Haitz's Law¶

The empirical LED regularity that light output per package rises ~20x per decade while cost per lumen falls ~10x — a log-linear trajectory arising because half a dozen loss terms improve multiplicatively, used as a roadmap and a below-trend diagnostic until efficiencies hit their thermodynamic ceilings.

Core Idea¶

Haitz's Law is the empirical regularity, named for Roland Haitz who articulated it around 1999, that the light output per LED package increases by roughly a factor of 20 per decade while the cost per lumen falls by roughly a factor of 10 over the same period — a compound doubling in lumens-per-package approximately every 18 to 24 months. The trajectory is not the product of a single engineering advance but of simultaneous, mutually reinforcing improvements along several loss-reduction axes: internal quantum efficiency (electrons-to-photons conversion fraction), light-extraction efficiency (photons escaping the semiconductor into the package), current-handling capacity per device, package thermal management (heat removal enabling higher drive currents without degrading junction lifetime), phosphor conversion efficiency (for white LEDs produced by downconverting blue emission), and manufacturing process yield. Because each axis contributes multiplicatively to the overall lumens-per-package figure, progress on any one of them compounds with progress on the others, yielding a log-linear trajectory in performance and cost against time that held remarkably well from the late 1960s through the mid-2010s. The law is the solid-state-lighting industry's structural analogue of Moore's law for transistors — a product-class-specific doubling-time regularity driven by stacked engineering improvement rather than by a single physical mechanism, and used in the same way: as a roadmap baseline that makes cost-crossover dates for applications predictable (a target application currently priced out by factor N becomes affordable in roughly 3·log₂(N) years at a three-year doubling), flags below-trend progress as evidence of a binding technical constraint deserving concentrated research investment, and informs capacity and fabrication-line planning. The trajectory eventually decelerates as individual efficiency terms asymptote toward their thermodynamic ceilings — internal quantum efficiency cannot exceed unity, and white-LED wall-plug efficiency by the 2010s was within roughly 30% of its thermodynamic limit for high-color-rendering-index phosphor designs — so the law is a time-bounded empirical regularity, not a permanent physical law.

Structural Signature¶

Sig role-phrases:

the device class — inorganic visible LED packages, with a measurable performance (lumens per package) and cost (cost per lumen)
the multiplicative loss axes — the half-dozen independently-improving terms that enter the composite multiplicatively: internal quantum efficiency, light-extraction efficiency, current-handling capacity, package thermal management, phosphor conversion, and process yield
the sustained R&D — decades of distributed industry engineering effort advancing each axis on its own timescale
the compounding — because the axes multiply rather than add, independent improvements compound, so progress on any one term advances the composite even while others plateau
the log-linear trajectory — the observed regularity: roughly 20× light output per decade and 10× cost reduction, a smooth exponential against time
the characteristic doubling time — the rate constant (lumens-per-package doubling every ~18–24 months) set by the industry's particular composition of improvement sources
the crossover arithmetic — the forecasting instrument: an application priced out by a factor N becomes affordable in roughly 3·log₂(N) years on the schedule
the below-trend diagnostic — a generation landing under the line as evidence that one loss term has become the binding constraint deserving concentrated investment
the bounded efficiencies — the thermodynamic ceilings (internal quantum efficiency cannot exceed unity, wall-plug efficiency near its limit) that make the law time-bounded
the asymptotic deceleration — the predicted lengthening of the doubling time as individual terms saturate, so the line must not be extrapolated forever

