Locality Of Reference

one_liner: Accesses cluster in time and space, making prediction and caching effective.

core_idea:
Locality of reference is the empirical structural regularity that accesses, events, or interactions are not spread uniformly across their possible targets but cluster: recently-used items are disproportionately likely to be used again soon (temporal locality), and items near a used one are disproportionately likely to be used next (spatial locality). The concept emerged in computer architecture from the observation, formalized by Denning (1968) in the working-set model, that a running program touches only a small, slowly-drifting subset of its address space at any instant rather than ranging freely over all of memory.<!-- FACT-D54-676 -->[^denning-1968] The pattern is fundamentally a statement about the *distribution of access* and not about any single access: usage is autocorrelated in time and space, so that knowing what was just referenced sharply narrows the prediction of what will be referenced next.<!-- FACT-D54-677 -->[^denning-2005]

What makes locality a prime rather than a mere observation about computers is that the same distributional shape recurs wherever a population of agents draws repeatedly from a space of targets. The reason a fast-but-small local store can stand in for a slow-but-large source is never that the local store is complete; it is that the access distribution is concentrated, so a tiny resident subset captures the overwhelming majority of demand. Locality names the precondition that makes any "keep the hot subset close" strategy worth attempting, and equally names its absence as the diagnostic that such a strategy will fail.<!-- FACT-D54-678 -->[^denning-2005]

structural_signature:
Locality of reference encodes a structural pattern: **a stream of accesses over a target space → autocorrelation in time and space → concentration of demand into a small, drifting working set**. It separates two regimes (uniform/random access versus clustered/autocorrelated access) and names the property of the access stream that distinguishes them. The signature is purely distributional: it says nothing about *what* is accessed or *why*, only that the empirical histogram of references is peaked and that the peaks move slowly and predictably.

**Recurring features:**

- Accesses cluster rather than spreading uniformly across targets
- Recently-used items are likely to be used again soon
- Items near a used one are likely to be referenced next
- A small working set captures most of the demand
- The access distribution is concentrated, not flat
- Usage is autocorrelated in time and in space
- The hot subset drifts slowly and predictably over time

The structural insight is robust across substrate: a CPU touching cache lines, a city whose interactions decay with distance, an epidemic spreading through households, a library whose circulation concentrates on a handful of titles, and a word stream where reuse is bursty all exhibit the same peaked-and-autocorrelated access shape.<!-- FACT-D54-679 -->[^denning-2005] The strength of locality is a measurable quantity, not a binary: a workload can have strong, weak, or no temporal locality, and the same stream can be highly local in space but not in time, or vice versa, which is why the two axes are treated as separable dimensions of a single distributional pattern.<!-- FACT-D54-680 -->[^hennessy-patterson-2017]

what_it_is_not:
Locality of reference is not a guarantee about any individual access. It makes no claim that the next reference *will* fall in the hot subset, only that it is far more likely to than a uniform draw would predict. A locality argument is therefore probabilistic and aggregate; betting that a particular access will hit the working set is a misuse, and locality offers no comfort against worst-case access patterns crafted to defeat it.<!-- FACT-D54-681 -->[^hennessy-patterson-2017]

It is also not the same as the existence of a hot subset in a fixed snapshot. Locality requires that the concentration *persist and drift slowly* over the access stream, not merely that some items are popular at one instant. A distribution that is concentrated but whose peaks jump erratically from moment to moment has high skew but poor temporal locality, because nothing learned from the recent past predicts the near future. The drift must be slow enough that the working set remains a useful predictor across the timescale at which a local store is maintained.

Locality is not a causal mechanism and does not explain *why* accesses cluster. Clustering may arise from program loops, from physical adjacency, from social network structure, from contagion dynamics, or from human attention; locality is agnostic to all of these. It describes the shape of the resulting access distribution, not its generator. Treating locality as if it were itself the cause ("the cache works because of locality") collapses a property of the workload into an explanation, when the real explanatory work is done by whatever process produced the autocorrelation.

Finally, locality does not assert that the whole space is small or that most of it is unused permanently. The full address space, the full set of geographic targets, or the full catalog may be enormous and may all eventually be touched. Locality claims only that *at any given window* the active subset is small relative to the whole, and that windows are correlated. Over a long enough horizon, demand may spread broadly even while remaining locally concentrated at every instant.

broad_use:
**Computer science:** Memory, cache, and disk accesses cluster, which is the reason caches, prefetching, paging, and the entire memory hierarchy work at all; the working-set model and the design of replacement policies (LRU and its approximations) are direct exploitations of temporal and spatial locality.<!-- FACT-D54-682 -->[^hennessy-patterson-2017]

**Geography (non-obvious):** Tobler's first law of geography — "everything is related to everything else, but near things are more related than distant things" — is spatial locality of interaction, and it underwrites spatial autocorrelation statistics, distance-decay models, and the design of spatial indexes.<!-- FACT-D54-683 -->[^tobler-1970]

**Epidemiology:** Contacts and infections cluster spatially and temporally (households, neighborhoods, recent exposure windows), so that case locations and times are autocorrelated rather than uniformly scattered; this is precisely why ring vaccination, local containment, and contact tracing are effective interventions.<!-- FACT-D54-684 -->[^knox-1964]

**Library and information science:** A small set of recently and frequently consulted works dominates circulation, and reserve collections, reshelving heuristics, and open-stack layout all exploit the fact that the next request is disproportionately likely to be for a recently-requested or topically-adjacent item.<!-- FACT-D54-685 -->[^trueswell-1969]

**Linguistics and text:** Word reuse is bursty — a word just used is disproportionately likely to recur soon, far more than its overall frequency would predict — which is the temporal-locality property that cache-based and adaptive language models exploit to outperform static frequency models.<!-- FACT-D54-686 -->[^kuhn-demori-1990]

clarity:
Locality names *why* a fast-but-small local store can substitute for a slow-but-large source: not because the local store is complete, but because the access distribution is concentrated and slowly-drifting. This is a clarifying move because it separates two questions that are easily conflated. The first is whether a resource is large; the second is whether its *use* is concentrated. A petabyte store with strong locality can be served well by a megabyte of cache, while a megabyte store with uniform random access cannot be meaningfully accelerated at all. Locality redirects attention from the size of the space to the shape of the demand on it.<!-- FACT-D54-687 -->[^denning-2005]

It also lets practitioners distinguish, before building anything, workloads with exploitable structure from genuinely random-access ones where no caching, prefetching, or local-intervention strategy can help. This converts an architectural decision into an empirical measurement: profile the access stream, estimate the hit rate a given working-set size would achieve, and only then commit to a hierarchy. Where locality is strong the engineering payoff is large and cheap; where it is absent the same engineering is wasted effort, and locality is the concept that tells the two apart in advance.

manages_complexity:
By asserting that the *working set* at any moment is small relative to the whole address space, locality justifies maintaining and reasoning about only a tiny active subset, collapsing a vast space of possible accesses into a manageable hot region. The combinatorial space of "everything that could be referenced" is replaced by the far smaller and slowly-changing space of "what is being referenced now," and correctness or performance arguments can be made against the working set rather than the entire universe of targets.<!-- FACT-D54-688 -->[^denning-1968]

This complexity reduction is what makes hierarchical design tractable across domains. A memory system need not make all of DRAM fast; it makes the working set fast. A public-health response need not surveil an entire population uniformly; it concentrates testing and tracing on the recent-and-near cluster. A library need not keep the whole catalog within arm's reach; it keeps the reserve shelf stocked. In each case locality lets a designer ignore the long cold tail of the distribution for the purposes of the active decision, dramatically shrinking what must be modeled, stored, or acted upon at any instant, while accepting a bounded miss rate on the rare excursions into the tail.

abstract_reasoning:
Recognizing locality supports the inference "if accesses cluster, then keeping the recent-or-near subset close yields a high hit rate" — and, just as importantly, the contrapositive warning that when locality is absent (uniform random access) caching, prefetching, and local intervention will fail no matter how well-engineered. It turns the design question "should we cache, prefetch, or localize?" from a matter of taste into an empirical question about the concentration and drift of the access distribution.<!-- FACT-D54-689 -->[^denning-2005]

The reasoning is also generative across the temporal and spatial axes independently. If a stream has strong temporal but weak spatial locality, the abstract response is to keep recently-used items resident but not to prefetch neighbors; if spatial locality is strong but temporal is weak, the response inverts to aggressive prefetching of adjacent items with rapid eviction. Locality thereby licenses a small family of structurally-distinct strategies and tells a reasoner which one a given workload calls for, by reading off which axis of autocorrelation is present. This same axis-decomposition transfers: an epidemiologist asks whether clustering is mainly temporal (recent-exposure windows) or spatial (geographic hotspots) and selects between time-bounded quarantine and place-bounded cordon accordingly.

knowledge_transfer:
The CPU-cache insight transfers directly to epidemiology: both treat a clustered access-or-contact distribution as the lever. A cache keeps the hot working set local and serves most requests from it; contact tracing keeps containment local to the recent-and-near cluster and intercepts most onward transmission there. The structural identity is exact — a concentrated, slowly-drifting distribution over targets — even though one substrate is silicon and the other is a population, and the transfer is explicit in the literature rather than merely analogical.<!-- FACT-D54-690 -->[^knox-1964] A practitioner who has internalized why LRU eviction works on memory pages already understands why recent-contact prioritization works in an outbreak: in both, recency is a strong predictor of near-future relevance because the underlying access stream is temporally autocorrelated.

