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+#import "@preview/unify:0.8.1": add-unit, qty
+
+// All units for the specification should be specified here
+#add-unit("ppm", "ppm", "upright(\"ppm\")")
+#add-unit("ppb", "ppb", "upright(\"ppb\")")
+#add-unit("inch", "\"", "upright(\"\\\"\")", space: false)
+#add-unit("digital voltage", "VD", "upright(\"VD\")")
+#add-unit("volt peak-to-peak", "Vpp", "upright(V_\"pp\")")
+#add-unit("milli volt peak-to-peak", "mVpp", "upright(\"mV\"_\"pp\")")
+#add-unit("micro volt peak-to-peak", "uVpp", "upright(mu V_\"pp\")")
+#add-unit("dBc", "dBc", "upright(\"dBc\")") // decibels relative to the carrier
+#add-unit("rack unit", "U", "upright(U)", space: false)
+
+= Introduction <introduction>
+
+== What is analog computing? <what-is-analog-computing>
+
+Analog computing is the action of leveraging the properties of physical
+phenomena to model mathematical principles. The actual phenomena can be as
+diverse as hydraulics, mechanics, or electrics. In an electronic analog
+computer, voltages represent variables and operational amplifier circuits
+perform mathematical operations on them.
+
+Modeling the mathematical principles being computed implies that the results are
+continuous in time and amplitude. This directly contrasts digital computing,
+where results are symbolic and discrete.
+
+== Short history of analog computing <short-history-of-analog-computing>
+
+=== Mechanical and hydraulic analog computers
+<mechanical-and-hydraulic-analog-computers>
+
+Analog computing traces its roots to ancient Greece, with the Antikythera
+mechanism. It re-emerged time and time again across the ages, notably with the
+invention of the Slide Rule for computation of multiplications and divisions in
+the 1620s, and Lord Kelvin's Tide-Predicting machine invented in 1872.
+Mechanical or hydraulic analog computers (sometimes electronically controlled)
+continued to be the standard until the late 1950s.
+
+=== First electronic analog computers <first-electronic-analog-computers>
+
+In 1941, Karl D. Swartzel Jr. of Bell Labs patented the first operational
+amplifier (op-amp). 1942 saw the birth of the first fully electronic analog
+computer for real-time computation by Helmut Hölzer, to calculate V-2 rocket
+trajectories. In 1950, Gilbert D. McCann, Charles H. Wilts, and Bart Locanthi
+developed the "Direct Analogy Electric Analog Compute" ("the largest and most
+impressive general-purpose analyzer facility for the solution of field
+problems" - James S. Small, "The Analogue Alternative: The Electronic Analogue
+Computer in Britain and the USA, 1930-1975" Routledge in 2001).
+
+In 1960, the first educational electronic analog computer, the Heathkit EC-1,
+was released. It was programmed with patch cords and featured nine operational
+amplifiers (op-amps).
+
+In the late 1960s, electronic analog computer designs were published in
+electronics magazines. This is notably the case for the PEAC (Practical
+Electronics Analog Computer), published in 1968 in Practical Electronics.
+
+=== Golden age of electronic analog computers
+<golden-age-of-eletronic-analog-computers>
+
+Starting with the EAI PACE TR-48, produced by Electronic Associates Inc. in
+1961, hybrid computers became the industry standard for high-performance tasks.
+These machines combined the speed of analog computation for solving differential
+equations with the logical control and storage of digital computers. They were
+heavily utilized in the aerospace and automotive industries for real-time
+simulation — such as modeling the Space Shuttle's flight dynamics or nuclear
+power plant operations — tasks where purely digital computers of the era were
+still too slow.
+
+=== Decline of analog computing <decline-of-analog-computing>
+
+The decline began in the late 1970s and accelerated swiftly throughout the
+1980s, driven by the "Digital Revolution." While analog computers were fast,
+they suffered from physical limitations like noise floors and component aging
+(drift), which limited their precision compared to the perfect repeatability of
+digital machines. Furthermore, programming an analog computer required
+physically rewiring "patch cords," a laborious process compared to the rapidly
+evolving software-based programming of digital systems.
+
+=== Current times <current-times>
+
+A new rise of analog computing is currently underway, often referred to as
+"Neuromorphic Computing" or "In-Memory Computing". This generation uses the
+physical properties of memory devices (like resistance) to perform calculations,
+mimicking the neural structure of the human brain to process information. In
+2021, startup Mythic introduced the M1076 Analog Matrix Processor, a chip that
+performs AI inference using the analog currents inside flash memory cells,
+delivering up to 25 TOPS (Trillion Operations Per Second) at incredibly low
+power. Mythic filed for bankruptcy in 2024, but managed to raise \$125 million
+in December 2025, showing that there is still turbulence in the neuromorphic
+startup space.
