{
  "version": 1,
  "stage": "Source comparison and selected calculations for the special-solution catalogue; no independent human review recorded.",
  "entries": [
    {
      "label": "rem:source-editions",
      "title": "The source editions",
      "kind": "remark",
      "file": "orientation.tex",
      "status": "editorial",
      "citations": [],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "rem:notation",
      "title": "Mean curvature flow and normalization",
      "kind": "remark",
      "file": "orientation.tex",
      "status": "editorial",
      "citations": [],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "rem:project-scope",
      "title": "Scope and illustrations",
      "kind": "remark",
      "file": "orientation.tex",
      "status": "editorial",
      "citations": [],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-expanding-corners",
      "title": "Even graphical corner expanders",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatDing20"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-rotational-expanders",
      "title": "Entire radial cone smoothings",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatDing20"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-two-sheet-expanders",
      "title": "Disconnected double-cone smoothings",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatAIC95"
      ],
      "dependencies": [
        "ex:catalogue-rotational-expanders"
      ],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-one-sheet-expanders",
      "title": "Connected double-cone smoothings",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatAIC95"
      ],
      "dependencies": [
        "ex:catalogue-two-sheet-expanders"
      ],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-mean-convex-expanders",
      "title": "Ding's smooth minimizing expanders",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatDing20"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-expanding-networks",
      "title": "Regular expanding trees with prescribed rays",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatINS19"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-stationary-catenoid",
      "title": "Minimal surfaces as stationary mean curvature flows",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatMan11",
        "CatChoppMinimal1993"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-whitney-sphere",
      "title": "A collapsing Lagrangian immersed sphere",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatViana18"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-degenerate-neckpinches",
      "title": "Angenent--Vel\\'azquez type-II singularities",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatAV97"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-angenent-oval",
      "title": "The ancient paperclip curve",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "BV11"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-ancient-torus-curves",
      "title": "Compact ancient torus curves",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatAAAW13",
        "CatSS19"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-eternal-helices",
      "title": "Helical curve-shortening flows",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatAAAW13",
        "CatSS19"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-double-plane-flow",
      "title": "Chen--Sun's noncompact multiplicity-two limit",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatCS26R3"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-double-sphere-flow",
      "title": "Chen--Sun's product-manifold construction",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatCS25Man"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-round-sphere",
      "title": "Round shrinking spheres",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CM12",
        "CatDLN2018"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-round-cylinder",
      "title": "Generalized shrinking cylinders",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CM12"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-plane-shrinker",
      "title": "Planes through the shrinker center",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CM12",
        "CatDLN2018"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-abresch-langer",
      "title": "Abresch--Langer closed shrinking curves",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CatAL1986",
        "CatCMComplexity2020",
        "CatDLN2018"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-angenent-torus",
      "title": "Angenent's shrinking torus",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CM12",
        "CatAngenent1992",
        "CatBerchenkoKogan2021",
        "CatDLN2018"
      ],
      "dependencies": [
        "ex:catalogue-drugan-nguyen-torus"
      ],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-drugan-sphere",
      "title": "Drugan's immersed shrinking spheres",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CatDLN2018",
        "CatDrugan2015"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-clifford-torus",
      "title": "The Clifford shrinking torus in four-space",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CatELS2020"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-curve-products",
      "title": "Products of closed shrinking curves",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CatSmoczyk2005"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-spherical-minimal",
      "title": "Higher-codimension spherical shrinkers",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CatSmoczyk2005",
        "CatSunZhu2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-moller-genus",
      "title": "Møller closed shrinkers of large even genus",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CM12",
        "CatDLN2018",
        "CatMoller2014"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-kkm-one-end",
      "title": "Kapouleas--Kleene--Møller shrinkers with one end",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatKKM2018",
        "CatSunWang2020"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-drugan-nguyen-torus",
      "title": "Drugan--Nguyen variational shrinking tori",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatChuSun2025",
        "CatDruganNguyen2018"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-bns-genus",
      "title": "Buzano--Nguyen--Schulz shrinkers of every positive genus",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatBNS2025",
        "CatChuSun2025"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-ketover-doubled-plane",
      "title": "Ketover self-shrinking doubled planes",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatKetover2024"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-spherical-doubling-shrinkers",
