STRUC-PERC-I
Full PRP Percolation Analyzer · Vulnerability Graph Engine
IDLE
v2.5.0 · UNNS Substrate Research Program · 2026
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
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BATCH RESULTS · REGIME TABLE 0 runs

# | File | n (gaps) | Verdict | Giant ratio | κ_conn | Isolated | Status
--- | --- | --- | --- | --- | --- | --- | ---

PERCOLATION SUMMARY · FULL PAIRWISE GRAPH
PHASE TRANSITION SIGNATURES EDGE DENSITY · GIANT COMPONENT RATIO · CONNECTIVITY THRESHOLD
SCALE TRACE & GRAPH VIEW LEFT: component count per κ-layer · RIGHT: vulnerability graph at κ* or κ_max
κ-LAYER TABLE · FULL PAIRWISE GRAPH PRIMARY OUTPUT

# | κ | ε | |E| full | density | mean deg | |C| full | giant ratio | Components (vertices) | In chain? | Chain-comp size
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---

GAP VECTOR Δ

i | Δᵢ | Δᵢ / med | vertex
--- | --- | --- | ---

FRAGMENTATION REPORT
OUTLIER REPORT Δᵢ > 10 × median(Δ)
ADAPTIVE κ EXTENSION BEYOND κ_max — PHASE COMPLETION PROBE
OPTIONAL — PATH-SUBGRAPH COMPARISON SECONDARY DIAGNOSTIC
NOT OPERATIVE — The path-subgraph (edges only between adjacent gap pairs) is shown for reference against STRUC-I v1.0.4 outputs. It is not the PRP manuscript graph and does not determine the percolation verdict. Differences between full-graph and path-subgraph component counts indicate the degree of non-local connectivity present in the gap structure.

# | κ | |E| path | |C| path | Components (path) | Δ|C| (full−path)
--- | --- | --- | --- | --- | ---

OPTIONAL — STRUC-I-STYLE LOCAL INVERSION PROXY DIAGNOSTICS LOWER-ORDER PROXY NOT USED IN VERDICT
PROXY ONLY — inv_C is computed as the count of adjacent descents within each full-graph component, acting as a lower-order proxy for the full pairwise inversion count of PRP Definition 3. ν_C reported here is the component-restricted admissible inversion capacity per the PRP manuscript; this instrument does not compute the full theoretical ν_C. These diagnostics are shown for STRUC-I alignment only and do not feed the percolation verdict.

# | κ | Comp | |C| | inv_C (adj proxy) | ν_C (not computed) | Local sat?
--- | --- | --- | --- | --- | --- | ---

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).