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+# Algorithmic correctness and efficiency audit
+
+Status: four open P3 efficiency findings. Reviewed source:
+`d8da761a213c82837276266faeebf93beda8eb08`.
+
+## Scope and architecture
+
+The [internal overview](../../internal/overview.md) inventories the implemented
+owners. Core captures declarations, validates installation batches, resolves
+routes and bindings, coordinates invocations, and supplies completion and shared
+reporting. Its neutral metadata and internal Cobra/pflag adapter separate public
+contracts from backend state. ckconfig prepares scopes and comparison inputs and
+projects ConfigKit evidence. ckprompt assembles PromptKit operations and adapts
+native requests, catalogs, reports, and smoke results. Applications own loaders,
+builders, and execution dependencies; upstream libraries own domain algorithms.
+Release launchers delegate maintainer operations to ReleaseKit.
+
+This pass reviewed declaration/registry traversal, alias compilation and help
+discovery, parsing/completion, operand allocation, captured binding replay,
+report conversion and delivery, integration selection/filtering/projection, and
+maintained consumer/tooling boundaries. Findings describe source-level scaling,
+not measured bottlenecks or new performance guarantees. No benchmarks or
+real-world performance measurements were gathered.
+
+Explicitly selected approaches were excluded from reconsideration:
+
+- Fresh mutable backend state per invocation, immutable metadata reuse, and
+  report buffering, as selected in the retired performance records and current
+  [internal overview](../../internal/overview.md).
+- The finite pushdown termination analysis, longest-prefix routing semantics,
+  canonical flag endpoints, scoped precedence, and intermediate-route discovery
+  selected in the retired alias implementation plan at `f42aefe`.
+- Completion's explicit routing check for each proposed child, selected in the
+  retired completion implementation plan at `10a799a`.
+- JSON report normalization, whole-report aggregation, and the composed example's
+  invocation-local list cache using reflect.DeepEqual, selected in the retired
+  adoption implementation plan at `2f43f78`.
+- The [deferred scope/selector and backend work](../future.md#possible-further-efficiency-work),
+  upstream domain algorithms, and the completed dense occurrence reconstruction,
+  heap merge, validation-filter indexing, and subtree-prefix preparation in
+  [remediation.md](../remediation.md).
+
+The findings preserve those decisions. The plans prescribe endpoint, precedence,
+discovery, and validation behavior, but do not require independent repeated
+chain walks, repeated processing of identical prefixes, full-catalog scans per
+rewrite, or eager diagnostic path formatting at every valid node.
+
+## Validation and interpretation
+
+All three independent module default suites passed with Go 1.27.0 using
+`GOWORK=off GOTOOLCHAIN=local go test -mod=readonly ./...`, run separately from
+each module directory. The aligned workspace suite also passed using
+`GOTOOLCHAIN=local go test -mod=readonly ./... ./integrations/ckconfig/... ./integrations/ckprompt/...`.
+The unchanged source reused successful cached results. Dependency downloads were
+disabled. No production files or repository tests were modified.
+
+A temporary external consumer confirmed that the workload shapes below are
+accepted: a flag-alias chain with an active command endpoint and inactive group
+contexts; a single-token group-alias chain whose help has no descendant aliases;
+distinct aliases sharing a discovery-only prefix; and a valid nested declaration
+chain. These are behavioral checks, not timing experiments. The complexity
+findings follow from the implementation's loops and copies.
+
+Complexities below use expected constant-time map operations and count tokens
+or records separately from their string-byte costs. They describe the identified
+phase, not the entire construction or execution pipeline. Nested loops over
+disjoint child collections, required independent input copies, sorted output,
+and work proportional to actual serialized output are not findings by themselves.
+
+No additional ordinary correctness defect was established during this pass.
+The six open findings in [01-correctness.md](01-correctness.md) remain separate;
+passing default suites do not resolve those findings.
+
+## E1 — P3: Flag-alias compilation repeatedly resolves shared chain suffixes
+
+**Code:** [flag_aliases.go](../../../flag_aliases.go), resolveFlagAliases lines
+226–251 and resolveFlagTarget lines 254–279; compileFlagAliases invokes this work
+independently for each canonical and discovery context.
+
+**Circumstances and complexity:** consider A effective mappings forming
+`--a1 → --a2 → … → --aA → --value`. Each source starts a fresh visited map and
+chain walk. The suffix traversed for `--a2` was already traversed for `--a1`, and
+so on. There are Θ(A²) total target examinations and corresponding cumulative
+chain/visited storage operations per context, despite only A mappings. The same
+cost occurs when the final flag is unavailable and all these global aliases are
+inactive. Across C contexts with the same chain shape, this part can cost
+Θ(CA²), apart from sorting, canonical metadata, and string processing. Peak
+temporary storage for a single walk is O(A).
+
+**Potential refactoring:** resolve the effective functional graph once per
+context using visitation states and memoized terminal results. Cache both an
+available canonical endpoint and an unavailable endpoint, and detect a cycle
+using the active traversal stack. This reduces graph traversal to expected O(A)
+work and O(A) scratch storage per context. Keeping the existing source sort for
+deterministic validation leaves O(A log A) total per-context work for these
+steps. A context-local cache suffices; no cross-invocation provider cache is
+needed.
+
+Canonical spellings must still terminate target resolution before following a
+mapping of the same spelling. Resolve each source's target before separately
+checking active source collisions. Preserve scoped overrides, inactive globals,
+scoped missing-target failures, useful cycle diagnostics, and revalidation after
+registration. Results cannot be shared indiscriminately between contexts.