      "title": "Closed shrinkers from spherical doubling",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatKapouleasMcGrath2023"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-nguyen-shrinking-saddles",
      "title": "Nguyen's one-ended shrinking saddles",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatNguyenShrinker2014"
      ],
      "dependencies": [
        "ex:catalogue-kkm-one-end"
      ]
    },
    {
      "label": "ex:catalogue-angenent-torus-cylinders",
      "title": "Angenent torus cylinders",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatAngenent1992",
        "CatBerchenkoKogan2021",
        "CatCLSZ2026"
      ],
      "dependencies": [
        "ex:catalogue-angenent-torus"
      ]
    },
    {
      "label": "ex:catalogue-iw-two-ended",
      "title": "Ilmanen--White two-ended shrinkers",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatIlmanenWhite2025"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-shao-zou-stacking",
      "title": "Shao--Zou plane stackings",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatShaoZou2025"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-hmw-platonic-polygon",
      "title": "Hoffman--Martin--White ray-avoiding shrinkers",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatHMW2026"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-hmw-one-ended",
      "title": "Hoffman--Martin--White sphere--plane family",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatHMW2026"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-hmw-three-ended",
      "title": "Hoffman--Martin--White three-ended family",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatHMW2026"
      ],
      "dependencies": [
        "ex:catalogue-hmw-one-ended"
      ]
    },
    {
      "label": "ex:catalogue-ketover-platonic",
      "title": "Ketover shrinkers with Platonic symmetry",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatKetover2016"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-swz-large-entropy",
      "title": "Sun--Wang--Zhou Gaussian-width shrinkers",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatSunWangZhou2024"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-chu-sun-genus-one",
      "title": "Chu--Sun lower-entropy genus-one shrinkers",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatChuSun2025"
      ],
      "dependencies": [
        "ex:catalogue-drugan-nguyen-torus"
      ]
    },
    {
      "label": "ex:catalogue-grim-reaper",
      "title": "The grim reaper and its cylinders",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHIMWGraphical18",
        "CatHIMWNotes19"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-tilted-grim-reaper",
      "title": "Tilted grim-reaper cylinders",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHIMWGraphical18"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-bowl-translator",
      "title": "The rotational bowl translator",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CSS07",
        "CatBrendleChoi19",
        "CatHIMWNotes19",
        "CatSunWang2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-translating-catenoid",
      "title": "Rotational translating catenoids",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CSS07",
        "CatHIMWNotes19"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-delta-wing",
      "title": "Strictly convex delta-wing translators",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHIMWGraphical18"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-wang-entire-translators",
      "title": "Nonrotational entire convex translators",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatXJWang11"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-prescribed-apex-translators",
      "title": "Translators with prescribed apex curvatures",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHIMWGraphical18"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-scherkenoids",
      "title": "Scherkenoid translators",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHIMWNotes19",
        "CatHMW20"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-pitchfork",
      "title": "The pitchfork translator",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHIMWNotes19",
        "CatHMW20",
        "CatMSTW26",
        "CatGMM25"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-nguyen-tridents",
      "title": "Nguyen translating tridents",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHIMWNotes19",
        "CatNguyen09"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-finite-genus-translators",
      "title": "Finite-genus translators with three ends",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatDPN17",
        "CatHIMWNotes19"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-sun-wang-torus-translators",
      "title": "Translators with an Angenent-torus end",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatAngenent1992",
        "CatSunWang2025"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-sun-wang-sphere-doubling-translators",
      "title": "Translators with high-genus spherical-doubling ends",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "formal_verification": "none",
      "citations": [
        "CatKapouleasMcGrath2023",
        "CatSunWang2025"
      ],
      "dependencies": []
    },
    {
      "label": "ex:catalogue-scherk-translators",
      "title": "Doubly periodic Scherk translators",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHMW20",
        "CatMSTW26"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-translating-helicoids",
      "title": "Helicoid-like translators",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHMW20",
        "CatMSTW26"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-translating-annuloids",
      "title": "Annuloid translators in slabs",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatHMWAnnuli24",
        "CatGMM25"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-mountain-pass-expanders",
      "title": "Mountain-pass self-expanders",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatBWMP20"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-high-genus-expanders",
      "title": "Expanders of unbounded genus at a fixed cone",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatHMWExpand26",
        "CatShaoZou2025a"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-knotted-expanders",
      "title": "Knotted self-expanders",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatMWKnotted26"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-hh-ancient-ovals",
      "title": "Haslhofer--Hershkovits ancient ovals",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatHH13",