What It Is Not¶

Not a law of physics. Haitz's law is a time-bounded empirical regularity sustained by decades of stacked engineering effort, not a permanent physical guarantee. Because it is the product of bounded efficiencies, it must decelerate as individual terms approach their thermodynamic ceilings — so the line cannot be extrapolated forever, and treating it as an immovable law mis-forecasts the saturation.
Not the result of a single breakthrough or mechanism. The trajectory is produced by the multiplicative compounding of roughly six independent loss-reduction axes — internal quantum efficiency, light extraction, current handling, thermal management, phosphor conversion, process yield. No one advance produces the line; it is the smooth average of stacked, mutually reinforcing improvements, which is why progress on any one axis advances the composite even while others plateau.
Not a guarantee of indefinite improvement. Internal quantum efficiency cannot exceed unity and wall-plug efficiency is hemmed by its thermodynamic limit, so the doubling must eventually slow. A chip generation landing below trend is not merely disappointing but evidence that one loss term has become the binding constraint — the regularity is a baseline to be diagnosed against, not a promise to be banked.
Not Moore's law, nor an export of it. Haitz's law is the solid-state-lighting sibling of Moore's law — and of Swanson's and Wright's laws — under a shared parent, the experience/learning curve, not a borrowing of any one of them. Each is the same stacked-engineering-improvement pattern instantiated on a different product class with its own slope; the cross-domain content belongs to the parent, not to Haitz specifically.
Not a causal mechanism that travels. It is a fitted empirical trajectory, so its forecasting use — the crossover arithmetic — transfers only as an instrument, and only where a doubling-time trajectory has actually been measured. Its characteristic over-reading is extending the line past the regime in which it was fitted; the substrate-spanning lesson (many small independent improvements compound multiplicatively) is owned by the learning-curve prime, not by the name "Haitz's law."

Scope of Application¶

Haitz's law lives within optoelectronics and solid-state lighting, across the device classes whose performance is the multiplicative product of several independently-improving loss terms under sustained R&D; its reach is bounded to that domain, and the famous companions (Moore's, Swanson's, Wright's laws) are siblings under the parent learning_curve_effects, not exports of this law.

LED device design — the home turf, where lumens-per-package and cost-per-lumen roadmaps scope new chip generations and below-trend results flag a binding loss term.
Solid-state-lighting industry strategy — capacity, fabrication-line, and product-line planning conditioned on the doubling-schedule cost-and-performance trajectory.
Solid-state-lighting public policy — efficiency mandates and incandescent phase-outs timed to Haitz-trajectory cost crossovers (DOE SSL programs cited it directly as a roadmap baseline).
Optoelectronic device cousins — infrared LEDs, UV-LEDs, and laser diodes, which show recognizable Haitz-shaped trajectories at different rates and offsets.
Display economics — micro-LED and mini-LED backplanes inheriting a slower version of the same stacked-improvement trajectory.

Clarity¶

Stating Haitz's law turns a vague industry sense that "LEDs keep getting brighter and cheaper" into a quantitative baseline against which any single chip generation can be judged. That baseline is what makes progress diagnostic: a generation that lands below trend is not just disappointing, it is evidence of a binding technical constraint — thermal droop, efficiency droop, phosphor degradation, packaging cost — that warrants concentrated research, while above-trend progress flags either a genuine process breakthrough or a measurement artifact to be checked. Without the regularity, each result is an isolated data point; with it, the result acquires a verdict, and the sharper question becomes "which loss term is holding us back?" rather than "is this good or bad?"

The law also makes the adoption horizon legible as a calculation rather than a guess. Because cost per lumen falls on a known doubling schedule, an application currently priced out by a factor of N becomes affordable in roughly 3·log₂(N) years, so cost-crossover dates for residential, automotive, and street-lighting markets become predictable to within a few years and can anchor capacity planning and even policy timing. Equally, framing it as a law named for an observed trajectory — the solid-state-lighting analogue of Moore's law — keeps a crucial distinction sharp: this is a time-bounded empirical regularity sustained by stacked engineering effort, not a permanent physical guarantee. That distinction is what lets a practitioner anticipate the eventual deceleration as individual efficiency terms approach their thermodynamic ceilings, instead of extrapolating the line forever.

