H-6 - The near-criticality of the Higgs potential parameters reflects an underlying dynamical or statistical principle
The authors’ interpretive proposal on top of the NNLO result: near-criticality of m^2 (the hierarchy problem) and of lambda (the stability boundary) may both point to an attractor critical point of an underlying statistical system, with the multiverse the natural candidate. Uncertain and explicitly speculative in the paper.
Link to original
H-43 - The near-criticality of the Higgs potential is an unexplained coincidence
Constructed complement minted at step 4b: the corpus proposes an underlying principle but no paper states the no-principle alternative, the logically needed competing answer.
Link to original
Principle against coincidence for the same explanandum. Exhaustive by construction: proposition and logical complement. A failure of the analysis — e.g. the near-criticality itself dissolving under shifted top-mass or coupling inputs — would remove the explanandum and thereby favour the second member (nothing left to explain).
Prior
# HC-11 prior — why the measured Higgs-potential parameters lie so close to the
# stability–metastability boundary. Members in HC-11.hypotheses order:
# [H-6 underlying dynamical/statistical principle, H-43 unexplained coincidence].
# Cluster is exhaustive_by_construction (a claim and its negation), so there is NO
# residual member and rule 4 does not apply.
#
# Inputs: the OUTSIDE VIEW only — the historical base rate at which apparent
# near-coincidences among fundamental-physics parameters turn out to rest on a genuine
# mechanism versus staying accidents. `no_observation_arguments.py --cluster HC-11`
# returned none. The cluster's three inbound E edges (E-20 / E-22 / E-23, correlation
# group CG-8) all carry the case-specific MEASURED near-criticality itself — the very
# datum that discriminates a principle from a coincidence — so NONE is marked
# used_for_prior; the whole group is priced at step 8. (A-6, the top-mass /
# no-new-physics scope caveat, attaches to those observations, not to a member, so it is
# likewise a step-8 concern and is not folded in here.)
#
# depends_on HC-10 (noted, NOT imported): an H-6 variant that dynamically drives
# lambda(M_Pl) -> 0 mildly correlates with HC-10's metastable-side outcome. Step 4 judged
# this cross-cluster coupling small, so the prior factorizes to good approximation; per
# rule 3 it is treated as an approximation in prose and no HC-10 weight enters this block.
# H-43 unexplained coincidence — the anchor / null. For this to be the answer, the
# proximity of m^2 and lambda to their critical boundaries is just an unforced draw of
# otherwise unrelated parameters, with no mechanism selecting it. Reference class:
# apparent fine-tunings and "large-number" coincidences in physics, a fair fraction of
# which have stayed bare accidents (or been dismissed as such) despite decades of
# mechanism-hunting. Anchored at unit weight; the more confident member because it posits
# no unobserved new physics.
w_coincidence = 1.0
# H-6 underlying principle — priced as odds against the coincidence anchor. For this to
# hold, some dynamical or statistical attractor (a multiverse distribution peaked on
# critical lines, self-organized criticality, or transplanckian dynamics pushing
# lambda(M_Pl) -> 0) must actually place the parameters near the boundary. The odds are
# built outside-view first, WITHOUT using this case's measured near-criticality (that is
# step 8's discriminating datum), so the prior mildly favours the null and lets the
# step-8 observations do the lifting toward H-6 if they warrant it.
r_base = 1.0 # reference-class odds: across fundamental-physics parameter near-coincidences,
# a genuine underlying principle is eventually confirmed about as often as the
# puzzle stays an accident — even odds, naturalness intuition offset by the weak
# historical track record of actually confirming such principles.
r_spec = 0.7 # downward adjustment: the specific mechanisms proposed for THIS case
# (multiverse self-organized criticality, transplanckian attractor) sit at the
# speculative end with no confirmed analog, and the source (Degrassi et al. 2012)
# itself flags H-6 as "explicitly speculative" — so shade below even in the prior.
w_principle = r_base * r_spec * w_coincidence
prior("HC-11", [w_principle, w_coincidence])