arXiv subjects

Faruk Alpay

Publications and source records attributed to Faruk Alpay.

At least 37 records · Page 2Linked to original sources

arXiv2026

Service-Cut Certificates for Aligned Eviction in Tiered Cache Networks

In a tiered cache, eviction is a graph decision: removing one aligned storage block can disconnect downstream demand that never addressed that block directly, so request recency alone cannot price the action. This paper studies aligned eviction as a vertex-separation problem and gives a selection rule whose decisions carry independently checkable service-cut evidence. For every candidate block, it computes the exact weighted downstream demand cut, rejects actions that disconnect protected demand, and selects the minimum-impact admissible eviction. Reclamation is characterized as vertex separation: minimum-location reclamation reduces to node-capacitated flow, while minimum aligned block actions are NP-complete. In two-hop cache networks, one streaming pass evaluates every candidate impact; a matching adversarial construction proves that a history-only victim selector has unbounded one-step damage. The packet-scale implementation combines a seed-indexed exact-cardinality residency structure with collision-aware, 32-bank impact counters. Replay compression makes the result auditable: counter intervals reproduce the stream, exact monoid summaries retain every reported additive statistic, and a counting lower bound quantifies the state required by any exact all-candidate summary. A 144-scenario evaluation processes 582.90 trillion packets (404.86 PiB of simulated payload), validates the coordinate expectations, and exposes a zero-impact extreme-value transition near $Nζ=\log m$. Complete impact vectors, decoded audit samples, telemetry, and logs remain within the ancillary-file budget. Finally, invalidation is monotone replicated state: fair asynchronous delivery converges without coordination, with a diameter bound under synchronous full-edge rounds. The architecture therefore binds capacity reclamation, path continuity, and distributed invalidation to one certifying interface.

cs.DS↗

arXiv2026

Single-Event Upsets in 3D Gaussian Splatting Rendering: Bit-Level Criticality, Spatial Extent, and a Parallel Support Guard

Three-dimensional Gaussian splatting is a standard real-time scene representation increasingly deployed on hardware exposed to transient faults, such as spaceborne processors and robotic edge devices where silent data corruption occurs. A trained model is a large array of floating-point parameters in GPU memory, where a single-event upset corresponds to a single flipped bit. This paper measures these effects and constructs a defense. A GPU-resident parallel fault-injection engine applies over 3.8 million controlled single-bit upsets across four scenes, six fields, all bit positions, and three numeric formats (fp32, fp16, bf16), using 5.3 GPU-hours. The effect is highly concentrated: most upsets leave the image perceptually unchanged due to high redundancy, but a small set of high-order bits principally the logarithmic scale's sign bit enlarge a single primitive to cover up to 75.7% of the frame. A closed-form perturbation bound derived from the IEEE-754 layout and pipeline activations predicts this per-bit ordering. This concentration motivates a support guard: a per-primitive clamp of each parameter to the coordinate box observed during training, costing 76 us per frame. Over 768,000 guarded upsets, the worst corruption footprint is restricted to 11.68% of the frame. We prove the guard leaves clean models unchanged and prevents frame-covering corruption. Under an accumulated dose of 20,000 simultaneous upsets, the unguarded renderer degrades to 10.6 dB, whereas the guarded renderer remains at 21.8 dB. The corruption footprint also dictates the number of tile/compositing nodes contaminated in distributed renderers, where the per-node guard contains it.

cs.GR↗

arXiv2026

Compute-Budgeted Exploitability Evidence Graphs for Prospective Vulnerability Triage

Defenders cannot patch every newly disclosed vulnerability at once, so exploitability prediction must be evaluated prospectively rather than retrospectively. We study compute-budgeted vulnerability triage in which each CVE is scored only from public evidence visible by a fixed decision time. Advisories, exploit archives, fix commits, and hacker-community discourse are represented as a temporal evidence graph; a budgeted selector admits only a few evidence documents per CVE, and every score is paired with an auditable certificate listing the supporting signals, timestamps, source layers, and leakage flags. On 12012 prospective CVEs from public sources, budgeted evidence selection raises leakage-safe prospective recall@50 from 0.010 for a severity-only baseline to 0.026, while two evidence documents per CVE capture most of the value. A strong cross-encoder reranker lowers prospective recall to 0.016, showing that semantic relevance to a CVE is not the same as evidence of exploitation. Most importantly, a naive random split with unfiltered evidence inflates apparent prospective recall by 8.5x and EPSS-high recall by 5.0x. The main contribution is a leakage-safe evaluation protocol and reproducible evidence certificates for contestable vulnerability-prioritization claims.