+
+The field is still very active, notably with the Innatera Pulsar or the Applied
+Brain Research TSP1, both released in 2025.
+
+== The case for modern general purpose analog computers
+<the-case-for-modern-general-purpose-analog-computers>
+
+We believe the time is ripe for a revival of the General Purpose Analog
+Computer. Reintroducing general-purpose analog computing is not an exercise in
+retro-computing; it is a solution to specific modern problems. By combining the
+transparency of "Golden Age" architectures with modern low-noise components, we
+can achieve a new standard of computing that is sustainable, secure, and
+strategically independent.
+
+=== Theoretical capabilities <theoretical-capabilities>
+
+Historically, the General Purpose Analog Computer (GPAC) was perceived as being
+limited to solving differential equations, distinct from the universal logic of
+Turing Machines. However, this distinction assumes a finite system. In a
+sufficiently large analog system (the same way a digital computer is a Turing
+Machine assuming sufficiently large memory), the combinatorial logic required
+for universal computation is inherent in the topology.
+
+We do not rely on discrete "extensions" like Sample & Hold to achieve Turing
+Completeness; we use them merely for convenience. The $I$$(I x = x)$, $K$$(K x y
+  = x)$ and $S$$(S x y z = x z(y z))$ Combinators (which are sufficient for
+Turing Completeness) are not a special digital mode; they are a description of
+signal distribution and modulation that exists in every analog patch. With
+enough modules, the "patch" becomes a computational engine of unbounded
+complexity, capable of recursive structures defined purely by feedback loops
+rather than iterative loops. This argument will be fully developed in further
+sections.
+
+=== Technological sovereignty <technological-sovereignty>
+
+In an era of chip shortages and trade restrictions, reliance on $qty(5, "nm")$
+or $qty(3, "nm")$ silicon creates critical vulnerabilities. A computer built
+from standard through-hole operational amplifiers and passive components does
+not require a multi-billion dollar foundry. It can be assembled in a standard
+electronics lab anywhere in the world.
+
+With a 100% open-source design and macro-scale components, the hardware is fully
+auditable. There are no hidden "black box" intellectual property cores or
+potential hardware backdoors, ensuring high confidence in the computing
+substrate for sensitive modeling.
+
+=== Cost and accessibility <cost-and-accessibility>
+
+High-performance simulation usually requires expensive workstations or licensing
+fees for proprietary software. By utilizing off-the-shelf components (common
+op-amps, resistors, standard capacitors), the Bill of Materials (BOM) is a
+fraction of the cost of a modern FPGA or GPU-based accelerator. The
+"Through-Hole First" design philosophy means these machines can be produced,
+modified, and repaired by students, hobbyists, or labs in developing nations,
+without the need for robotic surface-mount assembly lines.
+
+=== Energy efficiency <energy-efficiency>
+
+While digital computers must toggle millions of transistors at gigahertz speeds
+to approximate a differential equation, an analog computer simply is the
+equation. Solving a complex set of coupled differential equations on this
+standard requires only the static power to bias the amplifiers. It avoids the
+massive dynamic power consumption associated with the high-frequency clock
+cycles of digital processors. Using an analog architecture delivers results with
+significantly lower total energy consumption per solution, aligning with global
+goals for reduced carbon footprints in data processing. This will be fully
+developed in further sections.
+
+=== Sustainability through repairability <sustainability-through-repairability>
+
+A 100% through-hole and open-source design ensures that every component is
+human-accessible. There are no microscopic BGA chips; the machine can be
+maintained indefinitely, breaking the environmentally destructive cycle of
+planned obsolescence. It essentially enforces the right to repair while allowing
+a reduction of e-waste.
+
+== The SAME Analog Modular Ecosystem <the-same-analog-modular-ecosystem>
+
+With this specification, we introduce a new analog computing ecosystem. We
+believe that with the right infrastructure, modern components and the advances
+in electronics research, we can now build analog computers that address the
+three main points that caused the decline of analog computing in the 1980s:
+cost, precision and drift.
+
+=== Making analog computers reliable and sustainable
+<making-analog-computers-reliable-and-sustainable>
+
+Electronics components are cheaper than ever right now. Op-amps that once cost
+hundreds of euros now cost at most a few dozen euros. PCB manufacturing is
+democratized. The material conditions are here. New advances in electronics
+research have solved the two remaining issues: drift and precision: with a
+combination of laser-trimmed components and topological advancements (servo
+loops, automated gain control, pulse width amplitude modulation, etc.), it is
+now possible to design analog circuits that are able to reach 0.001% precision
+(10ppm), over a $qty(90, "dB")$ signal to noise ratio (SNR), in a bandwidth
+ranging from DC to more than $qty(20, "kHz")$.
+
+=== What SAME is not <what-same-is-not>
+
+SAME is not a modular synthesizer format. It is not Eurorack, Serge or Buchla.
