Dynamic Indexing Protocol: Entropy-Driven Restructuring of Semantic Flows

Mechanism

The dynamic indexing protocol maintains an index that maps semantic identifiers to flow partitions. Each partition holds a population of flows whose semantic addresses share a common prefix or class, and the partition is the unit on which the protocol operates. The protocol observes three signals on each partition: the mutation density, defined as the rate at which the partition's contents change per unit time; the access locality, defined as the joint distribution of read addresses within the partition; and the traversal frequency, defined as the rate at which the partition is visited as part of a multi-partition lookup. These signals are aggregated into a partition-level entropy estimate that drives the restructuring decision.

When the entropy of a partition exceeds an upper threshold, the partition splits. The split selects a discriminator from among the partition's address dimensions, divides the population along the discriminator, and emits two child partitions whose entropies are individually below the trigger. The discriminator selection is deterministic given the partition's contents and is recorded in the audit record so that the split is reproducible by an auditor that holds the partition snapshot. Split operations are executed atomically with respect to lookup traffic: a lookup either resolves against the parent or against the children, never against an intermediate state.

When the entropy of two adjacent partitions falls below a lower threshold and their union remains below the upper threshold, the partitions merge. The merge concatenates the populations, retires the prior partitions, and emits a single successor whose discriminator is the parent of the two retired discriminators. Merging is the inverse of splitting in the discriminator hierarchy but is not the inverse in the audit record: the merge emits its own evidentiary record rather than negating the prior split records. This asymmetry is what permits the audit log to be append-only.

Reclassification operates on individual flows rather than on partitions. When a flow's access pattern diverges from the distribution that characterizes its current partition, the flow is reclassified into a partition whose distribution it more closely matches. Reclassification is gated by a stability filter that prevents flows from migrating in response to transient bursts; a flow must exhibit divergent behavior over a window comparable to the partition-level observation window before reclassification is triggered. The filter's parameters are part of the protocol's configurable surface and are recorded in the audit log alongside each reclassification.

The cycle-free invariant is enforced by a strict ordering on partition identifiers. Each partition carries a generation number that is incremented on every operation that produces it, and the protocol forbids any operation that would produce a successor whose generation is not strictly greater than the generations of all its inputs. This ordering admits a topological sort over the partition lifecycle and forecloses the possibility that a sequence of splits, merges, and reclassifications could return the index to a previously visited configuration without an external observer being able to detect the recurrence.

Audit-required execution means that no restructuring is permitted to proceed until its evidentiary record has been committed to the lineage. The commit is local to the node that performs the operation, but the lineage is replicable, and any replica that reaches the post-condition can verify that the audit record is consistent with the observed transition. The protocol is therefore not merely auditable in the sense of leaving traces; it is audit-required in the sense that the absence of an audit record renders the post-condition invalid.

Operating Parameters

The upper and lower entropy thresholds are the principal operating parameters. They are selected to bound the expected cost of restructuring per unit of access traffic, and their ratio determines the protocol's hysteresis: a wider gap between the thresholds reduces the rate of split-merge oscillation around a stable workload, at the cost of admitting larger excursions in partition entropy before correction. Typical deployments select the upper threshold at the entropy that yields lookup costs at the 95th percentile of the service-level objective and select the lower threshold at half that value.

The observation window over which entropy is estimated is the second principal parameter. Short windows produce responsive restructuring at the cost of sensitivity to transient bursts; long windows produce stable structure at the cost of slow adaptation. The protocol supports adaptive windows that lengthen during stable periods and shorten during periods of structural change, with the window length itself recorded in the audit log to preserve reproducibility.

The discriminator-selection policy is parameterized by the number of candidate dimensions evaluated during a split and by the splitting criterion applied within each candidate. The reference embodiment evaluates all dimensions and selects the dimension that produces the most balanced split under information gain. Embodiments that operate under tighter compute budgets evaluate a fixed-size random sample of dimensions and accept the best within the sample.

The stability filter for reclassification is parameterized by the divergence metric and by the window over which divergence is integrated. Kullback-Leibler divergence against the partition's empirical distribution is the reference metric. The integration window is typically equal to or longer than the partition-level observation window to prevent a single bursty flow from triggering reclassification cascades.

The protocol's memory footprint is bounded by the number of partitions plus the size of the audit log. The number of partitions is bounded above by the entropy of the population divided by the lower threshold, providing a structural ceiling that does not depend on the access workload. The audit log is append-only and bounded by the number of restructuring events, which is itself bounded by the rate at which the entropy estimates cross thresholds.

Alternative Embodiments

The reference embodiment uses a binary discriminator hierarchy in which each split produces two children. Embodiments contemplated under the provisional admit n-ary hierarchies for n greater than two, in which a single split produces a fan-out of children chosen to balance entropy across the children. N-ary hierarchies reduce the depth of the index at the cost of increasing the per-split work and the per-merge work; they are appropriate for workloads where lookup latency is dominated by traversal depth rather than by partition-internal work.