The same insight transfers to recommender and search systems, which prefetch and pre-rank the predictably-near-next items, and to library science, where reserve collections are physical caches of the temporally-hot subset. The vocabulary of working sets, hit rates, and prefetching, developed in computer architecture, gives practitioners in geography, public health, and information science a precise language for what they were already doing intuitively, and the distance-decay intuition of the geographer reciprocally sharpens the systems engineer's sense of spatial locality. The transfer is grounded in shared distributional structure, not in surface resemblance, which is why insights move in both directions.

formal_abstract:
**Memory hierarchy and the working-set model:** A program executing a nested loop over an array references the same instruction addresses repeatedly (strong temporal locality) and walks through contiguous data addresses (strong spatial locality). Denning's working-set model formalizes this by defining the working set W(t, τ) as the set of pages referenced in the window (t − τ, t]; the key empirical claim is that |W| is small and stable relative to the full address space for most programs. A cache or page allocator that keeps exactly the working set resident achieves a hit rate far above what the cache's fractional size would suggest under uniform access. When the program transitions between phases, the working set drifts — old pages cool, new ones heat — but it does so slowly enough that an LRU policy, evicting the least-recently-used page, tracks the drift well. **Mapped back:** This is the canonical structural picture of locality. The access stream is autocorrelated in both time and space; the demand collapses onto a small, slowly-moving working set; and a local store sized to that working set, not to the whole space, captures most accesses. Strip away the words "page" and "cache" and what remains is a peaked, drifting distribution over targets — the prime itself.

**Spatial autocorrelation and Tobler's first law:** Consider any field measured over geographic space — soil pH, household income, disease incidence. Tobler's first law asserts that values at nearby locations are more similar than values at distant ones, which is spatial locality stated as autocorrelation. Formally, Moran's I or a semivariogram quantifies how correlation decays with distance; positive spatial autocorrelation is exactly the statement that the "access distribution" of similar values is spatially concentrated. A spatial interpolation that predicts an unmeasured point from its nearest neighbors works for precisely the reason a cache works: the relevant information is locally concentrated, so a small neighborhood stands in for the whole field. **Mapped back:** The target space here is geographic locations rather than memory addresses, but the structure is identical — autocorrelation makes the near-and-recent (here, near-in-space) disproportionately predictive of an unknown reference, so a small local subset suffices for most of the inferential work, and the absence of autocorrelation (a spatially random field) would defeat any neighborhood-based method.

applied_industry:
**Outbreak containment via contact tracing:** During an infectious-disease outbreak, new cases are not scattered uniformly across the population; they cluster in households, workplaces, and neighborhoods, and they cluster in time within the incubation-and-infectious window following an exposure. A contact-tracing program exploits this by treating each confirmed case as a recently-accessed item and prioritizing its spatial-and-temporal neighbors (household members, recent close contacts) for testing and isolation. The "working set" is the set of recently-exposed, near-in-network individuals; it is tiny relative to the whole population, and it drifts as the outbreak moves. Ring vaccination generalizes the same move spatially. The strategy succeeds exactly to the degree that transmission is autocorrelated; in a hypothetical pathogen that infected uniformly at random across the population, tracing the near-and-recent would offer no advantage. **Mapped back:** Substitute "individual" for "memory page" and "transmission" for "memory reference," and the epidemiological response is a caching strategy: keep the hot (recently-and-nearly-exposed) working set under close watch, accept that the cold tail of the population is unlikely to be the next case, and let the watched set drift with the access stream. The decision to trace at all is a bet on locality, and it is correct only when the contact distribution is in fact concentrated.

**Library reserve collections and circulation management:** An academic library cannot keep its entire catalog at the circulation desk, nor does it need to. Circulation data show that a small fraction of titles — current course readings, recent acquisitions, topically-trending works — accounts for the majority of checkouts, and that a title checked out recently is disproportionately likely to be requested again soon. The library responds by maintaining a reserve collection: a physically-local, fast-access cache of the temporally-hot working set, with short loan periods that force rapid eviction so the reserve shelf tracks the drift of demand. Reshelving and open-stack adjacency exploit spatial locality, since a patron who pulls one book on a topic is likely to want a neighbor on the same shelf. **Mapped back:** The reserve shelf is an LRU cache over the catalog, sized to the working set of currently-hot titles; the short loan period is an eviction policy that keeps it tracking demand drift; and shelf adjacency is a prefetch of spatially-local items. The whole apparatus is justified by, and only by, the concentration and slow drift of the circulation distribution — the same distributional property that justifies a CPU cache.

title: Locality is a property of the workload, not the system, yet systems are built to assume it

body: A cache, a tracing program, or a reserve shelf embodies a bet that the access stream is concentrated and slowly-drifting. But the stream is generated by something outside the system's control — a program, a population, a readership — and can change character without warning. The tension is that the engineering artifact is fixed-purpose while the property it relies on is contingent and external, so a workload shift can silently convert a well-tuned local store into dead weight that adds latency without adding hits.

title: Temporal and spatial locality can pull a design in opposite directions

body: A stream with strong temporal but weak spatial locality rewards keeping recently-used items resident and punishes prefetching neighbors; a stream with strong spatial but weak temporal locality rewards aggressive neighbor prefetch and rapid eviction. A system that assumes both, or that optimizes for the wrong axis, can perform worse than a naive design: prefetching neighbors in a temporally-local-only workload pollutes the cache with items that will never be touched. The single name "locality" conceals two separable and sometimes conflicting dimensions.

title: Exploiting locality can destroy the locality it depends on

body: Aggressive prefetching, batching, or reorganization aimed at exploiting an observed access pattern can change the pattern itself. A recommender that prefetches and surfaces the predictably-near-next items reshapes user behavior, potentially flattening or concentrating the very distribution it measured. In epidemiology, a containment that succeeds in breaking local transmission alters the future contact distribution, so the locality estimated from past data no longer holds. The act of measuring-and-exploiting is not neutral with respect to the thing measured.

title: A concentrated distribution is not the same as a locally-predictable one

body: High skew (a few very popular items) is easily mistaken for locality, but locality additionally requires that concentration persist and drift slowly enough to be predicted from recent history. A workload whose hot set is small but jumps erratically has strong skew and weak temporal locality; a frequency-based cache will do well on it while an LRU cache will thrash. Conflating concentration with predictability leads to selecting the wrong exploitation strategy and misattributing its failure.

title: Optimizing for the common case silently penalizes the cold tail

body: Every locality-exploiting design accepts a bounded miss rate on rare excursions into the unloved tail of the distribution. Usually this is the correct trade. But when tail accesses are disproportionately important — a rarely-touched safety record, an isolated outbreak in a sparsely-connected community, an obscure but critical reference work — the locality strategy systematically under-serves exactly the cases where a miss is most costly. The distribution's shape and the *value* of its regions need not align, and locality reasoning attends only to the former.

title: Locality justifies a local store but cannot bound the cost of a miss

body: The hit-rate argument says most accesses are cheap; it is silent on what happens on the misses. A system can have an excellent average hit rate and still be unacceptable if the penalty for the residual misses is catastrophic or highly variable. A memory hierarchy with a 99% hit rate may still be dominated by the latency of the 1% that reach disk; a tracing program with high local coverage may be undone by a single missed long-range transmission that seeds a new cluster. Locality reasons about frequency, not about the tail risk that frequency leaves untouched.

prose: _No catalogued solution archetypes reference this prime yet._

notes:
Locality is conventionally decomposed into two axes — temporal and spatial — but these are not exhaustive of the structures that travel under the name. Some workloads exhibit *branch* or *sequential* locality (the next instruction is usually the textually-next one), and others exhibit *associative* or *semantic* locality (the next reference is topically rather than physically adjacent, as in a citation network or a topical shelf). Each is a different generator of the same underlying distributional property: a peaked, slowly-drifting histogram over targets. The two-axis decomposition is a useful default but should not be mistaken for a complete taxonomy.

The strength of locality is workload-specific and time-varying, which is why measurement, not assumption, is the disciplined stance. A program has different locality in different phases; a population has different contact locality during a holiday than during a workweek; a library's circulation locality spikes at the start of a semester. Designs that assume a fixed locality profile tend to fail at exactly the transitions where the profile shifts, and adaptive policies (which re-estimate the working set continuously) exist precisely to track this non-stationarity.

There is a deep connection between locality and the heavy-tailed frequency distributions (Zipf's law, the 80/20 rule) that recur across the same domains. Skew and locality are related but, as the structural tensions note, not identical: skew is a property of the marginal frequency distribution, while locality additionally requires temporal autocorrelation — predictability of the near future from the recent past. A workload can be Zipfian in aggregate yet have weak temporal locality if its popularity ranking churns rapidly. Keeping the two notions distinct is essential to choosing between frequency-based and recency-based exploitation strategies.