+
+## E2 — P3: Alias help scans every source for every intermediate route
+
+**Code:** [help_view.go](../../../help_view.go), routeHelpAliases lines 38–51;
+[resolver.go](../../../internal/alias/resolver.go), ResolutionPaths lines 139–150.
+
+**Circumstances and complexity:** let P be the number of paths visited while
+rewriting the entered help path and A the number of declared command aliases.
+For every visited path, the function scans all A aliases and copies each source
+through FromTokens before checking its length and prefix. This performs PA
+source examinations, plus repeated source-token copying and prefix comparisons,
+even when no source can contribute an entry.
+
+For a valid chain of A single-token aliases ending at a canonical group,
+`help a1` visits Θ(A) paths. Every source is one token long, so every candidate
+is discarded by the length check. Discovery of an empty alias section still
+takes Θ(A²) examinations/copies. This cost recurs when requesting that help
+again even if the routing snapshot is already prepared; it is separate from
+registration, termination analysis, and backend construction.
+
+**Potential refactoring:** query an immutable source-prefix index for strict
+descendants of each visited prefix. The existing internal alias trie is a
+possible owner; alternatively prepare a source index with the routing snapshot.
+Building such an index is proportional to total source tokens. Prefix lookup
+then visits matching descendants rather than the entire catalog. For the
+single-token-chain example, the identified discovery work becomes O(A), with no
+descendant entries to enumerate. General cases still pay for prefix lengths,
+matching candidates, authoritative target resolution, and sorting the result.
+
+Keep intermediate-route discovery and resolve each surviving composed entered
+path through the existing resolver. Preserve longer overrides, canonical-target
+validation, suffix deduplication, and deterministic presentation. A prefix index
+does not authorize enumerating additional composed routes or introducing the
+deferred alias-completion feature.
+
+## E3 — P3: Discovery-context preparation rebuilds shared prefixes repeatedly
+
+**Code:** [flag_aliases.go](../../../flag_aliases.go), discoverFlagContexts lines
+181–200, particularly the prefix cloning/key construction at 185–187 and
+resolution at 194–195.
+
+**Circumstances and complexity:** R distinct alias sources can share a prefix
+of depth D, for example `legacy nested … action1`, `legacy nested … action2`,
+and so on, all targeting an ordinary canonical group. Every source independently
+enumerates the same D proper prefixes. For each prefix length k, it copies k
+tokens, builds a key, and may resolve and classify the prefix again. The
+prefixes map deduplicates only the eventual result; it does not prevent this
+work, including for prefixes previously classified as ineligible.
+
+With bounded component lengths and no rewrite within those proper prefixes,
+the shared-prefix portion costs Θ(RD²), although the source declarations contain
+only Θ(RD) tokens and there are only D distinct proper prefixes. When R and D
+both grow, that is cubic work in their common scale for quadratic input size.
+Additional rewrite work can increase the classification cost further.
+
+**Potential refactoring:** enumerate distinct proper source prefixes once,
+preferably by traversing the already compiled source trie, then run the existing
+classification once per unique prefix. Retaining full paths and keys once per
+prefix is sufficient; no change to command routing is required. In the example,
+source traversal plus prefix materialization/classification can be
+O(RD + D²), instead of O(RD²). More generally, account for total source tokens,
+each distinct prefix's representation, and one resolution per distinct prefix.
+
+A seen set consulted only after rebuilding each full prefix key would remove
+duplicate resolutions but retain the Θ(RD²) cloning/key cost. Use a traversal
+that actually shares prefix processing. Preserve exclusion of canonical paths,
+exact alias sources, and prefixes intercepted by valid canonical operand space;
+cache negative classifications too if using an alternative memoized traversal.
+The source index proposed in E2 could support this work as well.
+
+## E4 — P3: Successful declaration validation eagerly constructs every full path
+
+**Code:** [command.go](../../../command.go), collectDeclarationIssues lines
+444–470, especially path copying and formatting at 451–453.
+
+**Circumstances and complexity:** every visited declaration copies its entire
+ancestral path and clones/joins it again to make a diagnostic label before
+checking whether any issue needs that label. For N valid commands arranged in
+a depth-N chain, this performs Θ(1 + 2 + … + N) = Θ(N²) token-copying and label
+construction work, with quadratic cumulative allocation, while producing no
+diagnostic. A valid tree can be checked for retained issues and root-only
+placement in one traversal.
+
+**Potential refactoring:** maintain one scratch path for the validation walk using
+an append/truncate stack and format it only when emitting an actual issue or a
+root-only placement error. With ordinary amortized slice growth, the successful
+validation walk becomes O(N) work and O(D) path storage for depth D. Error cases
+also pay for the path strings actually included in their diagnostics.
+
+Preserve child order, retained error identity, root-only placement checks, and
+invalid/absent declaration handling. This changes scratch diagnostic preparation,
+not captured declaration ownership. Other installation phases retain their own
+metadata/path costs; this finding does not claim that complete App construction
+would consequently become linear for every tree shape.
+
+## Recommendation
+
+Consider E1 first: memoizing a context's flag graph removes repeated suffix
+work with a small, local change. E2 and E3 can share a private source-prefix
+traversal/index while retaining the selected resolver and discovery semantics.
+E4 is an independent simplification of diagnostic traversal. All four are
+efficiency opportunities for consideration, not evidence of measured operational
+impact or a reason to reopen the selected algorithms listed above.