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  "title": "Compatible supply and converging bottlenecks",
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  "description": "Converts independently manufactured inputs into a common finished-system basis.",
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  "revisionDate": "2026-10-07",
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  "topic": "Data-center physical systems",
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      "title": "Compatible supply and converging bottlenecks",
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      "title": "Converging supply bound",
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      "title": "If each package needs four HBM stacks, what can 400 compatible good stacks support before later losses?",
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    {
      "title": "Explore in Atlas",
      "url": "https://semiaifoundry.com/ai-atlas/#compatible-supply-capacity"
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    {
      "title": "TSMC CoWoS technology",
      "url": "https://3dfabric.tsmc.com/english/dedicatedFoundry/technology/cowos.htm"
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    {
      "title": "TSMC 2025 Annual Report",
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    {
      "title": "High-bandwidth memory stack",
      "url": "https://semiaifoundry.com/learn/atlas/hbm-stack/"
    },
    {
      "title": "Package substrate",
      "url": "https://semiaifoundry.com/learn/atlas/package-substrate/"
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      "title": "Commissioning a usable AI cluster",
      "url": "https://semiaifoundry.com/learn/atlas/cluster-commissioning-gates/"
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  "content": "Data-center physical systems · Atlas v1.3.0\n\n# Compatible supply and converging bottlenecks\n\nConverts independently manufactured inputs into a common finished-system basis.\n\n[Explore in Atlas](https://semiaifoundry.com/ai-atlas/#compatible-supply-capacity)Manufacturing supply to commissioned hall; time-dependent model\n\nLearning objectiveConvert supply quantities to one finished-unit basis without yield double counting.\n\n## The mechanism\n\nAccelerator packages require compatible logic dies, memory stacks, substrates and integration capacity to arrive together. HBM is manufactured and assembled on its own path before package integration. Facility deployment adds boards, racks, electrical service, cooling and software readiness. Counts from these stages use different units and cannot simply be added. A bill of materials converts each usable input into a possible number of finished units. The smallest compatible supply then bounds output for the chosen interval. TSMC’s packaging descriptions illustrate the convergence, while the laboratory model must keep screening, assembly yield and qualification as distinct steps.\n\n1.  Select a concrete bill of materials and finished-system boundary.\n2.  Convert each available qualified input into equivalent finished units.\n3.  Identify compatibility restrictions rather than pooling unrelated generations or package types.\n4.  Apply only the remaining assembly/test losses to already-screened input quantities.\n5.  Compare the resulting output with downstream rack and facility readiness during the same period.\n\n## Science and assumptions\n\n### Converging supply bound\n\n$$\nN_{\\mathrm{complete}}\\le\\min_i\\left\\lfloor\\frac{S_i}{b_i}\\right\\rfloor\n$$\n\nComplete products cannot exceed the smallest whole-number input count after each compatible supply is divided by its per-product requirement.\n\nSymbols and units\n\nN\\_complete\n\nComplete products supportable from the coavailable inputs\n\nproducts\n\nSᵢ\n\nUsable compatible input-i quantity\n\ninput-i units\n\nbᵢ\n\nPositive input-i requirement per finished product\n\ninput-i units/product\n\ni\n\nRequired input-type index\n\ninteger index\n\nSi is usable input-i units and bi input-i units per finished product; Ncomplete counts finished products.\n\nAssumptions Inputs are compatible and coavailable; later yield, timing and set overlap require additional treatment.\n\n## Engineering example\n\nSynthetic package needs one logic die, four HBM stacks and one substrate. Supplies of 150, 400 and 120 good units respectively bound assembly starts at 100, before any new assembly losses.\n\n## Distinctions and tradeoffs\n\nHBM does not appear after package manufacture; its own manufacturing branch converges with logic and package materials.\n\nBuilding inventory of one input may reduce later delay but ties up capital and does not compensate for a missing compatible component.\n\nLogic-wafer expansion cannot independently establish AI deployment capacity when memory, packaging or powered-rack readiness binds.\n\n## Specifications and interfaces\n\nCommon denominator\n\nFinished units per stated interval\n\nWafer starts, stacks and racks require conversion before comparison.\n\nInput quality basis\n\nRaw, screened or qualified\n\nApplying an earlier yield again to screened inputs double-counts losses.\n\n### Interfaces\n\nCompatible screened inputs Input\n\nLogic, HBM stacks, substrates and assembly slots\n\nFinished system output Output\n\nPackages or racks surviving the explicitly modeled stages\n\n## Check your understanding\n\n### If each package needs four HBM stacks, what can 400 compatible good stacks support before later losses?\n\n1.  400 complete packages regardless of design\n2.  1,600 packages\n3.  At most 100 packages\n\nAnswer and reasoning\n\nAt most 100 packages\n\nThe bill of materials converts stack count into a compatible finished-package bound.\n\n## Evidence and scope\n\nNo vendor capacity, queue or HBM wafer-intensity number is invented. Synthetic inputs are explicitly screened, avoiding repeated raw-die yield penalties.\n\nTrace compatible component rates, a bounded qualification/ramp scenario and package backlog; this is not a detailed fab queue or operator-allocation simulator.\n\n## Sources\n\n-   [TSMC CoWoS technology](https://3dfabric.tsmc.com/english/dedicatedFoundry/technology/cowos.htm)\n-   [TSMC 2025 Annual Report](https://investor.tsmc.com/sites/ir/annual-report/2025/2025%20TSMC%20Annual%20Report.E.pdf)\n\n[Published lesson data](https://semiaifoundry.com/ai-atlas/lesson-data/compatible-supply-capacity-7a526aaf0701ce73.json) · [Atlas releases and licensing](https://semiaifoundry.com/ai-atlas/licenses.html)\n\n## Continue exploring\n\n### Foundations\n\n-   [High-bandwidth memory stack](https://semiaifoundry.com/learn/atlas/hbm-stack/)\n-   [Package substrate](https://semiaifoundry.com/learn/atlas/package-substrate/)\n\n### Related lessons\n\n-   [Commissioning a usable AI cluster](https://semiaifoundry.com/learn/atlas/cluster-commissioning-gates/)"
}