{
 "slug": "why-are-snowflakes-symmetrical",
 "claims": [
  {
   "id": "libbrecht-caltech",
   "kind": "fact",
   "claim": "Kenneth Libbrecht, a physicist at Caltech who grows snow crystals in his laboratory",
   "source": "https://www.snowcrystals.com/",
   "excerpt": "Kenneth G. Libbrecht is a professor of physics at the California Institute of Technology (Caltech).",
   "where": "About the author",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-home.txt"
  },
  {
   "id": "six-from-lattice",
   "kind": "quote",
   "claim": "The six-fold symmetry you see in a snow crystal arises from the arrangement of water molecules in the ice crystal lattice.",
   "quote": "The six-fold symmetry you see in a snow crystal arises from the arrangement of water molecules in the ice crystal lattice.",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "The\nsix-fold symmetry you see in a snow crystal arises from the arrangement\nof water molecules in the ice crystal lattice.",
   "where": "Why six?",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "prisms",
   "kind": "fact",
   "claim": "A small crystal that grows slowly is a plain hexagonal prism, a slender column or a thin plate",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "Hexagonal prisms can be long, slender, hexagonal columns, or thin, flat, hexagonal plates, or anything in between.",
   "where": "The simplest snowflakes; also: These crystals result from slow growth, and they are usually small in size.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "matching-ornaments",
   "kind": "fact",
   "claim": "in a good specimen they are not just six: they carry matching ornaments at matching distances out",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "Thus the six arms grow in synchrony, yielding a complex, yet symmetrical shape.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "twins-2mm",
   "kind": "fact",
   "claim": "two lab-grown crystals of Libbrecht's measured 2.0 millimetres from tip to tip",
   "source": "https://www.snowcrystals.com/identicaltwins/identicaltwins.html",
   "excerpt": "each crystal\nmeasured 2.0 millimeters (0.08 inches) from tip to tip",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-identicaltwins.txt"
  },
  {
   "id": "oscillations",
   "kind": "quote",
   "claim": "some acoustical or quantum mechanical oscillations are enforcing symmetrical growth.",
   "quote": "some acoustical or quantum mechanical oscillations are enforcing symmetrical growth.",
   "source": "https://www.snowcrystals.com/myths/myths.html",
   "excerpt": "perhaps some acoustical or quantum mechanical oscillations are enforcing symmetrical growth.",
   "where": "Snowflake Perfection?",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-myths.txt"
  },
  {
   "id": "nothing",
   "kind": "quote",
   "claim": "What synchronizes the growth of the arms? Nothing.",
   "quote": "What synchronizes the growth of the arms? Nothing. The six arms of a snow crystal all grow independently, as described in the previous section. But since they grow under the same randomly changing conditions, all six end up with similar shapes.",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "What synchronizes the growth of the arms?\nNothing.\nThe six arms of a snow crystal all grow independently, as described in the previous section. But since they grow under the same randomly changing conditions, all six end up with similar shapes.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "same-path",
   "kind": "quote",
   "claim": "the six arms all took the same path, and so each experienced the same changes at the same times.",
   "quote": "the six arms all took the same path, and so each experienced the same changes at the same times.",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "But the six arms all took the same path, and so each experienced the same changes at the same times.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "tumbles",
   "kind": "fact",
   "claim": "a crystal tumbles through the cloud meeting ever-changing temperatures and humidities",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "As it tumbles through the clouds, the crystal experiences ever\nchanging temperatures and humidities",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "reiter-lafayette",
   "kind": "citation",
   "claim": "Clifford Reiter, of the mathematics department at Lafayette College, published a model of snow crystal growth in 2005",
   "source": "https://www.patarnott.com/pdf/SnowCrystalGrowth.pdf",
   "excerpt": "Department of Mathematics, Lafayette College, Easton, PA 18042, USA",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/reiter-2005-pdftotext-raw.txt",
   "doi": "10.1016/j.chaos.2004.06.071"
