STRUC-PERC-I v2.5.0 — Full PRP Percolation Analyzer

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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BATCH MODE · MULTI-LADDER PROCESSING calls runAnalysisFromData() per ladder — zero engine modification

DELAY (ms)

MAX LADDERS

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Drop multiple .txt / .csv ladder files here or click to browse · one number per line or whitespace-separated · each file = one independent ladder evaluation

INSTRUMENT LOG

// awaiting input

THEORETICAL STATUS REFERENCE

NECESSARY DIRECTION ESTABLISHED
Non-percolation (full graph, strict continuity) ⟹ admissibility violation. Constructively verified via adversarial ladder programme. If this instrument reports NON-PERCOLATING, a USL violation is guaranteed at κ*.

SUFFICIENT DIRECTION OPEN CONJECTURE
Percolation (full graph) ⟹ admissibility. This direction is not proven. A PERCOLATING verdict is consistent with Conjecture 1 of the PRP manuscript. Admissibility must be confirmed independently via STRUC-I v1.0.4.

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).