Located-In Relation

type: prime

one_liner: One entity is situated within the region of another at a time, without that entity being a part of, or strictly contained by, the location.

status: draft

core_idea:
A located-in relation says that one entity is situated within the region of another: an organ within a body cavity, a component within a subassembly, a person within a room, a subsidiary within a jurisdiction, a variable within a lexical scope. The relation is not parthood — the located thing need not be constitutive of the location, as a foreign body within a tissue is located in it but is no part of it<!-- FACT-D66-301 -->[^smith-etal-2005] — and it is not mere adjacency, since something can border a region without being inside it. It is the more general claim that "this thing's place is *within* that thing's region," where the region may be spatial, contextual, organizational, jurisdictional, or scoping. The structural commitments are four: a *locatum*, the entity being located; a *location*, the entity whose region contains it; an *inclusion region*, the specific region of the location within which the locatum sits; and a *relation-time*, the interval over which the relation holds. The last is essential and easily forgotten: located-in is not eternal — the person leaves the room, the subsidiary re-incorporates, the variable falls out of scope — so the relation is always indexed to a time.

What makes this a distinct relational primitive rather than a loose sense of "in" is the explicit separation from its mereotopological neighbors. Parthood, strict containment, located-in, and adjacency are four different relations with four different inference rules, and reasoning breaks when they are conflated. The located-in relation is precisely the inside-of relation shorn of any claim that the locatum is part of, or permanently enclosed by, the location — which is why it can hold transiently and asymmetrically, and why "where" becomes a substrate-independent question answered by substrate-dependent machinery.

structural_signature:
*the locatum (entity being located)* — *the location (entity whose region contains it)* — *the inclusion region* — *the relation-time interval* — *the within-not-part-of inclusion test* — *the separation from parthood, strict containment, and adjacency*

The pattern is present when each of the following holds:

- **A locatum.** Some entity is the thing being located — an organ, a component, a person, a subsidiary, a variable.
- **A location.** Some entity whose region the locatum sits within — a cavity, a subassembly, a room, a jurisdiction, a scope.
- **An inclusion region.** The specific region of the location within which the locatum sits; the inclusion-region test is decided by substrate-dependent machinery (geometric containment, set membership, scope rules, tenancy).<!-- FACT-D66-302 -->[^smith-etal-2005]
- **A relation-time.** An interval over which the relation holds. This is essential and easily forgotten: located-in is not eternal — the person leaves the room, the subsidiary re-incorporates, the variable falls out of scope — so the relation is always indexed to a time.
- **The within-not-part-of invariant.** The locatum's place is *within* the location's region without the locatum being part of, or strictly contained by, the location. This is the load-bearing distinction: a foreign body within a tissue is located in it but no part of it, so inferences valid for parthood (transitivity, permanence, constitution) are invalid here.

The relation is one of four mereotopological neighbors with distinct inference rules — parthood (constitutive belonging), strict containment (mereological enclosure), located-in (within-a-region-at-a-time), and adjacency (bordering without inclusion) — and reasoning breaks when they are conflated. Each missing commitment yields a determinate error: a missing relation-time gives stale-location bugs; located-in-as-parthood gives the transient-occupant-mistaken-for-part error; located-in-as-adjacency gives the bordering-mistaken-for-containment error.

what_it_is_not:
- **Not a bare `relation`.** A relation is any structured tie between relata; located-in is the *specific* mereotopological relation of within-a-region-at-a-time, with its own inference rules (no transitivity into parthood, time-indexed, non-constitutive). The generic relation carries none of these constraints.
- **Not parthood (a use of `composition`).** Parthood is constitutive belonging — the part is part of the whole, transitively and constitutively; located-in's locatum is *within* the location's region without being part of it. A gallstone is located in the gallbladder but is no part of it.<!-- FACT-D66-303 -->[^smith-etal-2005]
- **Not `containment` in the strict sense.** Strict containment is mereological enclosure of one region by another; located-in does not require the locatum to be enclosed or constitutive, only situated within a region. The two have different permanence and constitution entailments.
- **Not `boundary` or adjacency.** A boundary or adjacency relation has things bordering without inclusion; located-in requires the inclusion-region test to pass. Bordering a region is not being inside it, and conflating them grants false access or jurisdiction entailments.
- **Not `dimension`.** Dimension concerns the axes along which a space is measured; located-in concerns *position within a region* of a location at a time. One is about the coordinate structure; the other about a within-relation indexed to an interval.
- **Not `allocation`.** Allocation assigns a resource or share to a recipient; located-in merely situates an entity within a region. Being located in a place is not being allocated to it — the relation carries no distributive or assignment content.
- **Common misclassification.** Over-extending "in" to any relationship that connects two things — the user *likes* the venue, the subsidiary *trades with* the jurisdiction. The catch is the inclusion-region test: if the candidate only borders, associates with, or relates to the location without satisfying inclusion at the relevant time, it is not located-in and the relation's entailments do not fire.

broad_use: The four commitments recur across substrates with the inclusion-region test decided differently in each. In biological modeling, organs are located in cavities, cells in tissues, molecules in organelles, pathogens in host tissues, and the relation is given formal semantics distinct from parthood and strict containment precisely because conflating them corrupts anatomical reasoning.<!-- FACT-D66-304 -->[^smith-etal-2005] In engineering, components are located in subassemblies without being permanent parts of them — removable, replaceable, transferable. In geographic and political modeling, settlements are located in countries, properties in jurisdictions, events at venues, and topological predicates of within and contains are first-class.<!-- FACT-D66-305 -->[^egenhofer-franzosa-1991] In legal and organizational modeling, subsidiaries are located in jurisdictions, assets in trusts, cases in courts, each with consequences (tax treatment, governing law, regulatory regime) that depend on the relation holding at the relevant time. In computing, variables are located in scopes, processes in containers, files in directories, rows in partitions, users in tenants.<!-- FACT-D66-306 -->[^linux-namespaces-man7] In cognitive and social settings, people are located in conversations, meetings, and contexts, and reasoning about who can access or affect what often reduces to "where are they, and what does being located there entail?" In every case the substrate machinery varies; the four-commitment abstraction is constant.

clarity: The pattern is sharp at its operational test: for a given locatum and putative location at a given time, is the locatum's place within the location's region? The test is decidable substrate by substrate — geometric containment, set membership in a jurisdiction, scope rules in a programming language, membership in a cost center — and the pattern is bright at its edges, because failure of any of the four commitments is recognizable. A missing relation-time produces the classic error of asserting a location that was true only until some date and is now stale. Treating located-in as parthood produces the anatomical and engineering errors where a transient occupant is mistaken for a constitutive part. Treating it as adjacency produces the geographic and access-control errors where bordering is mistaken for containment. Naming the relation thus disciplines reasoning: loose associations — the user *likes* the venue, the subsidiary *trades with* the jurisdiction — do not instantiate located-in, because they fail the inclusion-region test, and the pattern is exactly the discipline that prevents over-extending "in" to any relationship that merely connects two things.

manages_complexity: Real systems contain many entities, and without a located-in relation every interaction must be reasoned about from first principles. With it, vast amounts of structural reasoning collapse into location lookups whose answers constrain everything downstream. Tax law uses jurisdictional location to determine treatment; anatomy uses location to predict the diffusion of a signal or the reach of a therapy; programming uses scope to predict variable visibility; access control uses tenancy to authorize operations. In each, "where is it?" is a single query whose answer determines a large set of further facts, so that the relation acts as a hub through which much else is computed rather than re-derived. The relation also composes with time cleanly: because located-in is indexed to an interval, a system can record the history of an entity's locations and reason about what was true when — which jurisdiction governed at the moment of a transaction, which scope a closure captured at the moment of its creation — without confusing a past location for a present one. This time-indexing is what lets the relation manage the complexity of entities that move through regions rather than staying put.

abstract_reasoning: Located-in is one of the basic mereotopological relations that any region-based ontology eventually distinguishes, and reasoning about a system requires identifying which of them is in play and applying its own inference rules. Parthood is structural belonging: the part is constitutive of the whole. Strict containment is mereological enclosure: the whole's region encloses the part's region without making it a part. Located-in is the locatum's place being within the location's region, at a time, with no parthood or strict-containment claim. Adjacency is borders touching without inclusion. These are not interchangeable, and the formal-ontology tradition spent decades disentangling them precisely because biological, medical, and engineering reasoning broke whenever they were collapsed<!-- FACT-D66-307 -->[^smith-rosse-2004] — a tumor in a lung is located in it but not part of it, and inferences valid for parthood are invalid for located-in.<!-- FACT-D66-308 -->[^smith-etal-2005] The abstract payoff is that recognizing the relation lets a reasoner ask, of any "in" claim, which of the four relations is meant, and then apply only the inferences that relation licenses. This prevents the characteristic error of importing parthood's transitivity or permanence into a relation that has neither, and it makes "where" a tractable question with well-defined inference rather than an ambiguous one.