  },
  {
   "id": "reiter-water",
   "kind": "quote",
   "claim": "the amount of water at that cellular location",
   "quote": "the amount of water at that cellular location",
   "source": "https://www.patarnott.com/pdf/SnowCrystalGrowth.pdf",
   "excerpt": "we view the value of any cell as measuring the amount of water at that cellular location.",
   "where": "section 2, p. 1113",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/reiter-2005.txt"
  },
  {
   "id": "reiter-receptive",
   "kind": "fact",
   "claim": "A cell is <i>receptive</i> if it is ice or touches ice.",
   "source": "https://www.patarnott.com/pdf/SnowCrystalGrowth.pdf",
   "excerpt": "These are the sites that are ice or that have an immediate neighbor that is ice.",
   "where": "section 2",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/reiter-2005.txt"
  },
  {
   "id": "reiter-boundary",
   "kind": "fact",
   "claim": "Far away, at the edge of the board, the water is held at a background level, β.",
   "source": "https://www.patarnott.com/pdf/SnowCrystalGrowth.pdf",
   "excerpt": "The boundary conditions are taken to be fixed at the background level at a fixed (Euclidean) distance from the initial cell.",
   "where": "section 2",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/reiter-2005.txt"
  },
  {
   "id": "reiter-not-physics",
   "kind": "quote",
   "claim": "while we use general physical notions to design our algorithm, we are not trying to fit equations of the physics.",
   "quote": "while we use general physical notions to design our algorithm, we are not trying to fit equations of the physics.",
   "source": "https://www.patarnott.com/pdf/SnowCrystalGrowth.pdf",
   "excerpt": "However, while we use general physical notions to design our algorithm, we are not trying to fit equations of the physics.",
   "where": "section 1",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/reiter-2005.txt"
  },
  {
   "id": "reiter-fall",
   "kind": "quote",
   "claim": "through air with different temperature and humidity",
   "quote": "through air with different temperature and humidity",
   "source": "https://www.patarnott.com/pdf/SnowCrystalGrowth.pdf",
   "excerpt": "This is motivated by the idea that naturally occurring snow crystals form as they fall through air with different temperature and humidity. Fig. 7 gives two examples. The first begins with parameters giving plate growth, then γ is changed so that dendrite growth occurs.",
   "where": "section 4",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/reiter-2005.txt"
  },
  {
   "id": "reiter-400",
   "kind": "fact",
   "claim": "His boards were about 400 cells across",
   "source": "https://www.patarnott.com/pdf/SnowCrystalGrowth.pdf",
   "excerpt": "We embedded a single isolated seed in an approximately 400 by 400 hexagonal arrangement of the background level.",
   "where": "section 2",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/reiter-2005.txt"
  },
  {
   "id": "reiter-formula",
   "kind": "citation",
   "claim": "His update is printed as u + (α/12)(−6u + the sum of the six neighbours)",
   "source": "https://www.patarnott.com/pdf/SnowCrystalGrowth.pdf",
   "excerpt": "u(t + 1, P) ≈ u(t, P) + (α/12) ( −6u(t, P) + Σ_{N ∈ nn(P)} u(t, N) )",
   "where": "section 3, transcribed from the page image",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/reiter-2005.txt"
  },
  {
   "id": "bentley-1884",
   "kind": "fact",
   "claim": "Wilson Bentley, a Vermont farmer who took his first photographs of snow crystals through a microscope in December 1884",
   "source": "https://archive.org/details/sim_monthly-weather-review_1924-11_52_11",
   "excerpt": "secured my first photomicrographs of snow crystals in December, 1884, when in my nineteenth year.",
   "where": "p. 530; farmer and Vermont: snowflakebentley.com/biography, \"Jericho, Vermont, A farmer by trade\"",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/bentley-1924-mwr.txt"
  },
  {
   "id": "bentley-4200",
   "kind": "quote",
   "claim": "in an article published in 1924, that his collection numbered 4,200,",
   "quote": "no two crystals being alike.",
   "source": "https://archive.org/details/sim_monthly-weather-review_1924-11_52_11",
   "excerpt": "until now my collection numbers 4,200, no two crystals being alike.",
   "where": "p. 530; datelined \"[Jericho, Vt., December, 1923]\"",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/bentley-1924-mwr.txt"
  },
  {
   "id": "rpp-bentley",
   "kind": "quote",
   "claim": "largely responsible for the widespread notion that no two snowflakes are alike.",
   "quote": "largely responsible for the widespread notion that no two snowflakes are alike.",
