZK value, so the E_1/2 match (O-37) is a coincidence under
# it. Not crushed: per A-23 (corrected) the E_1/2 test is evidence FOR the proton-GZK
# break, not an identification of it — it discriminates against source-spectrum
# explanations but a heavy-composition photodisintegration suppression can still sit
# near a similar energy, so H-12 keeps a moderate fit rather than near-zero.
lik_supp_H21 = 0.8 # 0.8x: above the ~10^18.5 eV dip H-21 makes the flux light extragalactic (protonic),
# which itself undergoes GZK losses — so it predicts a suppression and E_1/2 near the
# GZK scale almost as well as H-9. These two observations barely separate H-21 from
# H-9 (their discriminating power vs H-21 lives at the dip, not here); only slightly
# below the anchor for H-21's less-clean high-energy proton purity.
lik_supp_H37 = 0.3 # 0.3x: unlisted/exotic/instrumental cause, unconstrained — the instrumental branch
# predicts NO break at all, and no unlisted cause has a reason to reproduce a break at
# the exact GZK energy with a matching parameter-free E_1/2. Slightly below middling
# for that specific double coincidence; not near zero, since an exotic top-down source
# could mimic a cutoff (rule 3).
t_hires = 0.7 # cap = min trust_score over {O-36, O-37} = 0.8 (both via S-60). Docked below it: the
# load-bearing discriminator is the ABSOLUTE-energy match of the break and E_1/2 to
# the GZK scale, but D-9 carries a ~17% energy-scale systematic (fluorescence-yield /
# calibration / aperture-MC) common to both observations — it shifts break-location
# and E_1/2 together, so the shared witness could move the match without the
# per-observation error bars flagging it.
evidence("HC-6", ["O-36", "O-37"], [lik_supp_H9, lik_supp_H12, lik_supp_H21, lik_supp_H37], t=t_hires)