Software Diagnostics Library

The Trace Multiphysics analysis pattern applies several Trace Fields to the same sequence of trace messages and studies both their individual strengths and their interactions. A Trace Field associates every message in a trace domain M with a value in some analytical range T. Although the field is defined over M, its values need not be extracted solely from that trace. A value may be derived from the message itself, inferred from its surrounding context, or assigned using correlated evidence from other traces, logs, metrics, memory dumps, snapshots, models, or external knowledge sources. The value does not need to be numerical, although numerical or ordered values are useful when field strength must be visualized. For example, one field may represent execution significance, another resource pressure, and a third semantic or user-visible importance:

However, Trace Multiphysics is not merely the display of several independent Trace Fields: its essential feature is their coupling. A change in one field may affect another field. For example, increased resource pressure may slow execution. Slower execution may trigger retries. Repeated retries may further increase resource pressure. Eventually, the combined effect may change the semantic or user-visible outcome. The coupling diagram represents these relationships, and arrow thickness indicates coupling strength:

A simple conceptual form is: C_ij​(m)=g(f_i​(m), f_j​(m), R_ij​(m)), where f_i​: M → T_i and f_j​: M → T_j, f_i(m) and f_j(m) are the strengths or values of fields i and j at message m, C_ij(m) is the coupling between fields i and j at message m, and R_ij(m) represents evidence of an interaction between the two fields, obtained from the trace itself or from correlated diagnostic sources. This formula defines coupling at message m. More generally, a coupling may relate field values at different messages when the influence is delayed or propagated through the trace: C_ij​(m_a, m_b)=g(f_i​(m_a), f_j​(m_b), R_ij​(m_a, m_b)), where m_a ⪯ m_b. Here, R_ij​(m_a, m_b) represents evidence relating the value f_i(m_a) of field i to the value f_j(m_b) of field j, whether that evidence is contained in the primary trace or supplied through correlated artifacts. High values in two fields do not automatically establish strong coupling. The available diagnostic evidence must also support the conclusion that one field influences, constrains, amplifies, transforms, or explains the other. Such evidence may occur in the primary trace or in correlated traces, logs, metrics, snapshots, models, or other diagnostic artifacts:

The mapping f_i is defined over the trace domain M, but its construction may depend on evidence outside M. A more explicit form is: f_i(m) = h_i(m, E_i(m)), where E_i(m) is the evidence associated with message m. This evidence may come from the message itself, nearby messages, other traces or logs, metrics, snapshots, memory dumps, learned models, or other correlated diagnostic sources. Correlation may be established through timestamps, identifiers, causal links, shared entities, execution context, or other relations.

When no ordinary field value can be assigned, T_i may include special values representing unknown, unavailable, or not applicable, preserving the definition of the field over the complete trace domain.

In computational modeling, multiphysics simulation studies several aspects of a physical system and their interactions simultaneously. A model may combine thermal, structural, fluid, electromagnetic, or other processes, together with the coupling and boundary conditions between them. Trace Multiphysics transfers this structural principle to software diagnostics. The analogy does not imply that all software behavior should be described by physical equations. Instead, it provides a disciplined way to analyze several interacting dimensions without reducing the incident to one isolated perspective.

The connection is especially appropriate in software diagnostics because software can be its own model. Software execution states and execution artifacts can be copied, preserved, replayed, or analyzed independently. Traces, logs, metrics, memory dumps, and snapshots are symbolic and digital artifacts produced by the software system itself. In this diagnostic sense, software performs a form of self-simulation: its execution generates artifacts that model selected aspects of its own structure and behavior. A trace is not a complete reproduction of the running system. It is a selective, instrumented self-model. Different Trace Fields map messages in that self-model to values in different analytical ranges, each representing a distinct analytical dimension. Some values may be extracted directly from the trace, while others may be inferred, enriched, or projected from correlated traces, logs, metrics, memory dumps, snapshots, models, or external knowledge. Trace Multiphysics studies those fields together and examines how they interact. Thus, multiphysics simulation models several interacting physical processes, whereas Trace Multiphysics analyzes several interacting fields defined over a software-generated model of software behavior and potentially enriched from other diagnostic sources.

