structure

Cluster inventory (step 4b)

The structured hypothesis layer for the run’s question: “Was the risk that LHC collisions destroy the Earth (via stable micro black holes or other proposed mechanisms) truly put to rest, and what does that conclusion hinge on?”

1. HC-1 - Short-distance structure and fundamental scale of gravity — What is the structure and fundamental scale of gravity at short distances — is the quantum-gravity scale within LHC reach? (H-2, H-4, H-27, H-33)
2. HC-2 - Dominant collider manifestation of low-scale quantum gravity — If the quantum-gravity scale lies within collider reach, what would LHC collisions dominantly produce and show first? (H-3, H-5, H-15, H-34)
3. HC-3 - Nature and decay of an LHC-produced strong-gravity object — If an LHC collision produces a strong-gravity object, what is it and how fast does it decay? (H-7, H-10, H-14, H-24, H-35)
4. HC-4 - Fate of the Earth under a hypothetically stable trapped black hole — If a stable or long-lived LHC black hole were captured inside the Earth, what would happen? (H-8, H-22, H-36)
5. HC-5 - Accretion law for a small mass in an ambient medium — At what rate does a small trapped mass accrete from a surrounding medium? (H-16, H-38)
6. HC-6 - Origin of the UHECR spectral structure — What produces the observed structure — ankle, instep, and suppression — of the ultra-high-energy cosmic-ray spectrum? (H-9, H-12, H-21, H-37)
7. HC-7 - Stability of bulk strange quark matter — Is bulk strange quark matter absolutely stable at zero external pressure? (H-28, H-39)
8. HC-8 - Runaway growth of a stopped negative strangelet — Would a stopped negatively charged (meta)stable strangelet grow without limit by absorbing nuclei? (H-29, H-40)
9. HC-9 - Existence of a catalyzing GUT-monopole flux — Does a cosmic flux of GUT monopoles catalyzing nucleon decay exist at astrophysically relevant levels? (H-20, H-41)
10. HC-10 - Stability status of the electroweak vacuum — Is our vacuum a metastable false vacuum that can decay by bubble nucleation? (H-31, H-42)
11. HC-11 - Origin of the near-criticality of the Higgs potential — Why do the measured Higgs-potential parameters lie so close to the stability-metastability boundary? (H-6, H-43)
12. HC-12 - Stiffness of the cold supranuclear equation of state — What is the equation of state of cold matter at supranuclear densities? (H-1, H-44)
13. HC-13 - Validity of general relativity in the strong-field regime — Does general relativity correctly describe gravity in the strong-field regime of massive neutron stars? (H-13, H-45)
14. HC-14 - Locus of the residual LHC catastrophe probability — Is the all-things-considered LHC catastrophe probability dominated by the chance that the safety arguments themselves are flawed? (H-11, H-46)

Structure notes

The black-hole branch is a production ⇒ decay ⇒ consequence chain, kept as separate conditional clusters with the chain recorded in depends_on (HC-2 ← HC-1; HC-3 ← HC-1, HC-2; HC-4 ← HC-3, HC-5) rather than folded into combination clusters. The strangelet branch chains HC-8 ← HC-7 the same way. HC-6, HC-12, HC-13 carry the astrophysical legs (cosmic-ray flux reality/composition; neutron-star-survival bounds) of the safety arguments; HC-12 ← HC-13 because the mass measurements assume GR. HC-14 is the meta-level “what does the conclusion hinge on” cluster. Binary clusters use constructed complements and are exhaustive by construction; open-ended clusters carry one residual each, listed last.

Counts

1. H in (from step 3): 32
2. active after 4a: 24 (8 merged, 0 dropped)
3. minted at 4b: 14 (5 residual, 9 constructed complements)
4. active after 4b: 38
5. clusters: 14

generated: 2026-07-22