Manages Complexity¶

The performance of an LED package is, mechanistically, the joint product of half a dozen loss terms evolving on their own timescales — internal quantum efficiency, light-extraction efficiency, current-handling capacity, package thermal management, phosphor conversion, and process yield — each governed by its own device physics, each the subject of a separate research program, each capable of its own breakthroughs and plateaus. Forecasting where lumens-per-package and cost-per-lumen will stand in five years by modeling that coupled system would mean tracking the joint dynamics of all six, with their interactions and their distinct ceilings. Haitz's law collapses that high-dimensional engineering problem onto a single scalar: because the loss terms enter multiplicatively, their compounded effect on the composite metric is a log-linear trajectory with one characteristic doubling time. The strategist or device engineer no longer carries the six-axis model; they carry a rate constant and a baseline, and read the industry's whole future cost-and-brightness path off a straight line on a log plot. From that single line three qualitative judgments follow without re-deriving the physics. Adoption timing becomes arithmetic: an application priced out by a factor of N crosses into affordability in roughly 3·log₂(N) years, so crossover dates for residential, automotive, and street lighting are read off the schedule rather than guessed. The diagnostic verdict on any one chip generation becomes a comparison to trend: a generation below the line is not merely disappointing but is evidence that one loss term has become binding — the residual that the composite usually hides now points to the constraint deserving concentrated investment — while one above the line flags a genuine breakthrough or a measurement to recheck. And the trajectory's own endpoint is read off the same compression: since the composite is a product of bounded efficiencies, the analyst anticipates deceleration as individual terms approach their thermodynamic ceilings rather than extrapolating the line forever. The branch structure is therefore small and explicit — on trend, capacity and adoption planning proceed on schedule; below trend, isolate and fund the binding loss term; approaching the ceilings, expect the doubling time to lengthen — so a forecasting and research-prioritization problem that nominally spans six coupled physical mechanisms reduces to tracking one rate constant, one baseline, and the gap between the latest generation and the line.

Abstract Reasoning¶

Haitz's law licenses reasoning moves a solid-state-lighting engineer or strategist runs on the LED-package performance trajectory, all conducted on a single log-linear line — lumens-per-package and cost-per-lumen against time with a characteristic doubling — that stands in for the coupled six-axis loss model.

The predictive move is crossover-date arithmetic: from the known doubling schedule the analyst computes when a currently-unaffordable application becomes affordable, reasoning that an application priced out by a factor of N crosses into affordability in roughly 3·log₂(N) years at a three-year doubling. The procedure is mechanical — take the current cost-per-lumen, divide by the required affordability ratio, take the base-2 logarithm, multiply by the years-per-doubling — and it converts adoption timing from a guess into a calculation, letting the strategist anchor capacity planning, fabrication-line investment, and even policy timing (efficiency mandates, incandescent phase-outs) to dates read off the line rather than debated.

The diagnostic move runs from a single chip generation's position relative to the line back to the state of the underlying physics. The analyst reasons that a generation landing below trend is not merely disappointing but is evidence of a binding technical constraint — one of the loss terms (thermal droop, efficiency droop, phosphor degradation, packaging cost) has become the bottleneck — so the residual that the composite metric usually hides now points at the constraint deserving concentrated research investment. A generation above trend flags either a genuine process breakthrough or a measurement artifact to recheck. The sharper question this licenses is "which loss term is holding us back?" rather than "is this result good or bad?", and the move is to treat deviation from the line as a pointer into the six-axis model even while the line itself spares the analyst from carrying that model day to day.

The boundary-drawing move keeps the trajectory's time-bounded character explicit and predicts its own end. The analyst reasons that because the composite metric is a product of bounded efficiencies — internal quantum efficiency cannot exceed unity, wall-plug efficiency is hemmed by its thermodynamic ceiling — the log-linear line is an empirical regularity sustained by stacked engineering effort, not a permanent physical guarantee, and must decelerate as individual terms asymptote toward their ceilings. So the move is to refuse to extrapolate the line forever: confronting an efficiency term already within a small margin of its limit, the analyst predicts the doubling time will lengthen and adjusts forecasts accordingly, distinguishing the regime where the schedule holds from the regime where ceiling-proximity bends it. This is the order-of-events claim the law supports — sustained doubling first, then deceleration as the bounded terms saturate — and it guards against the characteristic error of pricing a future application off an indefinitely-extended straight line.