Trace Field provides the foundational assignment or mapping from trace messages to values in one analytical range. The field is defined over a selected trace domain, but the evidence used to assign its values may originate inside or outside that domain. Trace Multiphysics extends this principle by applying several Trace Fields to the same trace domain and analyzing their simultaneous values, changing strengths, overlap at individual messages, dependencies, feedback loops, coupling strengths, and combined explanatory effects. The relationship can be summarized as follows: Trace Field maps trace messages to values in one analytical range, while Trace Multiphysics studies several coupled Trace Fields defined over the same trace domain, with their values potentially derived from or enriched by evidence from multiple diagnostic sources.

Trace Multiphysics also connects to several recent analysis patterns. In Trace Reactance, inductive and capacitive effects can be understood as specific forms of inter-field coupling and temporal distortion produced by interacting state fields. Karnaugh Map is also multidimensional but primarily Boolean and combinatorial, whereas Trace Multiphysics accommodates continuous or graded fields, propagation, and feedback loops. Trace World may provide a broader shared diagnostic context in which coupled Trace Fields are interpreted. Bethe Ansatz is a constrained form of Trace Multiphysics in which global behavior is reconstructed from composable pairwise interaction motives.

The pattern is particularly relevant to AI/ML and agentic AI systems. Multiphysics approaches in machine learning usually apply ML to coupled physical processes or incorporate multiple physical priors into learning. Multiphysics-Inspired AI/ML Observability and Diagnostics, by contrast, treats the AI/ML system itself as a collection of interacting analytical fields, including data, optimization, information, computation, uncertainty, control, and semantic outcome fields, defined over a common trace domain constructed from correlated training, inference, and operational events. Its observability aspect concerns the instrumentation, correlation, and enrichment required to construct these fields from training logs, model evaluations, infrastructure metrics, distributed traces, tool-call records, user interactions, safety assessments, and other evidence sources. Its diagnostic aspect concerns how fields interact through their values and couplings, how disturbances propagate across fields, how feedback loops emerge among them, and how their combined effects produce system-level behavior.

In an agentic AI system, for example, increased tool latency may cause retries. Retries may enlarge the accumulated context and increase computational pressure. Context growth may change the relative prominence of relevant information and increase uncertainty, affecting planning, tool selection, and the final semantic outcome. A degraded outcome may provoke further retries, creating a reinforcing feedback loop. Observability provides the correlated evidence needed to construct, expose, and track these fields, while diagnostics analyzes their values and couplings to explain the resulting agent behavior. The behavior cannot be explained adequately by any one field in isolation.

In summary, Trace Multiphysics is a trace and log analysis pattern that examines several Trace Fields defined over the same trace domain, whether their values are derived from that trace alone or assigned using correlated evidence from other diagnostic sources. It studies the immediate, delayed, reinforcing, constraining, transforming, and explanatory couplings through which their combined behavior emerges. Multiphysics-Inspired AI/ML Observability and Diagnostics extends this principle to AI/ML and agentic systems: observability constructs and exposes the relevant fields from distributed evidence, while diagnostics analyzes their interactions and explains the emergent system behavior.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Even when all relevant events are present in traces and logs, they may still remain opaque because the analyst lacks the specialized skill needed to interpret their messages, abstractions, timing, domain vocabulary, failure semantics, or their role in the broader Trace World:

Trace Skill is a trace and log analysis pattern in which successful interpretation depends on a specific skill set required by the trace domain or Trace Ontology:

Some traces can be read with general diagnostic experience, especially if domain-independent analysis patterns are used. Others require specialist knowledge:

• Kernel tracing requires OS internals skill.
• Distributed traces require distributed systems skill.
• Database logs require query, transaction, and storage skill.
• Security logs require identity, policy, token, and threat-modeling skill.
• ML/AI traces require model, prompt, embedding, evaluation, and agentic workflow skill.
• Performance traces require latency, contention, scheduling, and resource-analysis skill.
• Business-process traces require domain workflow knowledge.

