Papers and articles

preprint/paper/2026-09-29

We study permutations obtained by reading increasing ordered trees in breadth-first order. For every integer k >= 2, a 312-avoiding permutation is realizable on a tree of maximum outdegree k if and only if it is realizable on the complete k-ary heap shape. A 231-avoiding permutation of length congruent to 1 modulo k is realizable with maximum outdegree k if and only if it is realizable on a full k-ary tree. Both proofs use the nondecreasing sequence of BFS parent positions. The binary specializations prove three identities between OEIS sequences, including A245899 = A246747. For 321, heap collapse first fails at length 4, while full binary collapse first fails at odd length 11, with 8095 unary-binary words and 8048 full binary words. The artifact supplies 28 additional sequence entries relative to the recorded baseline, the complete 47-word counterexample set, executable enumeration and verification programs, and Lean 4 proofs. The binary results are formalized on inductive trees; the arbitrary-k arguments are formalized over parent sequences. Exponential growth rate 4 follows from Defant's heap-growth theorem.

preprint/paper/2026-09-29

Trace retention is an incomplete predictor of observability cost: a sampler changes where work is avoided, how spans are grouped for export, and which evidence remains available. We study these effects in OpenTelemetry Collector Contrib v0.136.0 on one shared node with loopback transport. Five randomized blocks cross sampler placement with export path at 40,000 offered spans/s. Native uniform sampling at nominal 10% retention increases Collector CPU by 3.2% with JSON-only export and reduces it by 24.2% with JSON plus Jaeger. A pre-ingress gate retains identical trace IDs but avoids ingestion and excludes selection work from the Collector endpoint. Retain-all controls show that stateful release changes batching and CPU without discarding traces. A short-timeout CPU reduction at 250 spans/s disappears at 5,000 spans/s, where tail increases CPU at both tested timeouts. A separate SDK comparison, load sweep, and delivery probes distinguish application work, Collector resources, and complete evidence delivery. An illustrative localization task uses measured HTTP timings and ideal offline sampling without an SDK or Collector. Its results show how window size and selection-dependent reference evidence affect a fixed median-change scorer, conditional on the observed corpus. The study supports evaluating sampling at explicit component boundaries, measuring batching and serialization alongside trace counts, and defining the diagnostic evidence objective before selecting a rate. The research archive preserves frozen protocols, raw observations, failed attempts, and executable checks.

preprint/paper/2026-09-25

Consumer-progress acknowledgments in Redis Streams and NATS JetStream have different persistence implications even under always-synchronize append policies. We evaluate that distinction alongside recovery timing, consumer concurrency and publication cost using single-replica deployments on a two-node Kubernetes homelab. The study compares Redis 7.4.2/8.10.2 and NATS Server 2.10.24/2.15.0, preserving an original campaign and adding three deployments with fresh broker processes and stores, matched publication durations, CPU sensitivity and storage diagnostics. All 240 active follow-up recovery episodes completed, including live, deliberately unacknowledging consumers; twelve plain Redis read controls remained pending. Receipt timing followed residual eligibility plus policy-dependent excess. Redis's integrated CLAIM path exhibited greater excess than the tested explicit reclamation loop in this quiet, one-message workload. Sixteen consumers increased current memory/periodic drain throughput by 10.43–14.49 times across deployment-specific comparisons, while cycle p99 increased and driver capacity affected rates. At sixteen publishers, current periodic/memory publication ratios averaged 0.8257 for Redis and 0.8207 for JetStream. Ten of 72 planned always-profile publication trials failed (13.9%), including four warm-up failures, compared with one of 72 periodic trials and none of 72 memory trials. Timed failures returned five-second client timeouts with unknown confirmation outcomes. A compact analytical model and selected Lean-checked statements delimit the claims; full proofs and detailed results are included in the appendices. The licensed artifact retains timings, failures, configurations and reproducible analysis. These observations characterize specified policies and acknowledgment costs; they do not establish equal durability contracts, power-loss survival or hardware-independent rankings.

independently published/paper/2026-09-08

A backend application needs a composition model as well as a request handler. Its components must declare dependencies, initialize shared resources, expose routes, and coordinate operational behavior. Nidus organizes these responsibilities through explicit modules, typed providers, and controller metadata, while retaining Axum routing, Tower middleware, and Tokio execution. This paper explains the design through three separate stages: generated Rust declarations, application construction, and request execution. It describes the guarantees provided at each stage, follows a small feature from module declaration to handler invocation, and identifies the costs and limits of the abstraction. The implementation uses a runtime container keyed by Rust types and validates module structure during bootstrap. Module exports describe composition contracts; they do not enforce runtime access isolation. The account is anchored to Nidus 1.0.17 and supported by source inspection and focused executable checks.

independently published/paper/2026-07-06

A technical white paper on Locus, a domain memory pool for CPU LLM serving whose remote-free path is a per-worker lock-free chunk mailbox: a finished request's KV blocks are returned as one atomic push, and the pool owner drains every mailbox off the allocation hot path, so freeing never contends on a shared queue and the design carries zero tuning parameters. Developed under a falsification-first methodology, it is evaluated on LOCUS-EVAL v1, a frozen four-workload suite of deterministic serving-shaped KV traces run against jemalloc, mimalloc, and system malloc on Apple Silicon, where the mailbox ranks first on every workload. A self-critical touch-parity audit corrects the headline: at a one-byte-per-block parity the advantage is 1.6x to 2.7x over mimalloc on the three trace workloads and compresses to about 1.15x over system malloc once full KV writes dominate, with a transient burst-cancellation footprint of up to 1.5x the theoretical peak. The scope is deliberately narrow (a single macOS host, synthetic traces, an allocator-level measurement), with NUMA locality and end-to-end serving integration stated as future work.

independently published/paper/2026-06-07

A technical white paper documenting Purple Wolf's Rust workspace architecture, request normalization path, detector groups, policy semantics, Traefik http-wasm adapter, audit relay protocol, release surfaces, related WAF systems, and committed benchmark results against the Coraza http-wasm Traefik plugin.

independently published/paper/2026-06-07

A position paper proposing STRUT, an idempotent but unsafe HTTP method for server-driven, minimal-input resource creation. The paper defines candidate semantics, compares the method with POST plus Idempotency-Key, conditional PUT, WebDAV, and Prefer, and discusses security, caching, intermediaries, browser behavior, and deployment.