knowledge_transfer: The four-commitment diagnostic transfers across substrates because it interrogates the relation rather than the domain. What is the locatum? What is the location? What region of the location does the locatum sit in? Over what interval does the relation hold? These four questions, asked of a body within a cavity, a component within an assembly, a subsidiary within a jurisdiction, a variable within a function, or a person within a room, produce the same kind of structural answer and surface the same kind of bug when an answer is missing. The transfer is mechanical, not analogical: a practitioner who has learned to demand a relation-time when modeling corporate domicile holds exactly the tool needed to avoid the stale-location bug in an anatomical model or a closure-capture analysis, because the missing commitment is the same in each. The deepest carry is the distinction from parthood, which is the load-bearing modeling move in every substrate the relation touches. Recognizing that a therapeutic agent is *located in* a target region but not *part of* it lets a modeler predict both its action (it acts where it is located) and its clearance (it leaves when the relation ceases to hold), and the identical structure governs a vehicle located in a garage (with consequences for access and billing), a body incorporated in one jurisdiction (with consequences for governing law until reincorporation), and a closure variable located in an outer scope (with consequences for what the closure can read during its lifetime). A reasoner who has internalized the non-parthood of located-in in one domain carries it intact into all the others, because the relation is the same and the inference rules it licenses are the same.

formal_abstract:
Biomedical anatomy ontologies give the relation its most rigorously formalized worked instance, precisely because conflating it with parthood corrupted reasoning until the relations were disentangled. Consider a gallstone located in the gallbladder. The *locatum* is the stone; the *location* is the gallbladder; the *inclusion region* is the organ's lumen, with the inclusion test decided by geometric containment; and the *relation-time* is the interval before the stone is passed or removed. The within-not-part-of invariant is the whole point: the stone is located in the gallbladder but is no part of it<!-- FACT-D66-309 -->[^smith-etal-2005] — it is not constitutive of the organ, did not develop with it, and leaves without diminishing it. This blocks exactly the inferences that parthood would license. Parthood is transitive (a part of a part is a part of the whole) and tends toward permanence and constitution; located-in is none of these.<!-- FACT-D66-310 -->[^simons-1987] So from "the stone is located in the gallbladder" and "the gallbladder is part of the digestive system" one may say the stone is located in the digestive system's region, but one may *not* infer the stone is a *part* of the digestive system — the chain that would be valid for parthood is invalid here. The four mereotopological neighbors are kept distinct by their inference rules: a tumor located in a lung is not part of it (so resection logic differs from removing a lung lobe, which is a part); the pleura adjacent to the lung borders without inclusion. The relation-time commitment prevents the stale-location bug: an anatomical assertion true only during an episode must be indexed to that interval, or downstream reasoning will treat a transient occupant as a permanent fixture.

**Mapped back:** The gallstone-in-gallbladder case instantiates all four commitments — locatum, location, inclusion region, relation-time — and the within-not-part-of invariant is exactly what bars parthood's transitivity and permanence from corrupting the anatomical inference.

applied_industry:
Two practitioner cases run the identical four-commitment relation on substrates anatomy shares nothing with. In corporate and tax law, a subsidiary is located in a jurisdiction. The *locatum* is the subsidiary; the *location* is the jurisdiction; the *inclusion region* is the legal territory, with the inclusion test decided by incorporation and tenancy rules rather than geometry; and the *relation-time* is the interval until reincorporation. The within-not-part-of invariant matters: the subsidiary is located in the jurisdiction's regime without being a constitutive *part* of the state, so it can relocate, and the consequences — governing law, tax treatment, regulatory regime — depend on the relation holding *at the relevant time*, which is why the relation-time commitment is load-bearing. A model that omits the time index produces the stale-location bug in its costliest form: applying the governing law of a jurisdiction the entity has since left to a transaction, or vice versa. In programming-language semantics, a variable is located in a lexical scope. The *locatum* is the variable; the *location* is the scope (a function or block); the *inclusion region* is the lexical extent, with the inclusion test decided by scope rules; and the *relation-time* is the variable's lifetime<!-- FACT-D66-311 -->[^abelson-sussman-1996] — it falls out of scope, so the relation is not eternal. The within-not-part-of distinction governs closure capture: a closure captures variables *located in* an outer scope at the moment of its creation<!-- FACT-D66-312 -->[^abelson-sussman-1996], and reasoning about what it can read depends on the relation holding during its lifetime, not on the variable being a permanent part of the closure. The same four questions — what is the locatum, what is the location, what region, over what interval — produce structurally comparable answers in a tax model and a closure-capture analysis, and the same missing commitment (relation-time) produces the same stale-location bug in both.

**Mapped back:** Corporate domicile and lexical scope span law and software; in each, the four-commitment relation indexes a within-a-region claim to a time interval, and the non-parthood invariant plus the relation-time index are what license correct inference about governing law or closure visibility while preventing the stale-location bug.


Lock-In

one_liner: Forward-looking cost of switching exceeds the forward-looking cost of staying, even when a superior alternative exists.

review_flags: ACCEPTED as a prime from project-06 (Kurt, 2026-05-28 via E4 bundled-prime split). The compound `lock_in_and_path_dependence` was split (it had survived an earlier M-bucket merge of path_dependence_and_lock_in INTO lock_in_and_path_dependence); the structurally clean resolution drops both bundles, keeps path_dependence as its own prime, and adds lock_in as a distinct prime for the switching-cost concept.

review_flags: Distinct from `path_dependence` (path dependence is the historical-accumulation pattern; lock-in is the current state where switching costs exceed forward continuation costs, making reversal infeasible).

review_flags: Distinct from `commitment_device` (deliberate self-binding for strategic reasons; lock-in can be inadvertent).

review_flags: Distinct from `inertia` (general resistance to change; lock-in specifically describes a cost-structure asymmetry).

review_flags: Would parent: vendor_lock_in, qwerty_effect_keyboard_lock_in, network_lock_in, standards_lock_in, legacy_system_lock_in, ecosystem_capture, switching_cost_friction.

review_flags: substrate_independence scores are PROPOSER estimates, pending triangulation.

review_flags: 2026-05-28 schema reformat: original project-06-style v1 used the 5-section template; reformatted here to the canonical 8-section runbook v1 schema. Structural Signature content folded into Manages Complexity; heavy-v1 anti-drift content preserved in Notes per session-handoff guidance.

core_idea:
Lock-in is the **state in which the forward-looking cost of switching from a current commitment exceeds the forward-looking cost of continuing with it**, even when the original choice was suboptimal and a superior alternative is now available. The mechanism is asymmetric across time: at decision-time, alternatives were comparably costly; but subsequent investment, learning, network growth, infrastructure build-up, or standard-adoption has accumulated value *that does not transfer* to the alternative. Rational forward-looking calculation then favors staying — even though, from a clean-slate position, the alternative would have been chosen. This forward-cost framing, which David (1985) made canonical in his treatment of QWERTY persistence, is what distinguishes lock-in from related but structurally weaker notions of "stuckness."<!-- FACT-D56-286 -->[^david-1985]

Lock-in is the *current-state* concept: the asymmetry exists *now*, regardless of how it arose. It is sharply distinct from path dependence (the historical *process* that produced the asymmetry) and from sunk costs (the irrecoverable past expenditure that *should* be ignored but often isn't), a separation Arthur (1989) developed in his analysis of competing technologies under increasing returns.<!-- FACT-D56-287 -->[^arthur-1989] Lock-in is one of the principal reasons that markets, ecosystems, organizations, and institutions exhibit persistence far beyond what local optimization alone would predict, and one of the few mechanisms that lets analysts predict where such persistence will form before it does.

structural_signature:
Lock-in encodes a structural pattern: **initial commitment → accumulating complementary investment → non-transferability of that investment → cost asymmetry at the present moment**, formalized in the switching-cost economics tradition Klemperer (1995) consolidated.<!-- FACT-D56-288 -->[^klemperer-1995] It separates two states (free-choice and cost-locked) and names the asymmetry that has emerged between them — an asymmetry measured not in the past expenditures but in the forward migration cost relative to the forward continuation cost.

**Equivalent framings:**

- Forward switching cost exceeds forward continuation cost
- Accumulated complementary investment that does not transfer
- Cost asymmetry produced by non-transferable specificity
- Current-state lock, not historical process or past expenditure
- Initial commitment plus specific complement creates the trap
- Reversibility blocked by structure, not by rule or law

The structural insight is robust across substrates, a generality Liebowitz and Margolis (1995) examined critically in their typology of three "degrees" of path-dependence outcomes that culminate in true lock-in.<!-- FACT-D56-289 -->[^liebowitz-margolis-1995] A keyboard layout, a hospital's electronic-records database, a city's rail-gauge standard, a bird species canalized into an obligate symbiosis, and a specialist's two-decade career investment all exhibit the same barrier-asymmetry logic. The role-phrases above apply in all of these without change. Lock-in is not a metaphor borrowed from technology economics; it is a structural property of any system in which commitment plus non-transferable complement plus time produces a cost gap between staying and moving.

what_it_is_not:
Lock-in is **not** a past-cost concept. Sunk costs are irrecoverable; lock-in's switching cost lies in the future. A hospital that paid for an EHR a decade ago has sunk costs (the install fee, the original training); its lock-in is whatever it would cost *now* to migrate records and rebuild integrations. The two are routinely confused under the label "we've invested too much to change," but only one of them — lock-in — correctly enters the forward decision.

Lock-in is also **not** a psychological or motivational state. Status-quo bias, loss aversion, and organizational risk-aversion can amplify lock-in, but they are not it. Lock-in describes a real cost structure: even a perfectly rational, bias-free agent confronting a locked-in situation would compute that staying is cheaper than switching. Removing the bias does not remove the lock; reducing the switching cost (through adapters, standards, migration tools) does.