cs.CR↗

arXiv2026

Guarded Epoch Bloom Filters for Sliding-Window Membership

Approximate membership queries in streams often need recent-window semantics rather than membership over all items ever seen. This paper studies guarded epoch Bloom filters, a sliding-window alternative to counting and stable Bloom filters. The structure partitions a fixed bit budget into rotating epochs, inserts only into the current epoch, clears whole segments at epoch boundaries, and keeps one additional guard epoch. This guard yields a deterministic live-window invariant: every item inserted in the last W positions remains represented, while rotation-induced stale retention is bounded by one epoch beyond the target window. We give the construction, prove its live-coverage and bounded-staleness properties, derive a false-positive approximation, and include a blocked variant that improves locality by confining probes to one block per epoch. Experiments cover 225 synthetic streaming configurations and 45 configurations from a timestamp-ordered web-server access-log stream. At 14 bits per live item, the guarded epoch filter reduces median synthetic false positives from 0.191 for a four-bit counting Bloom baseline to 0.02225 while preserving zero measured live-key false negatives. The method is not a replacement for exact deletion; it targets systems where bounded stale positives are acceptable but false negatives inside the live window are not.

cs.DS↗

arXiv2026

Repair Entropy in Dynamic Geometric Nearest-Neighbour Structures

We study dynamic geometric data structures for exact nearest-neighbour maintenance under small motions. For each point we store a certificate consisting of its nearest neighbour and the two smallest neighbour distances, with clearance $c_i=d^i_2-d^i_1$. A triangle-inequality argument gives a sharp validity radius: after a step of maximum displacement $\varepsilon$, every certificate with $c_i>4\varepsilon$ remains valid, so all possible failures are confined to a repair frontier $F_t$. We introduce repair-frontier entropy $H(F_t)$, the normalized Shannon entropy of failed certificates over index cells, as a workload descriptor for choosing between event-driven repair, batched repair, and full rebuild. The resulting maintenance rule repairs only the frontier in $O(|F_t|\log N)$ time under bounded cell occupancy, while a full rebuild costs $Θ(N)$; moreover, entropy lower-bounds the number of frontier cells touched by event-driven repair and shifts the empirical repair-rebuild crossover. We evaluate ten motion families in $d\in{2,3}$, with $N$ up to $16,000$, using an exact tiled GPU oracle and a GPU grid rebuild as ground truth and competitor. Across $2400$ labelled transitions, the validity rule misses no invalid certificate, low-pressure frontiers are usually cheaper to repair incrementally, and diffuse frontiers of the same size are more expensive for event-driven repair but not for batched repair. The released dataset records frontier geometry, certificate audits, per-strategy times, and best-strategy labels.

cs.CG↗

arXiv2026

Rendering Separoid Information: Rate-Distortion Reconstruction of Convex Apartness Scenes

A convex scene communicates more than shape: the pattern of which groups of objects are mutually apart and which cross is a discrete relational payload. We treat the apartness table of a finite family of convex bodies, a separoid, as a source signal; a renderable convex scene as its encoder; and the rendered image as a noisy visual channel from which the apartness structure is decoded. For disjoint index sets $A,B$, the source bit records whether $\operatorname{conv}(\bigcup_{a\in A} C_a)$ and $\operatorname{conv}(\bigcup_{b\in B} C_b)$ are disjoint. Within this view, apartness-preserving rendering becomes a rate--distortion problem: the rate is a differentiable geometric code length for the carrier scene, while the distortion is closure-aware and weights maximal separations and minimal Radon partitions by the number of consequences they control. A differentiable support-function realization turns separability into a soft directional margin and represents each separation by a distribution over witnessing directions, yielding a variational lower bound on apartness mutual information $I(Σ;Y)$ and an information-theoretic account of view selection. Experiments on planar convex scenes show that scenes are recovered from the apartness table alone at 99.9% bit accuracy, with the certificate skeleton already determining the full table; coordinate quantization gives a clean operational rate--distortion frontier where certificate distortion is more stringent than Hamming error; and rendered $48\times48$ images transmit about 0.72 of the apartness-graph entropy under mild noise. Increasing the viewpoint-robustness term widens separating cones with only a modest geometry-rate surcharge. The result is a certificate-aware rendering objective for scenes whose purpose is to make relational convex structure recoverable rather than merely pixel-faithful.