The same trace may therefore be simple for one analyst and almost invisible for another. Even the same analysis pattern may be applied differently. The problem is not the absence of data but the absence of the interpretive skill needed to turn trace data into diagnostic meaning:

Trace Skill analysis pattern may be useful in the following situations:

• The trace contains relevant evidence, but the analyst does not recognize it.
• Messages are dismissed as noise because their domain meaning is unknown.
• A team reads only the parts of the trace matching its own expertise.
• Different specialists disagree because each understands only one layer.
• The trace crosses technical boundaries: application, infrastructure, security, data, ML, business logic.
• The incident is repeatedly escalated because no one possesses the required combination of skills.

Compared to other analysis patterns, Trace Viewpoints are perspectives from which the trace is read. Trace Skill is the competence needed to read from a viewpoint correctly. So a viewpoint can be chosen quickly, but a skill has to be possessed, acquired, or borrowed from someone else. Trace World allows movement across skill sets by creating a common diagnostic language, but Trace Skill explains why this is necessary: traces are often multi-skill artifacts. No single narrow skill may be enough. The analyst either needs multiple skills or needs to collaborate across skill boundaries using a shared Trace World.

We can also say that Trace Skill is needed to navigate traces and logs and their Trace World. Trace World provides the shared diagnostic terrain constructed from trace and log evidence, entities, relations, events, timelines, and viewpoints. Trace Skill is the specialized competence required to navigate both the raw evidence and the reconstructed world accurately, recognize relevant signals, switch between viewpoints, and avoid misinterpretation.

In summary, Trace Skill is a trace and log analysis pattern in which decisive diagnostic evidence can only be recognized by the appropriate specialist skill set.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

A single trace may reveal only a partial diagnostic world. An application trace may show requests and exceptions. A security trace may show tokens, scopes, and access decisions. An operations trace may show retries, timeouts, latency, and resource pressure. An AI/ML trace may show prompts, tool calls, agent decisions, model responses, and memory updates:

However, different traces are not only different in content. They may also belong to different Implementation Discourses. The earlier Implementation Discourse analysis pattern observes that non-trivial traces contain different discourses because components are written in different languages and follow different runtime environments, binary models, and interface frameworks. These implementation variations influence the structure, syntax, and semantics of trace messages; for example, .NET traces differ from file system driver traces or COM debugging messages:

Trace World builds on this idea: it is a trace and log analysis pattern in which multiple traces, logs, telemetry streams, and diagnostic Trace Viewpoints contribute to a shared ontology of entities, relations, events, and narratives. The key idea is that multiple traces do not merely sit side by side. They share and enrich the same diagnostic ontology. As more traces are added, the Trace World becomes richer: new entities appear, existing entities are connected, relations become clearer, and the common narrative becomes more complete:

Therefore, Implementation Discourse is the local linguistic form of trace evidence, while Trace World is the shared world model that allows those local discourses to be translated, aligned, and used together. Implementation Discourse: How this component, runtime, framework, or language speaks in the trace. Trace World: How many such trace languages contribute to one shared diagnostic world. This also clarifies the relationship to Trace Ontology, which extracts entities, events, and relations from a trace, whereas Trace World allows multiple traces and multiple implementation discourses to share and enrich the same ontology.

Compared to Trace Viewpoints, which are different ways of reading the same trace world, and Implementation Discourses, which are different trace languages used to express evidence, Trace World is the common diagnostic world that persists when we move across both viewpoints and implementation discourses:

In agentic AI systems, this becomes especially important. Prompt traces, tool-call traces, memory traces, policy traces, model inference traces, application logs, and infrastructure telemetry may all speak different implementation discourses. Trace World provides the common diagnostic world where agents, tools, prompts, observations, memories, users, services, policies, and failures can be connected.

