Analysis of HC-1 - Short-distance structure and fundamental scale of gravity

What the analysis says

The cluster asks whether the fundamental scale of gravity is within LHC reach, carving short-distance gravity into ordinary Planckian gravity (H-27), large flat extra dimensions (H-2, ADD/TeV-string), one warped dimension (H-4, RS1), and a residual (H-33). The prior [0.0524, 0.0429, 0.7937, 0.1111] puts ~79% on Planckian-standard, ~10% combined on the low-scale pair (odds p_lowscale = 0.12, a naturalness judgment with no reference class beyond “bold weak-scale solutions, none confirmed”), ~11% residual. The two wired-in discriminators — E-28 - O-7 × HC-1 — torsion-balance null down to tens of microns and E-29 - O-3 × HC-1 — TeV string scale survived all constraints known in 1998 — barely move it: posterior [0.0537, 0.0447, 0.7953, 0.1062]. The conclusion is essentially the prior; no observation did meaningful updating.

What the model may not capture

The largest gap is an absent discriminator. The cluster prose names “collider null results” as discriminating evidence, yet no such observation is wired into either likelihood block — the two edges are a sub-mm torsion null and a 1998 no-exclusion datum, both weak. The real empirical kill-shot on low-scale gravity — ATLAS/CMS 2010-2018 exclusions on M_D, KK gravitons, missing energy, no micro-BH production — is missing. Adding it (a step-8 edge) would push H-2/H-4 down and H-27 up far harder than anything present, so the current ~10% low-scale mass is likely overstated against the full evidence.

Second, E-28’s trust cap t = 0.3 inherits from S-30 (Plaga, trust 0.3), the paper O-7 was extracted from — though O-7 is a generally_known fact resting on Kapner et al. 2007, a rock-solid Eöt-Wash limit warranting near-full trust on its own provenance. This under-weights a firm physics limit. The practical effect on HC-1 is small: even at full trust, E-28’s lik_L_H2 = 0.82 (others ~1) shaves only H-2’s large-radius corner. Worth fixing for correctness, not because it flips this cluster.

Is the answer on the list? The members are genuinely exclusive geometries, but the low-scale branch rests on a naturalness motivation that weakened post-LHC once no BSM physics appeared — a shift the corpus-bound 1998 prior does not register. An unlisted low-scale completion (H-33) would be as consequential for the black-hole branch as ADD/RS1, so the residual’s ~11% is not harmless mass; it is the “scale could still be in reach by a route nobody named” hedge.

What would help

1. Direct LHC extra-dimension / micro-BH search limits (2010-2018) — exists, unread (unclear whether in-corpus); the biggest mover.
2. O-7 re-sourced to Kapner et al. 2007 / Eöt-Wash directly rather than via Plaga, lifting E-28’s t above 0.3 — exists, unread.
3. Post-LHC status of naturalness as the motivation for TeV-scale gravity — exists, unread.

Confusions and contradictions

Little irreducible conflict inside the cluster. Mild tension: E-28 nudges weakly against H-2 (large-radius corner) while E-29 nudges weakly toward H-2 (survival), pulling opposite ways on the same member, both too weakly to matter. The real oddity — prose asserting collider nulls discriminate while no such edge exists in the computation — has a nameable fix and so is a part-2 item, not a true contradiction.