STRUC-PERC-I v2.4.0 — Full PRP Percolation Analyzer

MEASUREMENT SCOPE — This instrument measures realizability structure: connectivity class, giant ratio, fragmentation, and κ-connectivity. It does not directly compute admissibility or USL violation. Use STRUC-I v1.0.4 for admissibility evaluation.
ENGINE MODEL — This instrument implements the true full pairwise vulnerability graph of the PRP manuscript: vertices index gaps Δᵢ; edges (i, j) ∈ Eκ whenever |Δᵢ − Δⱼ| ≤ ε(κ), where ε = κ · IQR(Δ) (fallback: κ · median(Δ) when IQR = 0). No window cap. No gap-value floor. Every pair within ε is an edge; the sliding-window + union-find correctly computes connected components in O(n log n + n·w̄) per layer. Connected components, percolation chains, and κ* fragmentation scale are derived from this graph. Strict no-reset continuity is enforced. Path-subgraph comparison is shown as optional secondary diagnostics only. When n exceeds the hard cap (200k gaps), downsampling is applied and the result is labelled APPROXIMATE — Theorem 1 is not assertable on surrogate ladders.

LADDER INPUT

ELEMENTS x₁ ≤ x₂ ≤ … ≤ xₙ (space or comma separated, n ≥ 3)

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Drop file here or click to browse · .txt / .csv · one number per line or whitespace-separated

κ GRID POINTS

κ MIN

κ MAX

DOMAIN ADAPTER

PRESET

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INSTRUMENT LOG

// awaiting input

THEORETICAL STATUS REFERENCE

RESTRICTED NECESSARY DIRECTION ESTABLISHED EMPIRICALLY
Only HARD-class persistent fragmentation is associated with the existence of deformations producing USL violation (revised PRP, Theorem 1). The original general claim (non-percolation ⟹ violation) is refuted: TAIL-class non-percolating ladders can remain fully admissible. This instrument measures realizability; admissibility must be evaluated independently via STRUC-I v1.0.4.

SUFFICIENT DIRECTION OPEN CONJECTURE
Percolation ⟹ admissibility: not proven. A percolating verdict is consistent with Conjecture 1 of the revised PRP but does not certify admissibility. Realizability and admissibility are independent structural coordinates (Dual Observability Theorem). Confirm USL status via STRUC-I.

GRAPH MODEL
Full pairwise: (i,j) ∈ Eκ iff |Δᵢ − Δⱼ| ≤ ε = κ · IQR(Δ) (fallback κ · median when IQR = 0). Components are arbitrary vertex subsets, not restricted to contiguous runs.

CONTINUITY + SPANNING
Strict no-reset: chain must be continuous from κ_min to κ_max. Additionally, the chain must span ALL n gap-vertices by κ_max — equivalently G_{κ_max}(L) must be connected. Two distinct failure modes: (A) mid-chain break, or (B) permanent fragmentation (isolated vertex groups whose |Δ| >> ε_max at all tested κ).