In summary, Trace World is the shared diagnostic world formed when multiple trace discourses enrich the same ontology, allowing analysts to move across viewpoints without losing entity identity, relations, or narrative continuity.

This analysis pattern is useful when:

• Several traces describe the same incident from different systems.
• Components use different trace languages, formats, and conventions.
• Different runtimes or frameworks produce structurally different messages, including Embedded Traces.
• The same entity appears under different names in different traces.
• A failure crosses application, infrastructure, security, data, or AI boundaries.
• A single trace discourse is insufficient to reconstruct the diagnostic story.

For constructing the Trace World, typical analysis steps may be these:

1. Identify the Implementation Discourse of each trace.
2. Extract Basic Facts from each discourse.
3. Identify local entities, events, and relations.
4. Map equivalent entities across discourses.
5. Merge them into a shared Trace World ontology.
6. Add relations that become visible only across traces.
7. Build a common narrative across implementation boundaries.
8. Use Trace Viewpoints to read the same world from different skill perspectives.

However, there might be some problems when using Trace World analysis pattern:

• Discourse isolation: each trace language remains separate.
• Translation gap: no mapping exists between local trace terms.
• Identity mismatch: the same entity has different names in different discourses.
• Semantic drift or incompatible Semantic Mappings: similar words mean different things in different traces.
• Partial or incompatible Trace Ontologies: one discourse lacks entities needed to explain another.
• Conflicting narrative: traces imply different causal stories.
• Unenriched world: traces are collected but not integrated.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

A typical trace or log is a detailed narrative, and one of the first analysis tasks is to check whether the expected Basic Facts are present: user name, machine name, process, component, time, operation, resource, or other problem-description facts. If those facts are absent or inconsistent, the trace may have been collected at the wrong time, on the wrong system, or under different conditions:

However, vocabulary alone is not enough. A trace may contain all expected words and identifiers, yet the analyst (human or AI) may still not understand what kind of things they are, how they relate, and what diagnostic roles they play. Usernames, process IDs, request IDs, sessions, endpoints, file names, transactions, queues, locks, models, agents, function and tool calls, or error messages are trace entities with roles and relationships. Trace Ontology is a trace and log analysis pattern that identifies the domain entities, classes, relations, and constraints, both explicit and implicit, in trace messages. It turns raw trace vocabulary into a practical structured diagnostic model:

Therefore, Trace Ontology extends Basic Facts from vocabulary recognition to structured diagnostic representation. In summary, Basic Facts answer the following question: What vocabulary from the problem description is visible in the trace or log? Trace Ontology answers: What kinds of things exist in this trace, how are they related, and what can be inferred from those relations?

Also, Trace Ontology, as a representational model, can be coupled with Semantic Mapping, a presentation transformation that relabels opaque identifiers with meaningful names. Note that trace ontologies may exist before traces are collected. In such a case, they simplify the analysis.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

In trace and log analysis, inductance and capacitance can serve as metaphors for two distinct forms of diagnostic behavior.

Trace Inductance is the tendency of a system to resist sudden changes in behavior. A new input, configuration change, request burst, or failure condition may not immediately appear in the trace as a new stable pattern. The existing execution flow has “momentum.” Threads, queues, retries, caches, locks, connection pools, batching, and background workers continue to reflect the previous state for some time:

Note that the cause may not be visible in the trace or log but may come from another trace and log, similar to Paratext in memory analysis.

Trace Capacitance is the tendency of a system to accumulate diagnostic potential before a visible discharge occurs. The trace or log may look normal while internal state, queues, memory pressure, retry debt, latency, pending work, or error counters are accumulating. Then the system suddenly emits a burst of Error Messages, warnings, Timeouts, or Phase Transitions.