+While those synthesizer formats are based on general purpose analog computers,
+they are not designed for precision computations or repeatability. While SAME
+can be used for sound design or experimental composition, it does not provide
+the abstractions and simplifications that make synthesizers powerful.
+
+SAME is not a digitally controlled or calibrated analog computer. It focuses on
+fully analog computer topologies. It advocates a "what you see is what you get"
+approach. It has no presets, no patch memory. But it is precise enough that a
+patch sheet and a pen and paper allow full patch repeatability. We believe this
+approach is needed as it is more educational, and eliminates black boxes in
+programming (patches) and design (topologies). It is also more sustainable, as
+a design doesn't depend on a microcontroller and code that might fail and be out
+of production in five years.
+
+SAME is not a system on a chip (SOC). The revival of analog computing in the
+2020s has been mainly driven by SOCs. We do recognize the importance of this
+approach, and its many benefits, notably in energy consumption. However, SOCs
+require digital control. With SAME, we aim at creating an infrastructure for
+sustainable electronics. A unit built in 2026 should still work in 2076. Some
+parts will have been changed, but by focusing on through-hole parts in
+production at the time of designing, we ensure that a human with a soldering
+iron will be able to repair them.
+
+=== The scope of this specification <the-scope-of-this-specification>
+
+In this specification, we will provide full details and rationale behind the
+SAME format. We will provide schematics, gerber files, CAD files, as well as
+ngspice simulations of a reference implementation. We will provide a validation
+methodology for our precision claims, as well as the data to support them.
+
+Finally, we will propose a tiered approach to precision: we believe that a
+topology that manages 10ppm precision and $qty(90, "dB SNR")$ SNR over DC to
+$qty(20, "kHz")plus$ bandwidth is worth using and studying even with a lower
+precision target of $qty(100, "ppm")$ or $qty(1000, "ppm")$. While to achieve
+$qty(10, "ppm")$ some parts might get expensive due to their very high
+precision, someone could still achieve great reliability with lower precision
+parts. For this reason, while we will propose only one specification for the
+SAME chassis and power distribution, for each module in the reference
+implementation, we will propose three bills of material (BOM): Educational,
+aiming at $qty(1000, "ppm")$; Industrial, aiming at $qty(100, "ppm")$; and
+Metrologic aiming at $qty(10, "ppm")$.
+
+=== Reader's guide <readers-guide>
+
+We recommend a reader not familiar with the field to first read this
+specification sequentially. Sections 2 and 3 will develop the core
+specifications of the SAME ecosystem. Section 4 will specify the module design
+principles that allows it to achieve its precision goals. Section 5 will explain
+how to verify conformity of a SAME product with this specification. Section 6
+will present a reference implementation of the system. Finally, sections 7 and 8
+will show how and when to use a SAME Analog Computer.
+
+== Document conventions <document-conventions>
+
+To ensure interoperability between modules, chassis backplanes, and signal
+routing standards within the SAME Analog Modular Ecosystem, this specification
+utilizes specific keywords to denote requirement levels.
+
+The key words MUST, MUST NOT, REQUIRED, SHALL, SHALL NOT, SHOULD, SHOULD NOT,
+RECOMMENDED, MAY, and OPTIONAL in this document are to be interpreted as
+described in IETF RFC 2119.
+
+/ MUST / SHALL / REQUIRED: These terms indicate an absolute requirement of the
+  specification. Hardware or documentation that fails to meet these criteria is
+  non-compliant. Imperative statements (commands) that do not employ specific
+  keywords are also considered to be in this default state.
+  - Example: "The reference voltage rail MUST maintain stability within ±0.01%
+    of the nominal 10V output."
+/ MUST NOT / SHALL NOT: These terms indicate an absolute prohibition of the
+  specification.
+  - Example: "Signal ground MUST NOT be tied directly to the chassis earth at
+    the module level."
+/ SHOULD / RECOMMENDED: These terms indicate that there may exist valid reasons
+  in particular circumstances to ignore a particular item, but the full
+  implications must be understood and carefully weighed and documented before
+  choosing a different course.
+  - Example: "Input impedance for operational amplifiers SHOULD exceed 1MΩ to
+    minimize loading effects."
+/ SHOULD NOT / NOT RECOMMENDED: These terms indicate that there may exist valid
+  reasons in particular circumstances when the particular behavior is acceptable
+  or even useful, but the full implications should be understood and the case
+  carefully weighed and documented before implementing any behavior described
+  with this label.
+/ MAY / OPTIONAL: These terms indicate that an item is truly optional. One
+  vendor may choose to include the item because a particular marketplace
+  requires it or because the vendor feels that it enhances the product while
+  another vendor may omit the same item.
+  - Example: "The integration module MAY include a digital overflow indicator
+    LED."