Mutation density may be measured as a count of mutations per unit time, as a count of distinct addresses mutated, or as a Shannon-entropy estimate over the mutation distribution. The reference embodiment uses the entropy estimate; the count-based variants are appropriate for workloads where the entropy estimator is too expensive to maintain online.

The audit record may be committed locally only, replicated synchronously to a quorum, or replicated asynchronously to all subscribed lineage holders. The reference embodiment commits locally and replicates asynchronously. Synchronous quorum embodiments trade restructuring latency for stronger reproducibility guarantees and are appropriate for deployments where the lineage must be available to auditors with bounded staleness.

Embodiments differ in how the cycle-free invariant is enforced. The reference embodiment uses a monotonic generation counter. Alternative embodiments use the hash of the partition contents as the partition identifier and rely on the collision-resistance of the hash function to enforce uniqueness; this approach removes the need for a counter at the cost of permitting two textually distinct configurations with identical contents to share an identifier.

Embodiments may compose the dynamic indexing protocol with an external entropy source that injects domain-specific signals into the entropy estimate. For example, an embodiment serving a query layer with explicit query plans may use the plans' selectivity estimates as an additional input to the partition entropy. The protocol is indifferent to the source of the entropy estimate provided the estimate is monotonic in the structural quantities the protocol is intended to track.

Composition

The dynamic indexing protocol composes with the broader memory-native protocol stack as the structural layer that translates between semantic addresses and flow partitions. Above the protocol, the cognition-compatible transport surface presents addresses without commitment to their physical layout. Below the protocol, the partition layer provides the storage and routing primitives that operate on concrete flow groups. The protocol is the dependency between the two surfaces, and its structural properties are visible to both.

Composition with the lineage layer is direct. The audit-required execution discipline produces lineage records that the lineage layer ingests and replicates, and the lineage layer's append-only commitment provides the substrate against which the protocol's cycle-free invariant is verified. The two layers are mutually reinforcing: the protocol could not enforce its invariant without an append-only substrate, and the lineage layer would have no structural events to record without a protocol that emits them.

Composition with the keyless identity system arises when partitions are addressed by identity-bound semantic identifiers. The dynamic indexing protocol's restructuring operations preserve the identity-bound addressing because the operations transform partitions but do not transform identifiers; a flow that bears an identity-bound address before a split bears the same address after the split, and the split's effect is to move the address into a child partition. This separation between addressing and partitioning is what permits identity-bound flows to participate in the index without creating an addressability dependency on the index structure.

Composition with downstream query and inference layers uses the partition structure as a hint rather than as a contract. A query planner that consults the index sees a snapshot of the current partition structure and may exploit the snapshot to schedule traversal, but the planner's correctness does not depend on the snapshot remaining valid for the duration of the query. The protocol's atomicity guarantees ensure that any restructuring observed mid-query is either complete or absent from the planner's perspective, never partially visible.

Prior-Art Boundary

The construction is bounded against several families of prior art. The first is adaptive B-tree and adaptive radix tree variants, which restructure their internal nodes in response to insertion and deletion patterns. These structures operate at the data-structure layer rather than at the transport layer, do not emit audit records, and do not enforce a cycle-free invariant beyond the topological consequences of tree operations. The dynamic indexing protocol described here is a transport-layer construct that produces evidentiary records as a structural requirement.

The second family is consistent-hashing and rendezvous-hashing schemes that rebalance partitions across nodes in distributed systems. These schemes restructure in response to membership changes rather than to access entropy, lack the audit-required discipline, and do not generally provide reclassification of individual records based on observed access patterns. The mechanism here treats access entropy as the principal trigger and reclassification as a first-class operation.

The third family is data-clustering and stream-sketching algorithms that maintain online summaries of evolving distributions. These algorithms produce summaries rather than indices; they do not directly support lookup, do not partition the underlying population, and do not maintain an addressable structure on which transport operations can be performed. The protocol described here uses techniques from this family within its entropy estimator but distinguishes itself by producing an indexed, addressable, audit-bound structure rather than a summary.

Disclosure Scope

The disclosure under Provisional 64/050,895 covers the entropy-driven restructuring construction, the split, merge, and reclassification operation set, the audit-required execution discipline, the cycle-free invariant and its enforcement through monotonic generation counters and content-hash variants, the operating-parameter envelope including threshold and window selection, the discriminator-selection policy and its sampling variants, the n-ary fan-out variant, the synchronous and asynchronous audit-replication variants, and the composition surfaces with the lineage layer, identity layer, and downstream query and inference layers. Embodiments that omit the audit-required discipline, that permit cyclic configurations, or that substitute centralized restructuring for the partition-local protocol fall outside the scope of the disclosure as filed.