Lock-in is **not** the same as choosing to commit. A commitment device is a deliberate self-binding act — Odysseus tying himself to the mast, a savings plan that imposes withdrawal penalties — chosen precisely so that future-self cannot easily defect, a contrast Schelling (1960) made central to his treatment of strategic pre-commitment.<!-- FACT-D56-290 -->[^schelling-1960] Lock-in is almost always *inadvertent*: it emerges from a sequence of locally reasonable choices, no one of which was intended to remove future options. Vendor lock-in is rarely the result of customers wanting to be locked in.

Lock-in is **not** physical irreversibility. Some processes cannot be reversed at any cost — entropy, broken eggs, certain biological canalization endpoints. Lock-in is reversibility-blocked-by-cost: the migration is *possible*, often even technically straightforward, but the cost of executing it exceeds the cost of staying. The asymmetry is economic, not thermodynamic. This matters because it identifies the leverage point: lower the switching cost, and the lock can dissolve.

Finally, lock-in does **not** claim that the current state is bad. A locked-in standard may be very good; QWERTY is a famously contested example, but USB, the metric system, and TCP/IP are all locked-in in the same structural sense and broadly serviceable. The prime is value-neutral. It names a cost-structure asymmetry that constrains future choice, whether or not the current state is itself good.

broad_use:
**Technology and standards.** QWERTY keyboards, VHS-vs-Beta, AC-vs-DC electrical grids, the x86 instruction set, USB connectors, and IPv4 addressing all illustrate lock-in. An early standard accumulates complementary investments (trained users, manufacturing tooling, deployed devices, software ecosystems) whose value does not transfer to alternatives, even technically superior ones. The economic-history literature on competing technologies, surveyed by Arthur (1994), treats these as canonical.<!-- FACT-D56-291 -->[^arthur-1994]

**Vendor and customer relationships.** Enterprise ERP installations, cloud-provider data-egress costs, proprietary file formats, and IDE ecosystems create lock-in by accumulating complementary investments inside one vendor's interface. The data is portable in principle, but the integrations, queries, operational knowledge, and downstream tooling are vendor-specific.

**Network effects and platform standards.** Social-network user bases, instant-messaging platforms, two-sided marketplaces, payment networks, and professional credentialing systems lock in through network value: the platform is worth using because others use it. Shapiro and Varian (1999) treat network-effect lock-in as one of the defining features of the information economy.<!-- FACT-D56-292 -->[^shapiro-varian-1999] Moving to an alternative requires either persuading the network to move with you or accepting a sharp loss of value during the transition.

**Infrastructure and urban systems.** Rail-gauge standards, road-network geometries, telecommunications wiring, and water-distribution layouts lock in choices made decades or centuries earlier. The complementary investment is the city itself; non-transferability is total. Changing a rail gauge means changing the rolling stock, bridges, tunnels, stations, and operational knowledge of every railway employee.

**Organizational lock-in.** Legacy IT systems, long-running vendor partnerships, multi-year contracts, and institutional knowledge concentrated in specific employees all create organizational lock-in. The "we cannot replace this person" feeling is often a precise lock-in calculation, even when not articulated as one.

**Biology.** Developmental canalization — Waddington's (1957) image of a landscape whose valleys, once entered, become progressively harder to climb out of — is biological lock-in at the level of the developing organism.<!-- FACT-D56-293 -->[^waddington-1957] Niche specialization, obligate symbiosis, and host-parasite mutualism are lock-in at the level of the species. Each illustrates the prime in a substrate with no humans, no economics, and no contracts — strong evidence that the pattern is not a technology-economics artifact.

**Cognitive and behavioral.** Skill specialization, learned heuristics, expertise in obsolete frameworks, and motor habituation all show lock-in. A surgeon trained for twenty years in open procedures faces real switching costs to retrain laparoscopically. The complementary investment is the trained nervous system; non-transferability is whatever portion of expertise is technique-specific rather than principle-general.

clarity:
Lock-in sharpens the distinction between three things that get conflated under the umbrella "we cannot change." First, **sunk costs**: irrecoverable past expenditure, which standard decision-theoretic advice says should be ignored going forward. Second, **path dependence**: the historical process by which we arrived at the current state, which is causally explanatory but not itself a forward decision-relevant cost. Third, **lock-in itself**: the *current* asymmetry where forward-looking switching cost exceeds forward-looking continuation cost. Of the three, only lock-in correctly enters the forward decision, a separation that depends on the sunk-cost / forward-cost distinction Thaler (1980) developed in his behavioral account of consumer choice.<!-- FACT-D56-294 -->[^thaler-1980]

Naming lock-in lets the analyst separate "we should ignore past investment" (correct sunk-cost reasoning) from "switching genuinely costs more than continuing" (correct lock-in reasoning). This is more than terminological hygiene. Discussions that lump the three together end up giving bad advice in both directions: sometimes telling decision-makers to ignore real switching costs because "that's sunk," and sometimes telling them to fight against switching because they have "already invested so much" — the textbook sunk-cost fallacy. The prime separates the two, and in doing so identifies which costs belong in the forward calculation and which do not.

The clarity extends to remediation. Once lock-in is named, the analyst can ask sharp leverage questions: Which investments are transferable, and which are not? Where are switching costs hiding (data, training, integration, social network)? What would lower them — adapters, standards, migration tools, parallel operation? Sunk-cost framing does not produce these questions because it locates the problem in the past; path-dependence framing does not produce them because it locates the problem in history. Only lock-in locates the problem in the current cost structure, where intervention is possible.

manages_complexity:
Lock-in decomposes a persistent-but-suboptimal situation into six concrete roles, each separately diagnosable and each separately addressable. An **initial commitment** (the choice that began the trajectory); **accumulated complementary investment** (infrastructure, learning, network ties, data, integrations built on top of the commitment); the **non-transferability** of that investment (the property that its value does not carry over to alternatives); **current switching costs** (the forward-looking total cost of migration, including downtime, retraining, integration rebuild, data conversion, and risk); **continuation costs** (the ongoing forward cost of staying — vendor fees, friction, opportunity cost, technical debt service); and the **cost asymmetry** itself (switching > continuation, with the gap measuring the depth of lock).

Once those six roles are named in a specific case, the analyst can ask sharp questions: which complementary investments are actually transferable (and were misclassified as locked)? Where are switching costs hiding inside numbers that look like operations rather than migration? What would lower them — standards adoption, adapter layers, parallel-run migrations, regulatory portability mandates? This converts an opaque "we are stuck" into a structured problem with identifiable leverage points. Farrell and Klemperer (2007) develop a similar decomposition in their survey of switching costs and network effects, using it to identify when policy intervention can dissolve a lock without destroying the value the lock protects.<!-- FACT-D56-295 -->[^farrell-klemperer-2007]

In organizations, this decomposition reframes legacy-system debates. Rather than "should we migrate off the old system?" — a question that often surfaces as identity-laden conflict — the lock-in frame asks "what specifically would migration cost, and what specifically would each year of continuation cost?" Both numbers are then estimable, comparable, and decomposable. The question becomes operational rather than political.

abstract_reasoning:
Lock-in supports a powerful counterfactual: "*at decision time, the choice was open; now the choice is structurally biased.*" That move lets analysts predict where persistence will exceed local-optimization predictions: any domain with accumulating complementary investment plus non-transferability will show lock-in, regardless of substrate, a counterfactual move Arthur (1989) used to predict where competing-technology markets would lock in before the asymmetry had fully formed.<!-- FACT-D56-296 -->[^arthur-1989] Predicting lock-in in advance — before the asymmetry has fully formed — is one of the prime's most useful applications. A new platform, technology, regulation, or organizational practice can be screened for its lock-in potential by asking: what complementary investments will accumulate on top of this? How transferable will they be? How fast will the asymmetry grow?