cs.GR↗

arXiv2026

Proof-Carrying Multimodal Timelines: Finite-Trace Modal Certificates for Video-Audio Consistency

Multimodal video systems often expose clip-level scores while hiding the local temporal failure that makes a video inconsistent. We formulate video-audio consistency as finite-trace modal monitoring over synchronized visual, audio, and subtitle/OCR atoms. A formula library specifies speech-speaker agreement, audio-visual event agreement, subtitle-video agreement, scene continuity, and edit-induced temporal shock. A certificate records the trace hash, formula identifier, verdict, violating indices, defect score, first counterexample window, execution engine, and certificate hash. The certificate is not a proof that a detector is correct; it is a reproducible witness that the finite-trace checker can independently reconstruct once the atom trace is fixed. The artifact decodes real MP4 video, extracts CLIP visual atoms, extracts AST audio atoms, runs dense counterfactual perturbation sweeps, emits CSV traces and JSON certificates, and renders manuscript figures from those files.

cs.MM↗

arXiv2026

Renderable Partial Representations for Dynamic Gaussian Splatting under Incomplete Delivery

Dynamic Gaussian compression is normally optimized for complete files or complete progressive prefixes, but interactive rendering encounters partial representations: some spatiotemporal regions are present, others missing, and late refinements cannot affect the displayed frame. We study dynamic Gaussian representations whose incomplete delivery states remain directly renderable and whose degradation is optimized in image space. Gaussian primitives are organized into independently addressable spatiotemporal clusters with a base level and three refinements; training samples partial dependency graphs, renders many counterfactual states in one GPU batch, and minimizes expected distortion, tail distortion, temporal inconsistency, rate, and prefix regressions. A counterfactual utility layer measures the marginal render contribution of each completion group across valid receiver contexts. The same graph admits a concrete delivery realization with MTU-bounded entropy-coded chunks, deadline-aware scheduling, and receiver-side dependency closure. On held-out views, the finest refinement has negative mean marginal utility in 3/32 D-NeRF bouncingballs, 49/64 HyperNeRF broom2, and 28/64 HyperNeRF chicken clusters; its lower-tail utility is negative in 21/32, 61/64, and 42/64 clusters, respectively. On broom2, render-utility ordering removes both PSNR regressions produced by nominal layer order at matched byte budgets; on chicken, utilities measured on disjoint training cameras improve held-out PSNR by 3.03 dB at the lowest matched budget. These scoped results show why nominal refinement order cannot substitute for render-conditioned utility: the formulation treats network delivery as a distribution over renderable scene states rather than as an external wrapper around a graphics codec.

cs.GR↗

arXiv2026

GPU-Accelerated Search and Certification of Bounded Indistinguishability in Finite Kripke Semantics

We study finite Kripke semantics as an explicit search and certification problem for modal formulas. Sets of worlds are encoded as integer bitmasks, so Boolean connectives, $\Box$, and $\Diamond$ reduce to word-level containment and intersection tests. This gives a deterministic evaluator with an independent certificate checker, then scales it through a fused CUDA kernel for exhaustive small-frame scans. Over $K,T,S4,S5$, a corpus of 5,624 formulas is evaluated on all frames through five worlds, performing $1.63\times 10^{14}$ formula evaluations in 45 minutes on one H100. All 20,990 emitted countermodel certificates verify. In this bounded corpus, every $K$-refutable formula has a countermodel on at most two worlds, far below the standard filtration bound $2^{|\mathrm{Sub}(φ)|}$. We then turn pairwise formula equivalence into a minimal-countermodel problem for biconditionals and synthesize semantic mirages: formulas that agree on every model up to a finite size and split only later. In particular, $α_2=(\Box\Diamond)^2\top$ and $α_3=(\Box\Diamond)^3\top$ agree on all frames of at most five worlds but are separated by a checked six-world path. Finally, we build a density-aggregated semantic atlas for representation-guided candidate retrieval and compare raw features, PCA, UMAP, spectral layouts, and random layouts under a common million-pair verifier budget. The result is a reproducible bridge between modal finite-model theory, GPU enumeration, certificate checking, and graphics-supported semantic exploration.