In summary, Trace Inductance explains delayed behavioral response, and Trace Capacitance explains delayed behavioral manifestation. The former asks: Why did the trace not change immediately after the cause? The latter asks: What was accumulating before the visible failure? Together they help avoid a common mistake: assuming that the first visible error is the real beginning of the problem. In many systems, the cause may appear before the symptom, because of inductance, and the symptom may appear suddenly because of capacitance.

We introduce Trace Reactance as a good umbrella analysis pattern name, with Trace Inductance and Trace Capacitance as two specializations of this pattern: Trace Reactance describes how diagnostic signals are delayed, smoothed, accumulated, or released by the system structure before becoming visible in traces and logs.

An agentic AI fits naturally here, too: agents accumulate context debt, token pressure, and retry state before a sudden degradation in output or a tool-call cascade both inductance and capacitance effects, for example (click on image to enlarge):

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Large traces and logs often contain many combinations of conditions. The analyst sees many individual events but struggles to see which combinations are essential and which are redundant, equivalent, or adjacent manifestations of the same underlying behavior. The trace appears complex because the diagnostic space is fragmented into many small observations.

Karnaugh Map analysis pattern is useful when trace or log fragments can be classified by several binary or categorical dimensions, for example, distinctive features of Marked Messages. We project events into a structured logical space, similar to how a Karnaugh map projects Boolean combinations into an adjacency-preserving logical grid. Grouping cells in this grid simplifies the apparent complexity of many observed failure combinations into a minimal Boolean diagnostic condition, separating essential root cause dimensions from incidental ones that vary freely without affecting the outcome.

For example, suppose we analyze failures using four binary dimensions:

• A - Auth token expired
• B - Cache miss
• C - Backend timeout
• D - Retry attempt

We collected many traces for both working and non-working (failure) cases, and at first, it looks like there are four different failure cases:

But in Karnaugh-map form, these four cases form one group. The varying dimensions are B and D, while A and C remain constant:

So the simplified diagnostic condition is: failure occurs when the auth token expires and the backend times out, regardless of cache state or retry state. Or, in Boolean-like form: Failure = A ∧ C. This means cache misses and retries are not root discriminators here. They are incidental dimensions.

Here is a similar example for agentic AI:

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Semantic Mapping is the trace and log analysis pattern where opaque runtime identifiers such as PIDs, TIDs, request IDs, handles, or session IDs are renamed or mapped to semantically meaningful diagnostic entities such as UI Thread, Worker Thread, Client Process, Blocking Thread, or Failed Request:

Additionally, in Semantic Mapping, we cannot only rename identifier values but also rename the Trace Schema itself, for example, changing column headers such as PID to Process and TID to Thread.

This analysis pattern differs from Trace Field, which is a mapping/function from trace messages to some other domain. It does not necessarily rewrite the trace presentation itself, but it may add additional ATID c to the Trace Schema. It is also different from Semantic Field, which is a semantic category/codomain/class into which trace messages are grouped, which is more about the meaningful domain of classification, not about rewriting trace labels. On the contrary, Semantic Mapping is a representation transformation that rewrites the trace into a more meaningful diagnostic form. It operates at two levels: instance level, renaming actual values, and schema level, renaming the fields/headers themselves.

Here is another example adapted to agentic AI:

Using mathematical analogies, Semantic Mapping is essentially a readability-preserving isomorphism: the structural information is unchanged, but a human (or AI analyst) now works in a named, meaningful coordinate system rather than an anonymous numeric one.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Usually, in traces and logs, messages from different components are highly interleaved. Direct chronological reading may cause confusion because every component’s Adjoint Thread of Activity appears entangled with every other one:

Bethe Ansatz analyzes such a trace by treating requests, threads, agents, transactions, or log-producing entities as “quasi-particles” whose global behavior can be reconstructed from many local pairwise interactions. The inspiration for the pattern name comes from Bethe ansatz, introduced by Hans Bethe in 1931. In physics, it is a method for constructing exact solutions of certain many-body systems: in integrable systems, complex many-body scattering can be represented through factorized two-body scattering processes. In trace analysis, we often face a “many-body” problem: many requests, threads, services, queues, locks, agents, retries, callbacks, and timeouts interact within a single shared diagnostic space. Instead of trying to understand the whole trace as one monolithic event cloud, we decompose it into stable activity lines and pairwise encounters that may explain the global behavior:

The Bethe ansatz has many forms, including coordinate, algebraic, analytic, functional, nested, and thermodynamic variants. For this pattern, the most useful metaphor is the coordinate Bethe ansatz: represent the global state by positions of entities and interaction effects between them. We have the following analogies:

• Particle/excitation: request, thread, transaction, agent, session, workflow
• Coordinate: timestamp, component, hop number, queue position, memory address, trace span
• Momentum/rapidity: (activity) rate, latency class, retry rhythm, priority, causal direction
• Two-body scattering: (pairwise interaction) lock contention, queue wait, API call, resource conflict
• Scattering phase shift: delay, reordered event, changed state, timeout extension, retry offset
• Factorized many-body scattering: whole trace explained as composition of pairwise effects
• Bethe equations: consistency constraints imposed by loops, boundaries, cycles, repeated paths
• Non-integrability: residual behavior not explainable by pairwise interactions

Interactions can be found among Motifs, Macrofunctions, and actors of Activity Theatre.

We suggest the following diagnostic analysis procedure:

1. Identify trace quasi-particles that preserve identity across the trace.
2. Choose a coordinate system: the trace can be read through coordinates other than time.
3. Detect pairwise encounters: look for places where two entities interact; these are diagnostic “scattering” events.
4. Estimate phase shifts where a pairwise encounter often changes the apparent trajectory of an activity. The phase shift is the observable deformation caused by interaction.
5. Test factorization by asking the question: Can the global anomaly be explained as a product of pairwise interactions?

If the answer to the last question is yes, then the system is “Bethe-like”: complex but decomposable. If the answer is no, there may be a true many-body effect, such as shared cache collapse, global scheduler starvation, cascading timeout storm, distributed deadlock, correlated retry amplification, emergent agentic loop, or resource exhaustion caused by collective behavior.

Additionally, we can form a Motivic Trace from the resulting pairwise interaction layers. Motivic Trace compresses a trace into explanatory motives. Bethe Ansatz compresses a trace into pairwise interaction motives whose composition reconstructs the observed global behavior. In this sense, Bethe Ansatz can be viewed as a structured route to Motivic Trace: first decompose the tangled chronological trace into stable activity lines and pairwise encounters; then integrate those encounters into higher-level explanatory motives such as queue delay, database lock wait, retry ordering, and response ordering. In summary: Motivic Trace is the broader compression pattern; Bethe Ansatz is a pairwise-factorized way to build it.

A historical note: this analysis pattern also extends physical analogies of debugging.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Usually, software traces and logs are sorted by time.

Spatial Form is a specialized Sorted Trace in which trace or log messages are sorted by spatial, topological, or diagnostic proximity to a chosen origin component, device, process, service, or subsystem. Instead of reading the trace solely as a chronological sequence, we choose a diagnostic origin and arrange messages by their distance from that origin. Within each distance layer, the original local time order may still be preserved.

The pattern name comes from Joseph Frank’s The Idea of Spatial Form that is associated with reading narrative structure through juxtaposition and relational arrangement rather than only through linear chronological progression; the concept was introduced into literary discussion through his 1945 essay and later collected with reconsiderations in his book.

Sorted Trace is the more general pattern: messages are sorted according to some attribute value, for example, by TID, ATID, message type, message invariants, or message data.

For Spatial Trace, the distance may come from network topology, service dependency graph, component containment, process/thread ownership, device hierarchy, pipeline stage distance, proxy/gateway chain, address-space relation, storage or shard topology, causal adjacency, and many others. The resulting trace is not anti-temporal. It is spatially primary and temporally secondary.