        "CatHS14"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-minimal-ancient-flows",
      "title": "Ancient flows from unstable minimal hypersurfaces",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatMP19",
        "CatChoiHuangLee2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-reapernoid",
      "title": "The eternal reapernoid",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatMP19"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-stacked-pancakes",
      "title": "Ancient stacked pancakes",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatMY26"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-ancient-spiral-curves",
      "title": "Compact nonconvex ancient spiral curves",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatZOKA23"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-grim-reaper-chains",
      "title": "Eternal curves from chains of grim reapers",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatAY18",
        "CatChoiSeoSuZhao2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-mobius-shrinker",
      "title": "The Lee–Wang self-shrinking Mobius bundle",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CatLeeWang2009",
        "CatBraxtonLeeZhu2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-jlt-compact-shrinkers",
      "title": "Compact periodic Lagrangian quadric shrinkers",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CatJoyceLeeTsui2010"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-jlt-translators",
      "title": "Joyce–Lee–Tsui small-angle Lagrangian translators",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatJoyceLeeTsui2010"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-jlt-rotating-translators",
      "title": "Explicit rotating Lagrangian translators",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatJoyceLeeTsui2010"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-jlt-expanders",
      "title": "Joyce–Lee–Tsui Lagrangian expander necks",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatJoyceLeeTsui2010",
        "CatImagiJoyceOliveira2016"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-ttw-expanders",
      "title": "Two-convex Lagrangian graphical expanders",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatTsaiTsuiWang2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-lawlor-necks",
      "title": "Lawlor necks as stationary Lagrangian flows",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatJoyceLeeTsui2010",
        "CatImagiJoyceOliveira2016"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-aryan-lee",
      "title": "Immortal curve shortening with nonunique geodesic limits",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatAryanLee2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-su-tsai-wood",
      "title": "Lagrangian torus necks collapsing at infinite time",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatSuTsaiWood2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-lee-tsai",
      "title": "Lagrangian sphere chains in Gibbons–Hawking spaces",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatLeeTsai2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-lw-quadric-shrinkers",
      "title": "Lee–Wang embedded quadric shrinkers",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "cited-example",
      "citations": [
        "CatLeeWang2010"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-lw-quadric-expanders",
      "title": "Lee–Wang embedded quadric expanders",
      "kind": "example",
      "file": "catalogue-expanders.tex",
      "status": "cited-example",
      "citations": [
        "CatLeeWang2010"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-su-glued-translators",
      "title": "Su translators obtained by gluing grim cylinders",
      "kind": "example",
      "file": "catalogue-translators.tex",
      "status": "cited-example",
      "citations": [
        "CatSu2022"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-su-wood-stationary",
      "title": "Su–Wood stationary products of Lawlor profiles",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatSuWood2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-stolarski-su",
      "title": "Stolarski–Su finite-time Lagrangian neck pinches",
      "kind": "example",
      "file": "catalogue-other-flows.tex",
      "status": "cited-example",
      "citations": [
        "CatStolarskiSu2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-chopp-cube",
      "title": "Chopp cubical shrinker candidate",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "numerical-candidate",
      "citations": [
        "CatChopp1994"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-chopp-octahedron",
      "title": "Chopp octahedral shrinker candidate",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "numerical-candidate",
      "citations": [
        "CatChopp1994"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-chopp-saddle",
      "title": "Chopp punctured-torus saddle candidate",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "numerical-candidate",
      "citations": [
        "CatChopp1994"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-chopp-two-handle",
      "title": "Chopp two-handled cone candidate",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "numerical-candidate",
      "citations": [
        "CatChopp1994"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-chopp-four-handle",
      "title": "Chopp four-handled cone candidate",
      "kind": "example",
      "file": "catalogue-shrinkers.tex",
      "status": "numerical-candidate",
      "citations": [
        "CatChopp1994",
        "CatAIC95"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-irrational-torus-curves",
      "title": "Ancient dense torus curves with irrational frequencies",
      "kind": "example",
      "file": "catalogue-aaaw.tex",
      "status": "cited-example",
      "citations": [
        "CatAAAW13"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-rotating-curves",
      "title": "Purely rotating curve-shortening solitons",
      "kind": "example",
      "file": "catalogue-aaaw.tex",
      "status": "cited-example",
      "citations": [
        "CatAAAW13",
        "CatHalldorsson2012",
        "CatHalldorsson2013"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-rotating-translating-curves",
      "title": "Rotating and translating curve solitons",
      "kind": "example",
      "file": "catalogue-aaaw.tex",
      "status": "cited-example",
      "citations": [
        "CatAAAW13"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-rotating-expanding-curves",
      "title": "Rotating and expanding curve solitons",
      "kind": "example",
      "file": "catalogue-aaaw.tex",