cs.LO↗

arXiv2026

Comparison Patrols on Drifting Orders: Certified Rank Maintenance, Evolving Planar Maxima, and Selection under Drifting Fitness

Rank-based selection in dynamic environments acts on order information that becomes stale while it is being used. Tournaments, elitism, truncation, and Pareto selection may therefore consume rankings that no longer match the current fitness order, while full re-evaluation competes with search for the same budget. This paper formulates the missing information layer as a data-structure problem. A hidden total order on $n$ items drifts by adjacent transpositions, while a maintainer receives one truthful pairwise comparison per step and must answer rank queries continuously. We introduce the comparison patrol, a constant-time maintained-order structure using $3n+O(1)$ words, one comparison per update, deterministic verification-age bounds, and per-item displacement certificates. We prove lower bounds showing that oblivious and location-oblivious maintainers incur expected Kendall error $Ω(\min(α,1)n)$, and show that the patrol operates at the same order. A bump invariant yields exact self-stabilization after drift-free corruption: if the maximum rank overstatement is $L$, recovery takes at most $L$ aligned cycles and cannot finish before $L-1$. This gives a deterministic shock-recovery calculus and a crossover with full rebuild near $L\approx \log_2 n$. The maintained order is then transferred to evolving planar maxima and to evolutionary selection rules, giving deterministic bounds for truncation, tournament, elitist, and two-objective Pareto decisions under drifting fitness. Experiments up to $n=65{,}536$ audit the certificates, recovery laws, equilibrium behavior, and equal-budget dynamic evolutionary loops, identifying when certified local rank maintenance outperforms global re-evaluation and when it should hand over.

cs.DS↗

arXiv2026

Split Tallies: A Discrete Certificate Calculus for Auditing Dynamic Ordered Sets in Constant Memory

We study retrospective auditing for dynamic ordered sets maintained by an untrusted party. A passive auditor watches insert, delete, membership, predecessor, successor, min, and max operations, stores five machine words and a flag, and receives a constant-size public tally record per operation. At audit time the maintainer discloses the claimed live vacant intervals. The method represents order semantics by maximal gaps: gaps are born, cited, consumed, and timestamped, while two hidden field accumulators test equality of the birth and consumption ledgers. Honest executions are accepted with probability one. If any answer in a T-operation session is wrong, acceptance occurs with probability at most (4T+1)/p over one secret field element, against computationally unbounded maintainers. We prove that deterministic and visible-coin auditors require linear state, and that removing the timestamp rule permits an exact replay forgery. A leaf-oriented (2,4)-tree implements the maintainer in O(log n) worst-case time per operation with one extra word per element, and its rebalancing events admit an auditable O(m) envelope over m updates. Checkpoint audits compose with additive error.

cs.DS↗

arXiv2026

Choric Masking in Ambient Release Systems: A Finite Certificate Calculus for Trace Indistinguishability under Bounded Audiences

This paper develops a finite certificate calculus for ambient release systems, staged probabilistic environments in which a protected coordinate is not observed directly but can remain statistically readable through visible roles, timing, repeated movement, bounded attention, linked rooms, and post-release state. The security notion, choric masking, requires the trace law induced by a protected locus to lie inside or near the convex hull of admissible cover traces under the tests available to a specified audience. For finite horizons, trace laws form polytopes, audiences induce measurement operators, and masking becomes intersection in the projected measurement space. Exposure is certified by separating hyperplanes, kernel obstructions, hypothesis-testing bounds, Fano-type localization lower bounds, and support separation in downstream rooms. The calculus distinguishes trace residue from carrier localization, full-trace exposure from attention-filtered exposure, first-room masking from delayed post-release exposure, and unresolved system pressure from carrier hazard. It proves measurement-polytope equivalence for exact and approximate masks, dual separation certificates, data-processing laws for attention lenses, aperture identities for gaze-thinned observation, lower bounds for mandatory unique gestures, composition rules for linked releases, and a repeated-room debt theorem showing how unresolved pressure can broaden selection and shift cost onto cover populations without localizing the source. The result is a finite, checkable language for auditing privacy, unlinkability, side-channel leakage, and accountability in public-facing release systems.

