{
 "_doc": "One result as verifycorelabs.com prints it: the headline, the problem and the buyer cut (never reworded) from the lab's plain-English account of the result, the one figure a buyer is shown and its limit, and the lab's current claim and limits verbatim, copied at the commit named in source. A field is left out, never reworded, when it uses a word this site keeps for its own process or names a file this site does not serve (not_reprinted).",
 "slug": "owned-3d-end-effect",
 "company": "ChipletOS",
 "order": 2,
 "rank": 6,
 "served_receipt": "packaging-extraction/results/owned-3d-end-effect.json",
 "lab_file_older": false,
 "headline": [
  "The lab built its own three-dimensional electrical solver, checked it first against textbook shapes whose answers are known exactly",
  "about 40% of its charge-storing capacity (capacitance) sits at its two ends, a share that the lab's flat, two-dimensional models leave out by design"
 ],
 "qualification": [
  "that flat models omit end effects is textbook",
  "but the corrected number is the 3-D solver's own answer, costing one 3-D solve per layout, and FastCap's own resolution (about 0.5%) is as large as that worst error",
  "Whether the omission changes any ratio the lab's models actually certify is untested"
 ],
 "why": [
  "A package model that treats each vertical connection as an infinitely long two-dimensional cross-section leaves out the capacitance at its ends"
 ],
 "buyer": [
  "chip-package and glass or silicon interposer design teams, and the extraction-tool vendors that serve them."
 ],
 "figure": "an independent FastCap N=8 cross-check at 0.80% diagonal / 1.04% dominant off-diagonal",
 "figure_from": "lab limits",
 "limit": "for one idealised vertical metal connection — a bare cylinder in a uniform insulator at one standard size, without the pads and metal planes a real package via ends in",
 "limit_from": "d1",
 "plain": "about 40%",
 "stronger": "Roughly 40% of a finite via's driven-pair capacitance is 3-D end-effect",
 "quotes": {
  "fastcap": "0.498% (max) and 0.308% (median) of FastCap on 86 pairs of 12 fresh layouts drawn from a pre-registered seed, against a 42.794% median error uncorrected"
 },
 "claim": "Roughly 40% of a finite via's driven-pair capacitance is 3-D end-effect that a 2-D per-unit-length model structurally omits — measured with our own 3-D solver, validated against exact references before use. Applied as a blocking correction to the 2-D spectral pair solver, it brings that solver within 0.498% (max) and 0.308% (median) of FastCap on 86 pairs of 12 fresh layouts drawn from a pre-registered seed, against a 42.794% median error uncorrected.",
 "limits": "Validated before use against sphere 2.8e-16, two-sphere Kelvin 3.1e-7, finite-coax 2.7e-7, long-via→2-D-spectral slope 5.4e-5, and an independent FastCap N=8 cross-check at 0.80% diagonal / 1.04% dominant off-diagonal. A learned head predicts the end-effect fraction geometry-disjoint at MAPE 0.61% / R² 0.9997 and rides every certificate as a NON-BLOCKING annotation. This is the honest answer to 'your whole stack is 2-D quasi-static'. The blocking correction is the MEASURED end term, not the head: the corrected solver equals the owned 3-D pair capacitance, so it costs one 3-D solve per layout (up to ~10 s at N=8 here). FastCap runs on the lab's own panelling, and its own coarse-to-graded change reaches 0.53%, the size of the corrected solver's worst error, so agreement finer than ~0.5% is not resolved. The bars were chosen after a three-geometry probe (disclosed in the prereg); the 12 layouts were drawn only after the prereg was committed.",
 "not_reprinted": [],
 "prior_work": [
  {
   "title": "Charge density on thin straight wire, revisited",
   "by": "J. D. Jackson, American Journal of Physics 68, 789, 2000",
   "url": "https://galileoandeinstein.phys.virginia.edu/Elec_Mag/EM_Lectures_Word/JacksonThinWireRevisited.pdf"
  },
  {
   "title": "Electrostatics of a finite-thickness conducting cylindrical shell: coupled elliptic-kernel integral equations",
   "by": "J. Ricardo de Sousa, arXiv 2601.00858, 2025",
   "url": "https://arxiv.org/abs/2601.00858"
  },
  {
   "title": "A Direct Solver for the Rapid Solution of Boundary Integral Equations on Axisymmetric Surfaces in Three Dimensions",
   "by": "Patrick M. Young, Per-Gunnar Martinsson, arXiv 1002.2001, 2010",
   "url": "https://arxiv.org/abs/1002.2001"
  },
  {
   "title": "Capacitance of a Cube and a Hollow Cylinder",
   "by": "Haiyong Gu, Liyuan Huang, Peide Yang, Tianshu Luo, arXiv 2505.13148, 2025",
   "url": "https://arxiv.org/html/2505.13148v1"
  }
 ],
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  "claims_sha256": "81776df15a1498abec7228ea179c952d01c54e031ffd4144498a30660963074b",
  "ranking_file": "views/VALUE_RANKING.md",
  "ranking_sha256": "2e980e26178b34dc49ec1d365f966be292f57d7c636143fc62c12feab72ae470",
  "dossier_sha256": "e13286af577cb590e06a7bb68d1cb8f6aef692a2aa8a3f248462dc94864eeabf",
  "commit": "25d755d2f06518b632c3658ae83f20312daac53e"
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}