Underlying these is a compounding-from-multiplicative-axes move: the analyst reasons that the trajectory is log-linear precisely because the six loss terms enter multiplicatively, so independent improvements on separate axes compound rather than merely add, and progress on any one term advances the composite even while the others plateau. This explains why the line held across decades despite no single dominating breakthrough — the stacked, mutually-reinforcing improvements averaged into a smooth exponential — and it lets the analyst predict that the trajectory is robust to any one axis stalling (the others carry it) but vulnerable when several terms approach their ceilings at once, at which point the multiplicative engine that produced the line runs out of room.

Knowledge Transfer¶

Within optoelectronics Haitz's law transfers as mechanism, and what carries is the whole apparatus: the single log-linear line standing in for the coupled six-axis loss model, the crossover-date arithmetic, the below-trend diagnostic that points at the binding loss term, the compounding-from-multiplicative-axes account, and the ceiling-deceleration boundary. The precondition is a class of solid-state emitters whose performance is the multiplicative product of several independently-improving loss terms under sustained industry R&D, and the cousins meet it — infrared LEDs, UV-LEDs, laser diodes, and micro-/mini-LED display backplanes all show recognizable Haitz-shaped trajectories at different rates and offsets. Across these the device differs but the log-linear forecasting line and its diagnostic and boundary uses are the same, because each is a genuine instance of the same stacked-engineering-improvement trajectory rather than a likeness of it.

Beyond optoelectronics the report points up rather than out, and the honest characterization is that the famous "cross-domain" companions are not exports of Haitz at all but siblings under a shared parent. Moore's law for transistors, Swanson's law for solar-PV module cost, and Wright's law for cumulative-production cost are each the same structural pattern — a manufactured-technology product class undergoing sustained, distributed, multiplicative engineering improvement, yielding a log-linear cost-and-performance trajectory — instantiated on a different product line with a slope set by that industry's particular composition of improvement sources. That shared pattern is the substrate-independent content, and it is owned by the parent prime: the experience / learning curve (learning_curve_effects), within which Haitz, Moore, Swanson, and Wright are co-exemplars differing only in product class and slope. So the cross-domain lesson — many small, independent engineering improvements compound multiplicatively because each addresses a different loss term, producing a smooth exponential in cost and performance over time — should carry the parent learning-curve prime, not the name "Haitz's law," whose distinctive cargo (the LED package, the specific loss axes of internal-quantum/extraction/phosphor/thermal/yield, the ~20×-per-decade and ~10×-cost figures, the solid-state-lighting roadmap and DOE policy timing) is optoelectronics furniture that does not and should not travel. Two further honesties sharpen the boundary. First, because Haitz is a fitted empirical trajectory rather than a causal mechanism, its forecasting use (the crossover arithmetic) transfers as an instrument wherever a doubling-time trajectory has actually been measured — but only there, and its characteristic over-reading is extrapolating the line past the regime where it was fitted. Second, the law is time-bounded: it is sustained engineering effort against bounded efficiencies, not a permanent physical guarantee, so the parent that travels is the experience curve including its eventual deceleration as the multiplicative terms approach their ceilings, not an indefinitely-extended straight line. Mechanism within optoelectronics; a shared abstract pattern — carried by the learning-curve parent, with Moore/Swanson/Wright as siblings rather than as borrowings of this law — beyond. This is exactly the boundary Structural Core vs. Domain Accent draws.

Examples¶

Canonical¶

Roland Haitz and colleagues, around 1999–2000, fitted the observed LED trajectory: across roughly three decades from the late 1960s, the light output of a commercial LED package had risen by about a factor of 20 every decade while the cost per lumen had fallen by about a factor of 10 per decade — equivalently, lumens-per-package doubling every 18–24 months. Plotted on a log axis against time, both series trace nearly straight lines. The forecasting instrument follows directly: an application currently priced out by a factor of N becomes affordable in roughly 3·log₂(N) years at a three-year doubling. If white-LED lighting is ten times too costly for a market, that is 3·log₂(10) ≈ 3·3.32 ≈ 10 years to cost crossover; a hundredfold gap, 3·log₂(100) ≈ 20 years. The straight line held because the underlying gains were multiplicative and mutually reinforcing.