The reasoning generalizes cleanly in the other direction as well: once the six roles are identified in a new domain, the analyst can predict whether and where lock-in will form, what its depth will be, and where its leverage points lie. It also enables a *de-lock-in* analysis: what would have to change (in switching cost, in alternative quality, in the migration path, in the transferability of complements) to dissolve the asymmetry? This counterfactual structure makes lock-in a tool for design as well as diagnosis — the prime can be used to deliberately engineer escape routes into new commitments, by ensuring complementary investments remain transferable.

knowledge_transfer:
The same six-role structure recurs across substrates with no loss of fidelity. Biological canalization — developmental decisions that lock organisms into body plans — and QWERTY persistence are instances of the same pattern, despite one having no humans involved at any point. The transfer is structural: identify the commitment, the complementary investment, the non-transferability, the current switching cost, the continuation cost, and the asymmetry. Each role is filled by a domain-specific thing (a developmental valley vs. an installed keyboard base), but the relations among the roles are identical, a transfer pattern Page (2006) treats as a defining feature of path-dependent and lock-in phenomena across social, biological, and technological domains.<!-- FACT-D56-297 -->[^page-2006]

An economist studying network effects, a biologist studying obligate symbiosis, an IT architect studying legacy-system migration, a cognitive scientist studying expertise transfer, and a city planner studying infrastructure renewal can recognize each other's problems as variants of one pattern and learn from each other's solutions. The biological literature on developmental plasticity offers organizations a vocabulary for distinguishing canalized from labile traits; the IT-migration literature offers biologists a quantitative framing of switching cost; the network-economics literature offers infrastructure planners a way to think about complementary-investment accumulation. This cross-traffic is what makes lock-in a prime rather than an economics specialty.

formal_abstract:
**Developmental canalization in biology.** Waddington's epigenetic landscape pictures development as a ball rolling down a surface scored by valleys. Early in development, the ball can be deflected into different valleys by relatively small perturbations; each valley represents a different developmental trajectory leading to a different mature form. As development proceeds, however, the valleys deepen and the ridges between them rise; small perturbations no longer suffice to switch trajectories. The organism becomes canalized into its current developmental path, a phenomenon Schlichting and Pigliucci (1998) frame as a reaction-norm property where developmental specificity accumulates non-transferable structure.<!-- FACT-D56-298 -->[^schlichting-pigliucci-1998] The initial commitment is the early developmental decision (which transcription-factor cascade was activated); the complementary investment is the downstream tissue differentiation, organ specification, and cell-type lineage commitment that builds on top of it; the non-transferability is that those downstream structures presuppose the early commitment and cannot be re-used under a different one; the current switching cost is the wholesale re-development that would be required; the continuation cost is normal ongoing developmental energy; the asymmetry is sharp. **Mapped back:** This is lock-in in a substrate with no economics, no contracts, no humans, no markets, and no choice in any meaningful sense — which is exactly what makes it strong evidence for the prime's structural status. The six-role decomposition fits without translation, and it identifies the same leverage point biology already knows: early-development interventions are the only ones cheap enough to redirect trajectory, because they precede the complementary-investment accumulation.

**Skill specialization in cognition.** A neurosurgeon completes a twenty-year trajectory through medical school, residency, fellowship, and accumulated clinical experience in open cranial procedures. The initial commitment was medical school plus the specialization decision; the complementary investment is the entire trained nervous system — motor patterns, perceptual chunking, case-pattern recognition, surgical-team coordination, hospital relationships, peer reputation — that sits on top of the original specialization; the non-transferability of this investment to, say, an internal-medicine practice is nearly total at the procedural level (though substantial at the principle level); the current switching cost is the years of retraining, the income loss during retraining, the loss of accumulated reputation and team, and the risk of mid-career incompetence; the continuation cost is normal practice; the asymmetry is enormous even when the neurosurgeon is no longer well-matched to the work. **Mapped back:** The six roles fill in cleanly with no recourse to economic language. This is why mid-career switches are rare even when individually justified: the lock is structural, not psychological. It also identifies the leverage: skill investments that are deliberately built around transferable principles (statistical reasoning, communication, anatomy at the conceptual level) reduce future lock; skill investments built around technique-specific procedural memory (the exact motor pattern for a specific approach) increase it. The same logic applies to programming-language specialization, instrument-specific musical expertise, and bureaucratic-system mastery.

applied_industry:
**Electronic health-records vendor lock-in.** A hospital installed an EHR system a decade ago. At the time, several vendors offered comparable products. Since then, the hospital has trained staff on this vendor's interface, customized workflows, built integrations with billing and lab systems, accumulated years of patient records in the vendor's proprietary format, and developed institutional knowledge about how to work around the system's quirks. The original commitment was the install; the complementary investment is training plus integrations plus the records plus the workaround knowledge; the non-transferability is that none of that value carries to a different EHR; the switching cost is migrating records, retraining staff, rebuilding integrations, validating downstream reports, and absorbing the downtime risk; the continuation cost is the vendor's annual fees and ongoing friction; the asymmetry is now stark — switching is far more expensive than staying, even when a competing EHR is technically superior. Christensen, Grossman, and Hwang (2009) treat EHR lock-in as a paradigmatic example of how complementary-investment accumulation produces persistence beyond what underlying product quality would predict.<!-- FACT-D56-299 -->[^christensen-grossman-hwang-2009] **Mapped back:** This is lock-in, not sunk cost — the migration cost is forward-looking and real, and the analyst's job is precisely to estimate it without inflating it with past-cost guilt. Path dependence explains how the asymmetry built up over the decade; lock-in is the current state itself; sunk cost is the original install fee, which is correctly ignored in the forward decision. The leverage points the six-role decomposition surfaces are: record-format standards (would reduce non-transferability), integration adapters (would reduce switching cost), parallel-operation migration patterns (would reduce downtime risk).

**Urban rail-gauge standard.** A city built its rail system in the late 19th century on a gauge that was locally reasonable at the time but is now incompatible with the regional standard that emerged later. The initial commitment was the original gauge choice; the complementary investment is the entire physical network — rails, ties, ballast, bridges, tunnels, stations, signal systems, depots, and the rolling stock fleet — plus the trained workforce and the operational procedures; the non-transferability is that none of this hardware fits the regional gauge; the switching cost is the cost of regauging the entire network, replacing rolling stock, retraining operators, and absorbing years of degraded service during conversion; the continuation cost is the ongoing inefficiency of incompatible interchange with the regional network, requiring break-of-gauge transfers at every junction. Puffert (2009) treats rail-gauge lock-in as one of the most precisely documented infrastructural cases, with switching costs in the billions and continuation costs that have been borne for over a century.<!-- FACT-D56-300 -->[^puffert-2009] **Mapped back:** The asymmetry has held for decades, and the city continues to absorb continuation costs rather than pay the switching cost. This is not irrationality; it is correct lock-in arithmetic. The leverage points the prime identifies are the same as in the EHR case at a different scale: standardization mandates (reduce future non-transferability for new lines), adapter mechanisms (variable-gauge axles), and staged-migration patterns (regauge segment by segment). The structural identity between an EHR migration and a rail-gauge conversion is what the prime makes visible.

title: Lock-in is value-neutral about the locked-in state, but in practice it is almost always invoked critically

body: The prime describes a cost-structure asymmetry; it does not claim that the current state is bad. Yet "lock-in" is almost never used to describe a well-functioning standard that we are glad to remain on (TCP/IP, USB, the metric system); it is reserved for cases where the speaker thinks the current state is suboptimal. This rhetorical loading creates a hidden normative claim inside what is structurally a neutral description, and analysts who use the term should be explicit about whether they are describing a cost structure or arguing that we should pay the switching cost.

title: Diagnosing lock-in requires distinguishing transferable from non-transferable complementary investment, and that boundary is contested

body: A hospital migrating off an EHR has to decide which of its accumulated investments are actually vendor-specific (and therefore non-transferable, and therefore part of the switching cost) versus which are general-purpose (and therefore transferable, and therefore not). The boundary is rarely sharp. Workflow customizations may be partially transferable; staff training is partially transferable; integration logic is partially transferable. The lock-in calculation depends heavily on where this boundary is drawn, and different stakeholders draw it differently in self-serving ways. Vendors emphasize non-transferability (deepening the perceived lock); migration consultants emphasize transferability (deepening the perceived business case).

title: Lock-in measurement is forward-looking but estimated from past data

body: The prime correctly identifies the relevant quantity as the forward-looking switching cost. But that quantity is almost never directly observable; it is estimated from past migrations, vendor quotes, or analogical reasoning from similar transitions. These estimates are systematically biased — past migrations were of different scope, vendor quotes are negotiating positions, and analogies break down at scale. The lock-in calculation is structurally correct but empirically fragile, and the gap between the correct structure and the available data is where most practical lock-in disputes live.

title: The same structural property — complementary-investment accumulation — that creates lock-in also creates network value

body: A platform with deep complementary investment is harder to leave but also more valuable to be on, because the complementary investment is what the platform provides. Distinguishing the part of the cost asymmetry that comes from value-delivery (the platform is good) from the part that comes from non-transferability (you are stuck) is structurally subtle, and policy interventions that target lock-in (interoperability mandates, data-portability requirements) can incidentally destroy the value-delivery side as well. The tension is unavoidable: the mechanisms are partly the same.

title: Inadvertent lock-in and deliberate commitment are structurally similar but consequentially different

body: A commitment device and an inadvertent lock-in both produce a state where future-self cannot easily defect, and they share the six-role decomposition. The difference is upstream: was the lock chosen for its commitment value, or did it emerge as a side effect of locally reasonable choices? Critics of lock-in claim it should be eliminated; defenders of commitment devices claim it should be sought. The prime does not adjudicate this — it merely identifies the cost-structure pattern, leaving the normative question of whether to seek, accept, or escape it to other primes (commitment device, autonomy preservation, antifragility).

title: De-lock-in interventions can create new lock-ins

body: Adapter layers, migration tools, and interoperability standards reduce the switching cost of an existing lock, but each is itself a commitment with complementary investment that accumulates on top of it. The standard becomes the new lock; the adapter ecosystem becomes the new complementary investment; the regulatory portability mandate becomes the new constraint. Liberation from one lock typically means entry into another at a different level of abstraction. The prime does not promise escape from lock-in in general — only from any particular lock-in, at the cost of entering a different one. Designing for transferability at every level is structurally impossible; the question is always which level deserves to be locked.

prose:
1. **Transferability-by-design.** Build complementary investments around transferable substrates (open standards, principle-level rather than technique-level skills, data formats with documented portability, modular architectures with clean interfaces). The lock-in asymmetry only forms when complementary investment is non-transferable; deliberately reducing non-transferability is the upstream intervention.