cs.CR↗

arXiv2026

A Calculus of Apartness over Separoids: Effective Convex Representation, Stratified Conservativity, and the Complexity of Entailment

Every finite family of compact convex bodies in Euclidean space induces an apartness relation between disjoint index sets: two sets are apart when the convex hulls of the corresponding unions are disjoint. This paper studies the finite theory obtained by taking apartness as the primitive relation. Its basic laws are symmetry, bilateral subsumption, and vacuity, equivalently the separation-polarity form of acyclic separoids. The main contribution is an effective rational realization theorem with uniform margins and the exact consequence theory it supports. Every finite apartness separoid is realized by rational polytopes whose coordinates are indexed by maximal separations. Maximal separations and minimal Radon partitions can be enumerated from a full table, generators, or a membership oracle; the coordinate values have controlled bit height; and each coordinate records a readable certificate of one maximal separation. The realization separates every apart pair with clearance at least 2, remains correct under outer parallel enlargement by any radius below 1, and yields full-dimensional convex bodies after thickening. The distance-function layer records standard convex-analytic stability through Lipschitz comparison, monotonicity under inclusion, and outer parallel bodies. On the logical side, positive entailment is exactly one-premise subsumption. Boolean consequence over Euclidean scenes is sound, complete, and decidable; satisfiability is NP-complete, validity is coNP-complete, and positive entailment is linear for sorted encodings. A stratification theorem shows that Boolean reasoning introduces no new atomic apartness beyond separoid closure. Fixed-dimensional consequence relations form a strictly decreasing hierarchy that stabilizes in dimension n minus 1 for n sites.

cs.LO↗

arXiv2026

Layer Order Semantics for Automata-Based Cybersecurity

Layered cybersecurity pipelines transform evidence before they decide on it, and the order of those transformations determines which security facts become visible to which layer. This paper gives layer order a finite-state semantics built from a layer-order automaton, deterministic sequential security transducers, evidence markers, and a final decision automaton. The worked case is HTTP request desynchronization: front-end and back-end processors compute incompatible request boundaries, and the same trace is detected or missed according to whether framing evidence reaches the parser-differential layer before it commits. The results separate completed-trace recognition, online editing, decision synthesis, and faithful enforcement; characterize faithful online enforcement as the regular prefix-closed case under causal visibility; and show that regular policies beyond that boundary remain recognizable without becoming deployable enforcers. The framework is monolithically equivalent to finite-output deterministic edit automata, while preserving layer-local invariants such as marker birth, marker survival, and reorder-sensitive visibility. A concrete parser-pair semantics identifies the forbidden marker factor with CL.TE, TE.CL, TE.TE, and HTTP/2-downgrade boundary disagreement under the stated abstraction, and a contextual reorder congruence classifies which component permutations induce the same decision language. The result is an automata-theoretic account of order-sensitive security failures and a compositional vocabulary for auditing, synthesizing, and comparing layered enforcement pipelines.

cs.CR↗

arXiv2026

Value-Refined Modal Fixed-Point Semantics with Certified Choice and Public Share-Alike Certificates

This paper presents a finite modal semantics where truth is closed under admissible continuation, then refined by discounted value, and finally certified by residual tests. The admissibility kernel is the classical greatest fixed point of a one-step predecessor expressing that some choice cell has all compatible successors inside a set. Certified choices are exactly local witnesses; the discounted value transformer is defined only over those witnesses; value-refined modal bisimulation is the coarsest local equivalence preserving formulas, kernel, certified choices, Bellman values, greedy sets, residual certificates, and public release certificates. A canonical pseudometric refines this equivalence: it is the unique fixed point of a Hausdorff-lifted choice-matching transformer over certified choices; its zero set is the value-refined bisimulation, and the optimal discounted value is one-Lipschitz with respect to it. Any approximate quotient incurs only a distance-bounded value error. Branching choice-cell and locus presentations place choice inside the model; the transition presentation is a conservative retraction. The same engine is applied to a public share-alike release fragment: attribution as label preservation, same-license propagation as derivative closure, no downstream restriction as admissibility, and the BY-SA witness as a residual-stable certificate. Finite examples show that altering the order of truth, admissibility, value, quotienting, public derivation, and certification changes the semantics.