Mapped back: The LED package is the device class, and its lumens-per-package and cost-per-lumen histories are the log-linear trajectory with an 18–24-month characteristic doubling time. That the line arises from stacked internal-quantum, extraction, phosphor, thermal, and yield gains is the multiplicative loss axes and the compounding; the 3·log₂(N)-year computation is the crossover arithmetic read straight off the schedule.

Applied / In Practice¶

The US Department of Energy's Solid-State Lighting program used the Haitz trajectory as its explicit roadmap baseline, setting efficacy and cost targets on the doubling schedule and tracking each LED generation against the line. The forecast played out in the market: commercial LED A-lamps that cost roughly $40–50 around 2010 fell below $5 within about five years as lumens-per-dollar climbed, crossing the affordability threshold for general household illumination. That crossover made incandescent phase-out policies (the efficiency standards in the US Energy Independence and Security Act of 2007, phased in from 2012) practical rather than punitive, because a superior-efficiency substitute had become cheaper on the predicted schedule. Below-trend generations, meanwhile, were read by device engineers as flagging a binding loss term — notably efficiency "droop" at high drive current — directing concentrated research.

Mapped back: The A-lamp price collapse is the crossover arithmetic realized in a real market, and DOE's target-setting treats the log-linear trajectory as a planning baseline. Reading droop-limited generations as under-the-line is the below-trend diagnostic pointing at a binding axis, while the eventual approach of white-LED efficacy toward its limit foreshadows the bounded efficiencies and asymptotic deceleration.

Structural Tensions¶

T1: One scalar line versus the six-axis physics it hides (the abstraction you must undo to act). The law's power is compression: a single log-linear line, one rate constant and a baseline, stands in for the coupled dynamics of six independently-improving loss terms, so a strategist forecasts the industry's whole future off a straight line without carrying the device physics. But the line earns its smoothness precisely by averaging the axes away, and its most valuable diagnostic use — reading a below-trend generation as a binding loss term — requires reaching back into the very six-axis model the line abstracted out. The tool that lets you not track internal-quantum, extraction, phosphor, thermal, and yield gains is also the tool that, the moment something breaks, tells you only that something broke, not which. The tension is that the abstraction is a forecasting asset and a causal veil at once. Diagnostic: Is the single-line view sufficient for the question at hand (timing, planning), or does acting on a deviation require re-opening the loss-term model the line deliberately hides?

T2: Empirical trajectory versus permanent law (a straight line with no internal bend signal). Called a "law" and drawn as a straight line on a log plot, Haitz's regularity invites indefinite extrapolation — and the crossover arithmetic depends on projecting the line forward. But it is a time-bounded empirical fit sustained by engineering effort against bounded efficiencies (internal quantum efficiency cannot exceed unity), so it must eventually decelerate. Crucially, the fit contains no signal of when it will bend: the ceilings are external physics, not parameters of the line, so the trajectory looks equally straight the year before saturation as a decade before it. The same smooth regularity that makes the instrument trustworthy inside its regime makes over-extrapolation seductive and gives no warning at the edge. The tension is that the law's reliability and its most dangerous misuse are the same straight line. Diagnostic: Is the forecast staying within the regime where the trajectory was fitted, and is the proximity of each efficiency term to its thermodynamic ceiling being checked outside the line before the line is extended?

T3: Multiplicative robustness versus simultaneous-ceiling collapse (the durability engine is the failure mode). Because the six loss terms enter multiplicatively, independent gains compound, and progress on any one axis advances the composite even while others plateau — which is exactly why the line held for decades with no single dominating breakthrough. That same multiplicative structure sets the terms of its end: the trajectory is robust to any one axis stalling but vulnerable when several approach their ceilings at once, at which point the compounding engine runs out of room and no axis is left to carry the composite. So the property that makes the law durable (many independent multiplicative axes) is the property that makes its eventual breakdown abrupt rather than gentle. The tension is that robustness and fragility here are two readings of the same mechanism, separated only by how many terms are near their limits. Diagnostic: Is the trajectory being sustained by axes with headroom carrying a stalled one, or are several loss terms nearing their ceilings simultaneously, so the multiplicative engine is about to lose its slack?