2. **Adapter layers and standards.** Where lock-in has already formed, introduce intermediating layers (data-format adapters, API gateways, gauge-converting axles, cross-platform abstractions) that reduce the switching cost without requiring the original commitment to be reversed. The adapter is itself a commitment, but it shifts the locus of lock-in to a more general substrate.

3. **Parallel-operation migration.** Rather than a discontinuous cut-over, run the existing commitment and the alternative in parallel for a transition period, allowing complementary investment to migrate gradually. This decomposes a single large switching cost into a stream of smaller ones and reduces the downtime-risk component that often dominates the switching-cost calculation.

4. **Lock-in screening at commitment time.** Apply the six-role decomposition before making the initial commitment, asking what complementary investment will accumulate, how transferable it will be, and how fast the asymmetry will grow. This converts lock-in from a discovery into a design parameter and shifts intervention upstream.

5. **Continuation-cost surfacing.** In organizations where lock-in has been quietly absorbed for years, make the continuation cost explicit and forward-projected. Often the lock persists not because switching is genuinely more expensive but because continuation is invisible (it is folded into normal operating costs) while switching is salient (a one-time large number). Surfacing the running continuation cost over a five- or ten-year horizon frequently reverses the asymmetry on paper.

6. **De-lock-in via complementary-investment substitution.** Identify the specific complementary investments that produce the non-transferability and replace them one at a time with transferable alternatives — for example, migrating proprietary data formats to open standards while still using the original system, then migrating the system once the data is portable. This sequences the de-lock work into independently completable steps, each of which reduces the depth of the lock.

notes:
Lock-in was surfaced from the E4 bundled-prime audit when the previously merged `lock_in_and_path_dependence` bundle was identified as itself a split candidate. The structurally clean resolution: both bundles drop, `path_dependence` stays as its own prime (history-shapes-options), and `lock_in` becomes a distinct prime (current-cost-asymmetry). Many long-tail children (vendor_lock_in, QWERTY effect, network_lock_in, standards_lock_in, legacy_system_lock_in, ecosystem_capture) now have a clean parent.

The load-bearing piece for v2 anti-drift: the "switching cost exceeds continuation cost" framing must remain visible across all application domains — technology, vendor, network, infrastructure, organizational, biological, and cognitive. The biological case (developmental canalization, obligate symbiosis) and the cognitive case (skill specialization) are the substrate-furthest instances and the strongest evidence that the prime is not a technology-economics artifact. Without them, the v2 entry would narrow toward technology-economics and lose its claim to substrate independence. The biology and cognition examples in the Formal/abstract section are placed there precisely to anchor the breadth.

The path-dependence / sunk-cost / commitment-device / inertia / irreversibility quadrangle is what the prime has to hold its ground against. The Distinction from Neighbors section treats each at length, but the discipline at v2-revision time is simpler: if any of those five concepts can be substituted into a paragraph without changing the meaning, the paragraph has drifted off the prime. Lock-in is specifically: current-state, forward-looking, cost-asymmetry, produced by non-transferable complementary investment, value-neutral about the current state. None of the five neighbors carries all of those properties together.

The prime operates across timescales — cognitive lock-in in years, organizational lock-in in years to decades, infrastructural lock-in in decades to centuries, biological lock-in in developmental or evolutionary time — and the six-role decomposition holds across all of them. Differences in timescale affect the intervention design (parallel operation is cheap in software, expensive in infrastructure, biologically impossible in canalization past a threshold) but not the structural pattern.

A standing question for future revision: whether lock-in's relationship to *increasing returns* (in the Arthur sense) deserves promotion from "parent" status to co-equal prime. Current judgment: increasing returns is a generative mechanism for the asymmetry; lock-in is the asymmetry itself.


Logarithmic Perception and Encoding

one_liner: Systems operating over wide dynamic range encode magnitude as its logarithm, so equal internal steps mean equal ratios.

origin_domain: synthesized

core_idea:
Logarithmic perception and encoding is the structural arrangement in which a system that must operate over a *very wide dynamic range* of some magnitude organizes its sensitivity, representation, or response as a *function of the logarithm of the magnitude* rather than of the magnitude itself. The essential commitment is to a *ratio scale*: equal increments on the system's internal axis correspond to equal *ratios* on the physical axis, not equal *differences*. The same arithmetic re-expression — convert multiplication to addition, exponents to coefficients, wide ranges to narrow ones — applies whether the substrate is a sensory neuron, an economic utility function, an instrument readout, or a graphical axis. The structure is a representational choice that lives in the *axis*, not in the data, which is precisely why it is so easy to overlook and so consequential when missed.

Three roles recur. First, a *wide-dynamic-range stimulus* whose values span many orders of magnitude on the physical axis. Second, a *proportional-importance regime*, the condition under which what matters is the ratio of values rather than their absolute difference — a doubling carries the same weight wherever it starts. Third, the *log re-encoding* that maps the multiplicative physical axis onto an additive internal one. With those three in place, three benefits follow automatically: the representation extends usable range without saturating, equal-importance changes become internally equal-spaced, and hard multiplicative reasoning collapses into easy additive reasoning. The cross-domain recurrence is not coincidence: when a representational substrate faces a wide range and a proportional-importance regime, log encoding is a *predictable* convergent solution to the same structural pressure.

structural_signature:
*the wide-dynamic-range stimulus spanning many orders of magnitude* — *the proportional-importance regime where ratio matters more than difference* — *the log re-encoding mapping the multiplicative axis onto an additive one* — *the ratio scale on which equal steps mean equal factors* — *the convergent-solution invariant: log encoding is the predictable response to the same structural pressure*

A system exhibits logarithmic perception and encoding when each of the following holds:

- **A wide-dynamic-range stimulus.** Some magnitude spans many orders of magnitude on the physical axis — sound pressure, wealth, frequency, ion activity, channel input.
- **A proportional-importance regime.** What matters is the ratio of values rather than their absolute difference; a doubling carries the same weight wherever it starts.
- **A log re-encoding.** The system maps the multiplicative physical axis onto an additive internal one, locating the representational commitment in the axis rather than the data.
- **A ratio scale.** Equal increments on the internal axis correspond to equal ratios on the physical axis, not equal differences.
- **Three inherited benefits.** Range compression (wide span fits a fixed resolution without saturating), arithmetic compression (products become sums), and equal-importance-equal-spacing follow automatically.
- **The convergent-solution invariant.** Wherever a representational substrate faces a wide range under a proportional-importance regime, log encoding is the predictable convergent solution, so cross-domain recurrence is structural pressure, not coincidence.

The components compose into one portable move and its repairs: re-encode to log when a wide-range input saturates, work in log-space when multiplicative composition grows unwieldy, and report on a log axis when comparing across orders of magnitude.

what_it_is_not:
- **Not `proportion_scale`.** A proportion/ratio scale is a *measurement-theory category* (a scale with a true zero and meaningful ratios); logarithmic perception and encoding is the *representational choice* to organise a system's sensitivity on the *logarithm* of magnitude so equal internal steps mean equal ratios — a transform of the axis, not a scale type.
- **Not `scale_invariance`.** Scale invariance is the property that a system looks the same under rescaling; log encoding is a *re-mapping* a system *performs* to handle wide range — the encoding choice, not an invariance the phenomenon already possesses.
- **Not `allometry_and_scaling_law`.** Allometry concerns power-law relationships *between* quantities; log encoding concerns representing *one* magnitude on a log axis — though a power law plots straight on log-log axes, the prime is the encoding move, not the cross-quantity scaling relationship.
- **Not `diminishing_returns`.** Diminishing returns is a falling marginal payoff; the Weber-style "minimum detectable change scales with baseline" is a *perceptual encoding* consequence, not an economic returns curve, and the prime's content is the ratio-scale axis, not a saturating benefit.
- **Not `representational_modality`.** Modality concerns which *form* (visual, verbal, spatial) a representation takes; log encoding concerns the *arithmetic of the axis* within a modality — equal steps as equal factors — independent of which modality carries it.
- **Common misclassification.** Applying a log axis reflexively. The pattern's preconditions are *both* a wide dynamic range (many orders of magnitude) *and* a proportional-importance regime (ratio matters more than difference); over a narrow range or where a fixed difference is operative, linear is correct and log distorts.