Spatial Trace analysis pattern may help answer these questions: What happened around this proxy? Which nearby component first showed abnormal behavior? How did the request propagate outward? Was the fault local, adjacent, or remote? It may help distinguish local symptoms, adjacent symptoms, downstream effects, remote dependencies, and external causes. It gives the trace a layered diagnostic structure and spatial Layered Periodization. The pattern is therefore both a sorting technique and a reading strategy.

This pattern is especially useful for distributed systems, microservices, network devices, storage stacks, cloud control planes, request pipelines, proxies, gateways, and agentic AI workflows where activity is spread across many components.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Trace Network is an analysis pattern in which traces and logs are treated as evidence for constructing an attributed interaction network N=(V, E), where vertices V are Motives, (Adjoint) Threads or Features of Activity, and their combinations, and directed edges E are created by an explicit correspondence rule between them, for example, request/response, causality, correlation propagation, spawn/join relation, or shared resource usage. A scope such as Time Delta or some filtering for Message Patterns may also be applied before the network construction.

Edge aggregation, weighting, and labels are part of the construction specification, so the result is not merely a drawing but a diagnostic network on which structural properties such as fan-in, fan-out, hubs, components, and derived measures such as Trace Divergence can be computed. This differs from Trace Graph, whose primary purpose is plotting or graphing trace data, and from Message Complex, whose primary elements are messages connected geometrically rather than identities connected relationally.

Trace Network analysis pattern differs from Causal History, Causal Messages, and Causal Chains in both primitive elements and construction intent. Causal History is a message-level structure whose arrows represent possible causation; Causal Messages are those messages selected as causally relevant within that history; and Causal Chains are abstractions of causal relations into linked 1-chains, 2-chains, and higher n-chains. By contrast, Trace Network is a general constructed network whose vertices are typically diagnostic identities rather than messages, and whose edges are induced by an explicitly declared relation derived from trace evidence, such as causal linkage, adjoint correspondence, request/response coupling, shared-resource mediation, or correlation transfer. Accordingly, a Trace Network may encode causal structure as one special case, but it is not restricted to causality and does not by itself imply chain-complex abstraction.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Sometimes, we want to count the number of (Adjoint) Threads of Activity corresponding to a specified ATID:

We can view this as (adjoint) threads coming into or out of the specified ATID, similar to divergence, which gives the name Trace Divergence log analysis pattern. This analysis pattern differs from Cord of Activity, which is not a number, and the latter may not have a single, unvarying source or target ATID to which other A(TID)s correspond. It is also different from Trace Flux, where the number of threads is an external variable not related to traces and logs, and from Message Flow, which operates on the individual message level, temporal in nature, and counters are set in advance.

Typical examples include SYN floods in network traces (src and dst ATIDs), the number of threads corresponding to the specific PID, or the number of threads contending for the specified API.

Activity Divergence may look similar, but its surface is temporal, whereas Trace Divergence’s, surface is structural. There can be several Trace Divergencies in the same trace or log since they are per ATID.

Formally, Trace Divergence is a property of a constructed graph, for example, D_in​(a)=∣{x∈V∣x→a}∣; Activity Divergence is a property of a constructed signal, interpreted as dynamics, for example, D_in​(a,t).

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

We write software based on requirements and then see its execution. The same analogy can be applied to Declarative Traces, which are “executed.” Trace Plans serve the role of tracing and logging requirements. The following diagram illustrates trace engineering and the lifecycle of tracing and logging:

We look at a resulting trace or log and relate it to its Trace Plan to find anomalies and problems not only in software execution but also in traces and logs themselves and improve tracing source code.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

When we get traces and logs, we are interested in Trace Context: an issue description, how its trace was collected, overall system information, related Adjoint Spaces, Trace Summary, and previous traces and logs and their analyses. This contextual information can be organized as a checklist to ensure situational awareness, diagnostic quality, and reduce the number of information request roundtrips.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Message Embedding, as a representational technique in ML, are a variant of Trace Field. We can also consider the sequence of Message Embeddings as a trace itself with columns as latent features, forming separate latent Features of Activity. We can also treat these embeddings as sentence embeddings when interpreting traces and logs as Text Traces.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