   "source": "http://www.its.caltech.edu/~atomic/publist/rpp5_4_R03.pdf",
   "excerpt": "Bentley’s images popularized the snow crystal as a winter\nicon and were largely responsible for the widespread notion that no two snowflakes are alike.",
   "where": "p. 858",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-2005-physics-of-snow-crystals.txt",
   "doi": "10.1088/0034-4885/68/4/R03"
  },
  {
   "id": "no-two",
   "kind": "quote",
   "claim": "since no two snow crystals follow the exact same path through the clouds as they fall, no two look exactly alike.",
   "quote": "since no two snow crystals follow the exact same path through the clouds as they fall, no two look exactly alike.",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "And since no two snow crystals follow the exact same path through the clouds as they fall, no\ntwo look exactly alike.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "twins-similar",
   "kind": "quote",
   "claim": "clearly very similar to one another, although they are not precisely identical.",
   "quote": "clearly very similar to one another, although they are not precisely identical.",
   "source": "https://www.snowcrystals.com/identicaltwins/identicaltwins.html",
   "excerpt": "these snow crystal twins are clearly very similar to\none another, although they are not precisely identical.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-identicaltwins.txt"
  },
  {
   "id": "twins-side-by-side",
   "kind": "fact",
   "claim": "two seed crystals side by side under one controlled, changing environment",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "We have made \"identical-twin\" snowflakes\nby exposing a pair of tiny seed crystals to nearly identical varying\nconditions as a function of time.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "symmetry-requires",
   "kind": "quote",
   "claim": "Snow crystal symmetry requires symmetrical growth conditions. If the six arms experience different environments, they will grow differently.",
   "quote": "Snow crystal symmetry requires symmetrical growth conditions. If the six arms experience different environments, they will grow differently.",
   "source": "https://www.snowcrystals.com/identicaltwins/identicaltwins.html",
   "excerpt": "Snow\ncrystal symmetry requires symmetrical growth conditions. If the six\narms experience different environments, they will grow differently.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-identicaltwins.txt"
  },
  {
   "id": "knight-flight",
   "kind": "fact",
   "claim": "on 1 November 1986, a research flight over Wausau, Wisconsin exposed an oiled glass plate to a cloud for 11 seconds",
   "source": "https://digital.lib.ku.edu/islandora/object/ku-udk%3A86071/datastream/OCR/download",
   "excerpt": "The two virtually identical crystals were collected Nov. 1, 1986, while researchers were studying clouds.\nThe crystals were collected on a glass plate coated with oil, which was exposed to the cloud for 11 seconds at an altitude of nearly 20,000 feet.",
   "where": "AP report, University Daily Kansan, 15 June 1988, p. 7 (OCR); also: \"on a glass slide exposed in a cloud on a research flight over Wausau, Wis.\"",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/knight-1988.txt"
  },
  {
   "id": "knight-ncar",
   "kind": "fact",
   "claim": "Nancy Knight of the National Center for Atmospheric Research found two crystals on it that were, if not identical, very much alike.",
   "source": "https://digital.lib.ku.edu/islandora/object/ku-udk%3A86071/datastream/OCR/download",
   "excerpt": "But, she found a striking example of two snow crystals which, if not identical, were very much alike.",
   "where": "AP report; \"Nancy C. Knight of the National Center for Atmospheric Research in Boulder, Colo.\"",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/knight-1988.txt"
  },
  {
   "id": "knight-letter",
   "kind": "citation",
   "claim": "Her letter appeared in the <i>Bulletin of the American Meteorological Society</i> in May 1988 under the title its editor gave it",
   "source": "https://news.ucar.edu/5025/nancy-knight-life-singular-scientist",
   "excerpt": "says Charlie, who notes that it was the BAMS editor who named the paper.",
   "where": "UCAR 2011; May issue per AP: \"in a letter published in the May issue of the Bulletin of the American Meteorological Society\"",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/knight-1988.txt",
   "doi": "10.1175/1520-0477-69.5.496"
  },
  {
   "id": "knight-deluge",
   "kind": "quote",
   "claim": "the deluge of publicity",
   "quote": "the deluge of publicity",
   "source": "https://news.ucar.edu/5025/nancy-knight-life-singular-scientist",