broad_use:
- **Psychophysics (Weber/Fechner)** — just-noticeable differences are proportional to baseline intensity; subjective magnitude is logarithmic in physical intensity for many channels.<!-- FACT-D66-326 -->[^fechner-1860]
- **Sensory neuroscience** — individual neurons in vision, audition, and olfaction encode intensity logarithmically over their working range; adaptive normalization extends it.<!-- FACT-D66-327 -->[^thompson-1967]
- **Economics (Bernoulli)** — diminishing marginal utility of wealth is canonically modelled as log-utility; a proportional gain feels comparable across starting points.<!-- FACT-D66-328 -->[^bernoulli-1738]
- **Numerical cognition** — the mental number line is log-spaced in non-symbolic estimation; distance and ratio effects are signatures of log encoding.<!-- FACT-D66-329 -->[^dehaene-2003]
- **Audition and music** — pitch is perceived on a log frequency scale; the octave (doubling) is the natural unit; equal temperament divides it into twelve log-equal steps.<!-- FACT-D66-330 -->[^loy-2006]
- **Instrument scales** — pH, Richter and moment-magnitude, stellar magnitudes, and decibels are all logarithmic re-encodings of physical quantities.<!-- FACT-D66-331 -->[^richter-1935]
- **Engineering displays** — Bode plots, log-log plots for power laws, and semi-log axes wherever data span many decades.
- **Information theory** — bits are log of the alphabet; entropy is built on log-probability; the log base reflects the measurement scale.<!-- FACT-D66-332 -->[^shannon-1948]

clarity:
Naming the arrangement makes visible a representational commitment that is otherwise invisible because it sits in the *axis choice* rather than in the data. A pH scale and a Richter scale look like ordinary numbers; they conceal a logarithmic re-encoding whose properties — equal-spacing-in-ratio, additive composition under multiplication of stimuli, compressed range — are silently inherited by every downstream reasoning step. Misreading a log scale as linear is a category mistake with operational consequences: a magnitude-7 earthquake releases roughly thirty-two times the energy of a magnitude-6, not "one unit more."<!-- FACT-D66-333 -->[^gutenberg-richter-1956] The clarifying force is to convert the felt impression "these numbers behave strangely" into the precise statement "this axis is a ratio scale, so its arithmetic is multiplicative."

The arrangement also explains why scale choices across unrelated fields converge. The recurrence of log encoding in psychophysics, finance, acoustics, and seismology is not a string of historical accidents but convergent design under shared structural pressure. Once that is seen, the cross-domain coincidence becomes a *predictive* tool: confronted with a new wide-range, proportional-importance setting, the analyst can anticipate that a log re-encoding will be the natural representation and can read existing log-scaled quantities for the properties the encoding guarantees.

manages_complexity:
The arrangement compresses two distinct simplifications into one move. First, *range compression*: stimuli spanning many orders of magnitude are mapped into a narrow internal range, avoiding both saturation at the top and underflow at the bottom, so a fixed bit depth or a fixed neural firing range can cover the whole span with usable resolution. Second, *arithmetic compression*: multiplicative composition of stimuli — chained gains, products of probabilities, compound interest — becomes additive composition of internal representations, which simplifies inference, comparison, and storage. A system that adopts log encoding pays a small fixed cost (calibrating the base, interpreting ratios) and harvests a large simplification across every downstream operation.

The leverage is portable as an intervention, not only as a description. When a system mis-saturates on a wide-range input, the standard repair is a log re-encoding. When multiplicative composition is producing unwieldy expressions, the standard repair is to work in log-space. When a quantity must be compared across orders of magnitude, the standard reporting is a log-scale axis. Each of these is the same structural move, recognizable across substrates because the pressure that motivates it is shared.

abstract_reasoning:
Logarithmic perception and encoding trains a reasoner to ask:

- Does the underlying quantity span many orders of magnitude, and is ratio rather than difference the operationally relevant comparison?
- On this axis, does a fixed increment mean a fixed multiplicative factor — and have I read "growth," "decay," and "difference" accordingly?
- Can I turn a product of physical quantities into a sum of internal ones, simplifying the inference?
- Would a power-law relationship here appear as a straight line on log-log axes, and what would its slope reveal about the underlying multiplicative process?
- Does the minimum detectable change scale with the current value rather than an absolute floor — Weber's law as a structural prediction rather than a curiosity?
- Is a reader at risk of misreading this log scale as linear, and what does that misreading cost?

The non-obvious inferences cluster around equivalences the encoding makes free. Sums of logs are logs of products, which is the operational reason engineers prefer decibels and chemists prefer pH. Equal increments encode equal ratios, which governs how "doubling" and "halving" map onto fixed internal steps. And sensitivity proportional to baseline turns Weber's law from an empirical oddity into a derivable consequence of the encoding choice.

knowledge_transfer:
Role mappings across domains:

- **Wide-dynamic-range stimulus** ↔ sound pressure / wealth / frequency / hydrogen-ion activity / channel input
- **Proportional-importance regime** ↔ ratio matters / relative change matters / proportional gain matters
- **Log re-encoding** ↔ companding / log-utility / pitch scale / pH / decibel / log-probability
- **Ratio scale** ↔ internal axis where equal steps mean equal factors
- **Range compression** ↔ avoiding saturation / fitting wide range at fixed resolution
- **Additive composition** ↔ products become sums / chained gains add / compound rates add

A sound engineer choosing μ-law companding, a chemist recording concentration as pH, an astronomer reporting brightness in magnitudes, and an economist modelling utility as the log of wealth are all making the same structural choice: take a quantity that spans orders of magnitude under a proportional-importance regime and re-express it on a ratio axis where equal steps are equal factors. The transfers are direct and documented. Auditory volume controls are exponential because perception is logarithmic, so the sensory-neuroscience finding ports straight into interface design. Bernoulli's insurance reasoning about log-utility transfers into behavioural models of diminishing marginal utility and into financial log-returns<!-- FACT-D66-334 -->[^bernoulli-1738], which compose additively across instruments and horizons in a way percentage returns do not. Information-theoretic encoding efficiency for wide-range stimuli aligns with the log-base encoding seen in sensory pathways, suggesting why log encoding is so widespread biologically. What moves between fields is not a loose analogy but the literal ratio-scale commitment together with its arithmetic consequences: the same equal-step-equals-equal-ratio property, the same product-to-sum collapse, and the same Weber-style sensitivity prediction, each recognizable once the encoding is named — and the same portable repairs (re-encode to log, work in log-space, report on a log axis) follow wherever the wide-range, proportional-importance pressure is found.

formal_abstract:
The Weber-Fechner law in psychophysics is the canonical formal instance, and it derives the log encoding from a measured local rule. The *wide-dynamic-range stimulus* is physical intensity — sound pressure or light luminance spanning many orders of magnitude. The empirical starting point is Weber's law: the just-noticeable difference $\Delta I$ scales with the baseline intensity $I$, so $\Delta I / I$ is constant<!-- FACT-D66-335 -->[^fechner-1860] — a *proportional-importance regime* established by measurement rather than assumed. Integrating that local rule ($dS = k\, dI / I$) yields the *log re-encoding*: subjective magnitude $S = k \ln I + c$, Fechner's law.<!-- FACT-D66-336 -->[^fechner-1860] This is the *ratio scale* in its purest form — equal increments of internal sensation $S$ correspond to equal *ratios* of physical intensity $I$, so a doubling of sound pressure feels like a fixed step wherever it starts. The *three inherited benefits* follow automatically: range compression (a neuron's bounded firing rate covers many decades of intensity without saturating), arithmetic compression (chained multiplicative gains add in log-space), and equal-importance-equal-spacing (the JND is a fixed internal step). The *convergent-solution invariant* is what elevates this from curiosity to structure: Weber's law is not an oddity of one sense but the *predicted* consequence of any representational substrate facing wide range under proportional importance, so its recurrence across vision, audition, and olfaction is convergent design under shared pressure, not coincidence.

**Mapped back:** Weber-Fechner instantiates every role — intensity as the wide-range stimulus, the constant Weber fraction as the proportional-importance regime, Fechner's logarithm as the re-encoding, the JND as the equal internal step — and turns Weber's law from an empirical oddity into a derivable consequence of the log encoding.

applied_industry:
Audio engineering and the pH scale are two applied instances sharing the identical commitment across unrelated substrates. In audio, the *wide-dynamic-range stimulus* is sound pressure, spanning the roughly twelve orders of magnitude from the threshold of hearing to the threshold of pain.<!-- FACT-D66-337 -->[^everest-pohlmann-2009] The *log re-encoding* is the decibel, and the *proportional-importance regime* is perceptual: because hearing is logarithmic (the Weber-Fechner result), what matters is the ratio of pressures, so a fixed decibel step is a fixed perceived loudness step. This is why a volume control is wired *exponentially* — equal knob rotation must produce equal perceived-loudness increments, so the sensory-neuroscience finding ports straight into interface design, and μ-law companding re-encodes the wide-range signal to fit a fixed bit depth without saturating (*range compression*). The *additive-composition* benefit is the engineer's reason for working in decibels: cascaded gains and losses through a signal chain *add* rather than multiply. The pH scale is the same move in chemistry: hydrogen-ion activity spans many orders of magnitude, pH is its negative logarithm, and the *misreading-as-linear* hazard the prime warns of is acute — a pH-4 solution is not "twice as acidic" as pH-2 but a hundred times *less* acidic<!-- FACT-D66-338 -->[^harris-2010], a category mistake with operational consequences identical to reading a magnitude-7 earthquake as "one unit more" than a magnitude-6 rather than ~32× the energy.

**Mapped back:** Decibels and pH are the same ratio-scale commitment as Weber-Fechner, with sound pressure and hydrogen-ion activity as wide-range stimuli — equal steps meaning equal factors, products collapsing to sums, and the linear-misreading hazard following directly from the log axis being invisible in the data.