T4: Below-trend verdict versus attribution ambiguity (a deviation is a pointer, not an answer). The diagnostic move treats a generation landing below the line as evidence of a binding technical constraint deserving concentrated research, and one above the line as a breakthrough or a measurement to recheck. This converts each result from an isolated data point into a verdict — a genuine gain. But the deviation alone does not say which loss term binds (that needs the six-axis model), and a single below-trend generation can equally reflect measurement error, a one-off yield problem, market-pricing noise, or a true plateau. So the confident verdict ("fund the binding constraint") is under-determined by the gap to the line, and over-reacting to one noisy generation is as available as correctly spotting droop. The tension is that the line's diagnostic authority is real over many generations but weak on any single one, exactly where decisions are made. Diagnostic: Is the below-trend reading corroborated by an identified loss term and a persistent pattern, or is a single generation's deviation — possibly noise or mismeasurement — being promoted to a research verdict?

T5: Autonomy versus reduction (an LED trajectory or an instance of the experience curve). Haitz's law is a named optoelectronics regularity with specific cargo — the LED package, the internal-quantum/extraction/phosphor/thermal/yield axes, the ~20×-per-decade and ~10×-cost figures, the solid-state-lighting roadmap and DOE policy timing — and within optoelectronics it transfers as full mechanism to IR-LEDs, UV-LEDs, laser diodes, and micro-LED backplanes, which are genuine instances of the same stacked-improvement trajectory. But its cross-domain companions are not exports of Haitz at all: Moore's, Swanson's, and Wright's laws are siblings under a shared parent — the experience/learning_curve_effects — each the same multiplicative-improvement pattern on a different product class with its own slope. The substrate-independent lesson (many small independent improvements compound multiplicatively into a smooth cost-and-performance exponential, decelerating as the terms saturate) belongs to that parent, and Haitz's forecasting use transfers only as an instrument where a doubling trajectory has actually been measured. The tension is between a named law that earns its keep with LED specifics and the learning-curve parent that actually carries across industries. Diagnostic: Resolve toward the parent (learning_curve_effects, with Moore/Swanson/Wright as co-siblings) when carrying the compounding-improvement lesson to another product class; toward the named law when the LED loss axes and solid-state-lighting roadmap are the actual subject.

Structural–Framed Character¶

Haitz's law sits near the middle of the spectrum — best read as mixed, closely parallel to the Giffen good in one respect: an evaluatively neutral empirical regularity that is real whether or not anyone names it, but bound to a human-industry substrate rather than to nature, and pinned to optoelectronics vocabulary. On evaluative_weight it reads structural: the law is a neutral fitted trajectory — lumens up, cost down, on a log-linear line — that praises and blames nothing; even its diagnostic use (a below-trend generation flags a binding loss term) is a technical pointer, not a verdict. On human_practice_bound it reads mixed: the trajectory genuinely occurred — LEDs really did get ~20× brighter and ~10× cheaper per decade whether or not Haitz articulated it — so it is not observer-constituted; but unlike Gloger's rule or Haldane's rule, which are facts of nature, Haitz's law is a regularity about human technological development, sustained by "decades of distributed industry engineering effort" and only meaningful against manufacturing, R&D, and markets, so it is bound to a human-practice substrate. Institutional_origin is likewise mixed: the law is a fitted, named regularity (Haitz ~1999, used as a DOE roadmap baseline), yet what it fits is a real trajectory of stacked improvement, not a mere convention. On vocab_travels it reads framed: lumens-per-package, internal quantum efficiency, light-extraction, phosphor conversion, wall-plug efficiency are irreducibly optoelectronic. And on import_vs_recognize the transfer is bimodal exactly as the entry documents — within optoelectronics the apparatus is recognized intact across IR-LEDs, UV-LEDs, laser diodes, and micro-LED backplanes (genuine instances of one stacked-improvement trajectory), while the famous companions Moore, Swanson, and Wright are siblings under a shared parent, not exports of Haitz.