   "excerpt": "“The most surprising thing to Nancy and me was the deluge of publicity it produced,” says Charlie",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/knight-1988.txt"
  },
  {
   "id": "knight-columns",
   "kind": "fact",
   "claim": "They were hollow columns, about a quarter of a millimetre long",
   "source": "https://digital.lib.ku.edu/islandora/object/ku-udk%3A86071/datastream/OCR/download",
   "excerpt": "The pair of crystals photographed by Nancy Knight are shaped like columns with vase-shaped hollow centers. They are tiny - one quarter millimeter (0.009 inch) the long way, slightly less on the short side.",
   "where": "AP report",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/knight-1988.txt"
  },
  {
   "id": "knight-husband",
   "kind": "fact",
   "claim": "her husband and colleague Charles Knight",
   "source": "https://digital.lib.ku.edu/islandora/object/ku-udk%3A86071/datastream/OCR/download",
   "excerpt": "said her husband, Charles Knight, also a researcher at the center.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/knight-1988.txt"
  },
  {
   "id": "charles-alike",
   "kind": "quote",
   "claim": "Lots and lots of snow crystals are ‘alike,’ meaning similar,",
   "quote": "Lots and lots of snow crystals are ‘alike,’ meaning similar,",
   "source": "https://news.ucar.edu/5025/nancy-knight-life-singular-scientist",
   "excerpt": "“Lots and lots of snow crystals are ‘alike,’ meaning similar, but “no two alike’ seemed to translate in people’s minds to ‘no two identical’.”",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/knight-1988.txt"
  },
  {
   "id": "charles-translate",
   "kind": "quote",
   "claim": "seemed to translate in people’s minds to ‘no two identical’.",
   "quote": "seemed to translate in people’s minds to ‘no two identical’.",
   "source": "https://news.ucar.edu/5025/nancy-knight-life-singular-scientist",
   "excerpt": "but “no two alike’ seemed to translate in people’s minds to ‘no two identical’.”",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/knight-1988.txt"
  },
  {
   "id": "nakaya",
   "kind": "fact",
   "claim": "after Ukichiro Nakaya, who with his collaborators mapped it in a cold laboratory in the 1930s.",
   "source": "https://www.snowcrystals.com/morphology/morphology.html",
   "excerpt": "The\nSnow Crystal Morphology Diagram was discovered in the 1930s by Japanese\nphysicist Ukichiro Nakaya and his collaborators, and it is sometimes\ncalled the Nakaya Diagram for\nthis reason. They grew snow crystals in their cold lab",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-morphology.txt"
  },
  {
   "id": "temps",
   "kind": "fact",
   "claim": "thin plates near −2 °C, slender columns near −6 °C, large thin plates near −15 °C, and more branching when the humidity is high.",
   "source": "https://www.snowcrystals.com/morphology/morphology.html",
   "excerpt": "thin plate-like crystals appear at temperatures near -2 C (28 F),\nslender columns grow near -6 C (21 F), large thin plates grow near -15\nC (5 F)",
   "where": "also: \"More complex, branched forms appear when the humidity is high\"",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-morphology.txt"
  },
  {
   "id": "capped",
   "kind": "fact",
   "claim": "the capped columns that grow a plate on each end after drifting into colder air",
   "source": "https://www.snowcrystals.com/morphology/morphology.html",
   "excerpt": "forming a stout columnar crystal. Then the wind carried it to\ncolder temperatures, so thin plates grew on the ends of the columns.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-morphology.txt"
  },
  {
   "id": "cannot-explain",
   "kind": "quote",
   "claim": "cannot explain",
   "quote": "cannot explain",
   "source": "https://www.snowcrystals.com/morphology/morphology.html",
   "excerpt": "What science still cannot explain is why snow crystals grow as thin plates or slender columns depending on temperature.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-morphology.txt"
  },
  {
   "id": "not-symmetrical",
   "kind": "quote",
   "claim": "the vast majority of snow crystals are not very symmetrical",
   "quote": "the vast majority of snow crystals are not very symmetrical",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "Now, let me assure you that the vast majority\nof snow crystals are not very symmetrical.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "irregular-common",
   "kind": "fact",
   "claim": "the irregular ones are by far the most common.",
   "source": "https://www.snowcrystals.com/science/science.html",
   "excerpt": "irregular crystals (see the Guide to Snowflakes )\nare by far the most common type.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-science.txt"
  },
  {
   "id": "thousands",