We can view traces and logs as abstract polynomials that consists of abstract monomials. For example, if we have trace messages A,B,C, and D, the trace ABCACACACCD represents a single monomial. The multiplication operation in monomials represents message concatenation. But we can also split the trace as an abstract sum of several monomials, for example, ABC + AC + AC + AC + CD, or ABC + 3*AC + CD. The addition operation is a concatenation of traces even if concatenated traces consist of just one message. Note the distinction here between concatenation of messages and traces. By Trace Polynomial we mean a canonical abstract polynomial representation where we divide the trace by monomial when the next message in the message stream is already contained in the previous monomial, for example, ABC + 2AC + AC^2D.

Both addition and multiplication are non-commutative, and no distributivity between them. Mathematically speaking, we have the so-called a non‑distributive bi‑semigroup, or, in a category-theoretic sense, such abstract polynomials are objects in a free 2‑semigroupal category without interchange.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Trace Precision and Recall analysis patterns are borrowed from information retrieval and machine learning. In essence, Trace Precision is the fraction of trace messages used for successful diagnostics among all selected trace messages, for example, among CoTrace messages to reduce the noise. Trace Recall is the fraction of trace messages used for successful diagnostics among all relevant messages (these can also be messages not included in the trace, see Trace Bias).

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Traces and logs can be considered models of computation as was first proposed in Trace Bias analysis pattern. Borrowing metaphors from machine learning we can consider trace messages as Trace Parameters having associated values, for example, through Trace Field. These values can be numerical weights or linguistic values, for example, as proposed by Zadeh. Message values can be field values themselves, for example, Counter Values. As was noted in Trace Variance, different tracing environments with their set of “features” can be considered input data. if we use an artificial neural network metaphor, trace analysis itself can be considered as an activation function. CoTraces, as models of trace analysis, may form other “hidden” layers with “backpropagation” updating message weights. Tracing configuration parameters including Trace Schemas can be considered as Trace Hyperparameters. These concepts can be roughly illustrated by the following diagram:

To reduce the number of Trace Parameters we can use Quotient Traces.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

In some cases, when we have two trace messages we can infer the missing Implicit Message. This trace augmentation may help when we Sparse Traces and we want to train ML models on them. To illustrate, we asked ChatGPT:

We have a log file with two messages: 1. Reading file test.txt 2. Access denied. There is an implicit message in between.

The implicit message between the two log entries is:

“Attempting to open file ‘test.txt’.”

Reasoning:

1. “Reading file test.txt” → This suggests that the system or user has issued a command to read the file.
2. Implicit step (not logged explicitly) → The system attempts to open the file to read its contents.
3. “Access denied.” → The attempt fails due to permission restrictions or security policies.

Thus, the missing step is the system trying to open or access the file, which leads to the access denial.

Implicit Messages are different from Silent Messages which are padding messages to occupy the minimum resolution gaps.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

The fact that messages have types is mentioned in some trace and log analysis patterns but have never had its own analysis pattern. Trace and log messages may have the same Message Type if they have the same Adjoint Thread of Activity ATID (or Message Metadata) value, for example, “Warning”. Or they may have the same structure, for example, the same constants or message invariants, or belong to the same Trace Schema in Container Traces.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -

Trace Sketch can have several Trace Models (borrowed from model theory with sketches representing the logic of traces and logs) when messages satisfy trace and log analysis patterns sketched in Dia|gram language illustrations:

The same Trace Sketch induces an equivalence relation between different Trace Models, yet another Trace Similarity measure. Also, models of traces and logs having the same Trace Shapes may not be equivalent.

- Dmitry Vostokov @ DumpAnalysis.org + TraceAnalysis.org -