The portable structural skeleton is learning_curve_effects (the experience curve) — many small, independent engineering improvements compounding multiplicatively into a smooth cost-and-performance exponential that decelerates as the terms approach their ceilings. That skeleton genuinely spans product classes, but it is exactly what Haitz's law instantiates as one co-exemplar (alongside Moore/Swanson/Wright), not what makes "Haitz's law" itself travel: the cross-domain lesson belongs to the learning-curve parent, while the LED package, the specific loss axes, the _20×/10× figures, and the solid-state-lighting roadmap stay home; the crossover arithmetic transfers only as an instrument, and only where a doubling trajectory has actually been measured. Its character: an evaluatively neutral, genuinely-occurring empirical trajectory of human technological improvement — mixed, structural in the multiplicative-compounding learning-curve skeleton it instances and in its observer-independent occurrence, framed in its industry-practice substrate and irreducibly optoelectronic vocabulary.

Structural Core vs. Domain Accent¶

This section decides why Haitz's law is a domain-specific abstraction and not a prime, and carries the case for its domain-specificity in one place.

What is skeletal (could lift toward a cross-domain prime). Strip the optoelectronics and one thin relational structure survives: when a manufactured technology's performance is the multiplicative product of several loss terms that independent, sustained engineering effort improves in parallel, the composite traces a smooth log-linear cost-and-performance exponential over time, which decelerates as the terms approach their ceilings. The portable pieces are abstract — a product class with a scalar performance metric, several independently-improving multiplicative axes, distributed R&D effort, and a resulting exponential with a characteristic rate and an eventual saturation. Nothing there mentions lumens. This is exactly learning_curve_effects (the experience curve), and it genuinely spans product classes — Moore's law for transistors, Swanson's for solar-PV cost, Wright's for cumulative-production cost are recognizable co-exemplars. But that compounding-improvement core is what Haitz's law instantiates as one co-exemplar, not what makes it Haitz's law; and its famous "cross-domain" companions are siblings under the parent, not exports of it.

What is domain-bound. Almost all the content is optoelectronics furniture, and none of it survives extraction. The device class is not generic — it is the inorganic visible LED package, measured in lumens per package and cost per lumen. The multiplicative axes are worked device physics — internal quantum efficiency, light-extraction efficiency, current-handling capacity, package thermal management, phosphor conversion, process yield. Its rate is a specific fitted figure (~20× light output and ~10× cost per decade, doubling every 18–24 months), its ceilings are specific thermodynamic limits (internal quantum efficiency ≤ 1, wall-plug efficiency near its high-CRI limit), and its instruments (the crossover arithmetic, the below-trend loss-term diagnostic) and worked uses (the DOE Solid-State Lighting roadmap, the LED A-lamp price collapse enabling incandescent phase-out) are all solid-state lighting. The decisive test: remove the LED device and its loss physics and there is no Haitz's law left — a solar module or a transistor traces its own exponential with its own slope and its own axes, and is a sibling instance of the experience curve, not Haitz's law applied; what remains after stripping the LED specifics is the bare learning-curve skeleton, a more general thing.

Why this does not clear the prime bar. A prime's vocabulary travels and its transfer is recognition of the same mechanism, not analogy. Haitz's law's transfer is bimodal. Within optoelectronics it moves as full mechanism — the single log-linear line, the crossover arithmetic, the below-trend diagnostic, the compounding-from-multiplicative-axes account, and the ceiling-deceleration boundary carry intact to IR-LEDs, UV-LEDs, laser diodes, and micro-/mini-LED backplanes, which are genuine instances of the same stacked-improvement trajectory at different rates and offsets. That is genuine within-domain mechanism transfer. Beyond optoelectronics the report points up, not out: Moore, Swanson, and Wright are not the LED trajectory relocated but co-instances of the shared parent, each on its own product class with its own slope, and Haitz's forecasting apparatus (the crossover arithmetic) transfers only as an instrument, and only where a doubling trajectory has actually been measured — its characteristic over-reading being extrapolation past the fitted regime. And when the bare cross-domain lesson is wanted — many small independent improvements compound multiplicatively into a smooth cost-and-performance exponential that decelerates as the terms saturate — it is already carried, in more general form, by learning_curve_effects. The cross-domain reach belongs to that parent (with Moore/Swanson/Wright as co-siblings); "Haitz's law," as named, carries the LED package, the specific loss axes, the _20×/10× figures, and the solid-state-lighting roadmap that should stay home.