   "kind": "fact",
   "claim": "he typically glances over thousands of crystals on his collection board before selecting one to photograph.",
   "source": "https://www.snowcrystals.com/myths/myths.html",
   "excerpt": "I typically glance over\nthousands of crystals on my collection board before selecting one to\nphotograph",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-myths.txt"
  },
  {
   "id": "stunted",
   "kind": "fact",
   "claim": "once the branches of one began interfering with the other's, the inner branches had no room and became stunted.",
   "source": "https://www.snowcrystals.com/identicaltwins/identicaltwins.html",
   "excerpt": "the branches of one crystal began interfering with the branches\nof the other.\nHere\nare the same two crystals after some additional growth. The outer\nbranches grew nearly identically on both crystals, but the inner\nbranches had no room to grow, so they became stunted.",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/libbrecht-identicaltwins.txt"
  },
  {
   "id": "bentley-neighbours",
   "kind": "fact",
   "claim": "he explained that in a thick snowstorm the crystals form close together and are distorted by their neighbours",
   "source": "https://snowflakebentley.com/mary-mullet-article",
   "excerpt": "\"Well, when a snowstorm is very thick, the crystals have formed in closer proximity to one another and we find them distorted by their neighbors.",
   "where": "transcription, not an original scan",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/bentley-1925-mullett-american-magazine.txt"
  },
  {
   "id": "bentley-symmetric",
   "kind": "quote",
   "claim": "To be perfectly symmetrical, they must be outside the range of influence of other crystals.",
   "quote": "To be perfectly symmetrical, they must be outside the range of influence of other crystals.",
   "source": "https://snowflakebentley.com/mary-mullet-article",
   "excerpt": "To be perfectly symmetrical, they must be outside the range of influence of other crystals.",
   "where": "Bentley as quoted by Mullett; transcription, not an original scan",
   "fetched": "2026-10-08",
   "kept": "research/why-are-snowflakes-symmetrical/sources/bentley-1925-mullett-american-magazine.txt"
  },
  {
   "id": "d-1949",
   "kind": "data",
   "claim": "for history A over 1,949 steps it never once moves a cell across the line into ice.",
   "source": "research/why-are-snowflakes-symmetrical/results.json",
   "where": "clean.A; verify section B"
  },
  {
   "id": "d-54",
   "kind": "data",
   "claim": "only 54 per cent of the frozen cells, on average, have all five rotated copies frozen as well.",
   "source": "research/why-are-snowflakes-symmetrical/results.json",
   "where": "noisy.cellIdentical.mean = 0.539"
  },
  {
   "id": "d-cell",
   "kind": "data",
   "claim": "Cell for cell, an arm's likeness to its own five sisters averages 0.754, and its likeness to the arms of a twin averages 0.755.",
   "source": "research/why-are-snowflakes-symmetrical/results.json",
   "where": "byScale[1]"
  },
  {
   "id": "d-16",
   "kind": "data",
   "claim": "Through 16-cell blocks the two are 0.937 and 0.935.",
   "source": "research/why-are-snowflakes-symmetrical/results.json",
   "where": "byScale[16]"
  },
  {
   "id": "d-002",
   "kind": "data",
   "claim": "The difference is never more than 0.002 at any of the five block sizes.",
   "source": "research/why-are-snowflakes-symmetrical/results.json",
   "where": "byScale; verify section D"
  },
  {
   "id": "d-B",
   "kind": "data",
   "claim": "0.607 cell for cell, 0.820 through 16-cell blocks.",
   "source": "research/why-are-snowflakes-symmetrical/results.json",
   "where": "byScale[1|16].farHistory"
  },
  {
   "id": "d-gap",
   "kind": "data",
   "claim": "from about 0.10 cell for cell to 0.029 through 16-cell blocks.",
   "source": "research/why-are-snowflakes-symmetrical/results.json",
   "where": "byScale twins minus nearHistory"
  },
  {
   "id": "d-flat",
   "kind": "data",
   "claim": "through 16-cell blocks two of them are 0.970 alike on average",
   "source": "research/why-are-snowflakes-symmetrical/results.json",
   "where": "flatControl[16].twins"
  },
  {
   "id": "d-burst",
   "kind": "data",
   "claim": "has coated all six of them out to the same distance, 45 cells from the centre on a board of radius 100.",
   "source": "verify-why-are-snowflakes-symmetrical.mjs",
   "where": "section D: history A without noise, the cells that froze in steps 700 to 799"
  },
  {
   "id": "d-075",
   "kind": "data",
   "claim": "even twins grown through one history score only 0.755",
   "source": "research/why-are-snowflakes-symmetrical/results.json",
   "where": "byScale[1].twins.mean"
  }
 ]
}