bare LLM
Claude · no anchor
Responds without Meta-Globàlium system prompt — natural prose, no canonical codes.
𝓗 harmonic
0.00
𝓦 wisdom
0.00
0/8 quadrants ·
0 codes
Same question. Three responses. Two metrics. The structural verifier projects each response onto the eight canonical poles of the Meta-Globàlium and computes 𝓗(r) ∈ [0, 1] (harmonic completeness, coverage) and 𝓦(r) ∈ [0, 1] (wisdom score, relational depth). 𝓗 catches breadth; 𝓦 catches whether the breadth is dialectical or merely listed — and exposes reward-hacking.
Responds without Meta-Globàlium system prompt — natural prose, no canonical codes.
System-prompted to traverse the 8-station cycle. Subtitles like "ANA — Analysis (FEN→TEO)" anchor mediators.
New system prompt v2: tension before synthesis, mediators as operations, closure of cycle. Codes load-bearing.
Tries to score high on 𝓗 by citing all 8 cardinals plus mediators — but with semantically empty filler. The honest test: does 𝓦 catch this?
𝓗 = 0.5·(n_quadrants/8) + 0.5·(entropy/log 8)
Counts how many of the 8 cardinals are touched and how evenly. A bare LLM with no anchored codes scores 0; an enumeration of all 8 cardinals scores ~0.97 — even if the content is empty.
𝓦 = 0.30·cov + 0.20·ent + 0.25·pair + 0.15·tension + 0.10·synth
Adds three relational components: dialectical pairs (poles of an axis in the same paragraph), tension markers ("yet", "however", "in tension with" near codes), and synthesis anchoring (mediators like SIN/AMO referencing what they integrate). 𝓦 is what catches reward-hacking that 𝓗 misses.
bare — Claude alone, no codes, no signal extractable.
list — system prompt v1: enumerate cardinals; high 𝓗, moderate 𝓦.
dialectical — system prompt v2: tension before synthesis; high 𝓗, high 𝓦.
adversarial — citations without substance: high 𝓗 (passes), low 𝓦 (caught).
api/verifier.php, api/wisdom_score.php). See opengea/arkadium for the source.