Relationships to Other Abstractions¶

Current abstraction Haitz's Law Domain-specific

Parents (1) — more general patterns this builds on

Haitz's Law is a kind of Learning Curve Effects Prime

Haitz's Law is a Learning Curve Effect specialized to LED packages whose light output rises and unit cost falls predictably with cumulative engineering and production experience.

Hierarchy paths (3) — routes to 3 parentless roots

Haitz's Law → Learning Curve Effects → Increasing Returns

Show alternative paths (2)

Not to Be Confused With¶

Moore's law. The transistor-density (and later, cost-per-transistor) doubling regularity for integrated circuits, roughly every two years. It is Haitz's most-cited analogue and the two are constantly equated, but Moore's law is a sibling co-exemplar on a different product class (silicon logic, not LED packages), with its own slope and its own loss axes — not the source Haitz borrows from. The kinship runs through the shared parent, not between them. Tell: is the device class transistors on a die (Moore) or light-emitting packages measured in lumens per package (Haitz)? Same log-linear shape, different substrate and rate.
Wright's law (the learning/experience curve in its original form). Cost falling by a fixed fraction per doubling of cumulative production — indexed to units built, not to calendar time. Haitz (like Moore) is fitted against time. When production volume grows exponentially the two coincide, but they diverge whenever output accelerates or stalls, and Wright's is the more mechanistically fundamental statement. Tell: is the x-axis cumulative units produced (Wright) or years (Haitz)? If a production slowdown would bend the curve, you are reasoning in Wright's terms.
Swanson's law. The observation that solar-PV module price drops ~20% per doubling of cumulative shipped volume. Another sibling under the same experience-curve parent, on photovoltaic modules rather than LEDs. Readers group "Haitz for LEDs, Swanson for solar" as if one implied the other; they are independent instances with independent slopes. Tell: is the product class photovoltaic modules (Swanson) or inorganic visible LEDs (Haitz)? Neither exports to the other — each is fitted on its own industry.
Learning curve / experience-curve effects (the parent prime). The substrate-neutral pattern Haitz instantiates: many small, independent engineering improvements compounding multiplicatively into a smooth cost-and-performance exponential that decelerates as the terms approach their ceilings. This is the umbrella that genuinely travels across product classes (with Moore, Swanson, Wright as co-siblings), treated more fully as its own prime. Tell: strip the LED package, the specific loss axes, and the _20×/10× figures and what remains — compounding improvement over a manufactured product class — is the learning curve, a more general thing than Haitz's law.
Economies of scale. Unit cost falling because fixed costs spread over larger output at a point in time — a static volume effect, reversible if volume shrinks. Haitz's trajectory is cumulative, ratcheting technical improvement (better efficiency, extraction, yield) that does not un-happen when volume falls. The two often co-occur in a cheapening product but are distinct mechanisms. Tell: would the cost gain reverse if this year's production volume dropped (economies of scale) or is it locked-in learning that persists regardless of current volume (Haitz / experience curve)?
A law of physics. A permanent, mechanism-grounded invariant (e.g. the thermodynamic ceilings — internal quantum efficiency ≤ 1 — that actually bound Haitz's trajectory). Haitz's law is by contrast a time-bounded empirical fit sustained by engineering effort, guaranteed to decelerate as those true physical ceilings are approached. Confusing the fitted line for a physical law is exactly what produces over-extrapolation past saturation. Tell: does the relation follow from a conservation principle or bound that cannot be engineered around (physics), or is it a fitted trajectory that a binding loss term could bend next generation (Haitz)?

Neighborhood in Abstraction Space¶

Haitz's Law sits in a sparse region of the domain-specific corpus (97^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Unclustered & Miscellaneous (309 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12