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arXiv · 2607.04070

Conductance-Repair Evidence Graphs for Prospective Security Retrieval

Faruk Alpay·Taylan Alpay
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Abstract

Security retrieval is often evaluated as ranking over complete evidence, but operational triage is prospective: CVE descriptions, weakness metadata, fix commits, EPSS scores, KEV membership, validation-vector metadata, and side-channel benchmark routes arrive through separate channels, and many are missing, delayed, poisoned, or visible only after the decision time. We introduce conductance-repair evidence graphs, a timestamped framework in which retrieval is performed over a temporal admissibility mask and missing channels are widened by a deterministic graph-flow recurrence rather than by a learned predictor. The method emits a repair certificate recording source probes, decision time, withheld edges, repaired channels, forbidden post-decision edges, backend availability, numerical deviation, and verifier results. The theoretical layer gives an adaptive \(\lceil\log_2 N\rceil\) lower bound for missing-channel identification, an NP-hardness result for minimum harmful repair, and a fixed-parameter certified search bound for \(q\) questionable channels. The current artifact materializes 30 deduplicated public security records, 57 terms, and 58 withheld admissible document-term edges. Under random edge withholding, conductance repair changes recall@\(k\) from 0.017 to 0.069 and average precision from 0.062 to 0.060, while a synthetic security fixture improves recall@\(k\) from 0.055 to 0.099; the public AP drop exposes a limit of broad admissible repair under random edge corruption. The implementation benchmarks the same flow/SVD/einsum kernel under NumPy, PyTorch, JAX, and TensorFlow when available, recording unavailable backends rather than silently substituting them. BBBC019 and LIVECell metadata are retained only as structural controls for sparse evolving source channels, with no clinical or biological performance claim.

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Faruk Alpay, Taylan Alpay. 2026-07-05. Conductance-Repair Evidence Graphs for Prospective Security Retrieval. https://arxiv.org/abs/2607.04070

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