cs.LO↗

arXiv2026

The Cascade Log: Reference-Stable Windowing over Tiered Append Sequences

A long-running append-mostly sequence, such as an edit log, event store, or versioned working set, is usually tiered into a bounded hot stratum and colder folded summaries. This saves memory but breaks stable references: a handle minted while a record is hot may later be resolved after the record has moved into a digest, after it has been superseded, or while a fold is in flight. We define the resulting cross-tier anomalies--dangling, stale, corrupt, and snapshot-skewed resolution--and present the Cascade Log, a reference-stable tiered append structure. The structure keeps a single persistent coalescing interval map over handles as the sole authority on each live version; folding a contiguous run replaces many singleton entries by one digest-backed interval node, and immutable roots provide snapshot tokens. Its cost is characterized by the fragmentation $A$, the number of index pieces, namely live handles plus maximal same-digest runs. The index uses $Θ(A)$ space, resolves a point in $O(\log A)$, reports a $k$-handle range in $O(\log A+k)$, and performs $a$ appends and $s$ supersedes in $O((a/B+s)\log A)$ update work for fold block size $B$. Matching lower bounds show that $Ω(A)$ space and $Ω(\log A+k)$ ordered range cost are unavoidable, and an adversary can force $A=Θ(s)$. Thus the index is sublinear on append-dominated histories and grows linearly only under fragmenting edits. A reference implementation and reproducible experiments to $10^6$ records validate the anomaly-freedom and the fragmentation bounds.

cs.DS↗

arXiv2026

Quantifying Side-Channel Leakage in Public Metrology Releases

Public scientific and metrology releases can leak the hidden settings that produced them. We formalize and quantify this risk as a profiled statistical side-channel audit: a release map exposes finite-band statistics of a power spectral density (PSD), a profiled observer trains labeled template spectra under an explicit budget, and a challenge release is drawn from one of two utility-equivalent recipes separated by a protected coordinate. Averaged PSD bins follow a gamma channel, replaced by a covariance-weighted log-spectrum channel when the bins are correlated; this yields exact Kullback-Leibler divergences, Chernoff exponents, protected-bit advantage bounds, and finite-training, finite-library, finite-compute, and model-mismatch corrections. Our headline result is a finite-band transport-leakage law: after amplitude and blur are eliminated, the protected acid-transport information obeys $I_{λ|α,β}(K) = (64/1225)\, w λ^{6} K^{9} + O(w λ^{8} K^{11})$ for $Kλ\ll 1$, a ninth-order exponent with a closed-form safe band. A step-by-step protocol turns a measured release into these numbers, and a fixed-seed reproducibility package regenerates every table and figure. We instantiate the audit on screened extreme-ultraviolet (EUV) roughness spectra as a model-conditioned case study, with deployment on measured releases the next step.

cs.CR↗

arXiv2026

Finite Certificates for In-Context Determinacy and a Threshold Theory of Emergence in Language Models

This paper develops a model-theoretic framework for verifying context-conditioned language-model behavior by replacing benchmark labels with finite semantic certificates. The first problem is finite determinacy: when do examples in a context force the answer to a query without changing model parameters? In finite-field linear task families, we prove an exact row-space criterion, compute the residual hypothesis count, derive full and query-local identification curves, and show that extracting a smallest forcing subcontext is NP-complete even for binary outputs. The second problem is threshold emergence: when does an apparent benchmark jump reflect a semantic transition rather than a discontinuity of the scoring map? We prove an anti-mirage theorem separating thresholded metrics from semantic confidence and give a rate-sensitive crossing bound for latent commitments becoming visible above threshold. The common semantic object is a confidence functional on definable events. We show that it is a Boolean probability measure, equivalently a Keisler measure on the relevant type space, whose measure-one formulas form a proper filter and whose Stone-space representation is invariant under definitional expansion. The resulting calculus provides finite context certificates, pair-separator hitting sets, query teaching dimension, prompt-preservation criteria, and scale-limit witnesses. Exact-arithmetic ancillary scripts reproduce the finite-field and threshold calculations and generate the data used by the figures.

cs.LG↗