      "status": "cited-example",
      "citations": [
        "CatAAAW13",
        "CatHalldorsson2012"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-rotating-shrinking-curves",
      "title": "Rotating and shrinking curve solitons",
      "kind": "example",
      "file": "catalogue-aaaw.tex",
      "status": "cited-example",
      "citations": [
        "CatAAAW13",
        "CatHalldorsson2012"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-halldorsson-dense-shrinkers",
      "title": "Nonclosed shrinking curves dense in an annulus",
      "kind": "example",
      "file": "catalogue-halldorsson.tex",
      "status": "cited-example",
      "citations": [
        "CatHalldorsson2012"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-halldorsson-helicoidal-translators",
      "title": "Halldorsson helicoidal rotating translators",
      "kind": "example",
      "file": "catalogue-halldorsson.tex",
      "status": "cited-example",
      "citations": [
        "CatHalldorsson2013"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-halldorsson-minimal-helicoids",
      "title": "Helicoidal minimal surfaces as stationary flows",
      "kind": "example",
      "file": "catalogue-halldorsson.tex",
      "status": "cited-example",
      "citations": [
        "CatHalldorsson2013"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-drugan-kleene",
      "title": "Drugan--Kleene immersed shrinking families",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatDruganKleene2017"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-riedler-isoparametric",
      "title": "Riedler shrinkers from isoparametric foliations",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatRiedler2023"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-anciaux-legendrian-shrinkers",
      "title": "Anciaux shrinkers with minimal Legendrian leaves",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatAnciaux2006",
        "CatMadnickWood2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-anciaux-legendrian-expanders",
      "title": "Anciaux expanders with minimal Legendrian leaves",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatAnciaux2006",
        "CatMadnickWood2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-nguyen-grim-configurations",
      "title": "Nguyen translators from grim-reaper configurations",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatNguyen2013",
        "CatNguyen2015"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-polyhedral-slab-translators",
      "title": "Convex slab translators with polyhedral asymptotics",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBourniLangfordTinaglia2022"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-castro-lerma-pairs",
      "title": "Castro--Lerma Lagrangian translators from curve pairs",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatCastroLerma2012"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-su-wood-translating-helicoids",
      "title": "Su--Wood Lagrangian translating helicoids",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatSuWood2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-su-wood-paired-translators",
      "title": "Su--Wood paired-profile translators",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatSuWood2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-nonconvex-entire-translators",
      "title": "Nonconvex entire graphical translators",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatDavilaPinoWei2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-graphical-cone-expanders",
      "title": "Graphical expanders from general Lipschitz cones",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatEckerHuisken1989"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-lawson-osserman-expanders",
      "title": "Expanders based on generalized Lawson--Osserman maps",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatLee2023"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-birotational-expanders",
      "title": "Bi-rotational expanding hypersurfaces",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatNeto2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-birotational-shrinkers",
      "title": "Complete bi-rotational shrinking continuations",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatNeto2026a"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-ancient-sine-wave",
      "title": "The ancient sine wave",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatNakayamaIizukaWadati1994",
        "CatAY18"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-ma-halfplane-ancient",
      "title": "Immersed ancient curves spanning a half-plane",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatMa2021"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-nonplanar-eternal-reapers",
      "title": "Nonplanar eternal curves from grim reapers",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBourniMramor2023"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-collapsed-ancient-pancakes",
      "title": "Rotational collapsed ancient pancakes",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBourniLangfordTinaglia2017"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-polyhedral-ancient-pancakes",
      "title": "Ancient pancakes with polyhedral asymptotics",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBourniLangfordTinaglia2022"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-convex-eternal-nontranslators",
      "title": "Convex eternal flows that do not translate",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBourniLangfordTinaglia2022"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-reduced-symmetry-ancient-ovals",
      "title": "Ancient ovals with reduced symmetry",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatDuHaslhofer2021"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-ancient-doughnuts",
      "title": "Non-self-similar ancient doughnuts",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBourniLangfordMramor2020"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-isoparametric-ancient-euclidean",
      "title": "Ancient isoparametric flows in Euclidean space",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatLiuTerng2020"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-isoparametric-ancient-sphere",
      "title": "Ancient isoparametric flows in spheres",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatLiuTerng2020"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-flows-emerging-from-cones",
      "title": "Non-self-similar flows emerging from cones",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChen2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-bounded-mean-curvature-singularities",
      "title": "Hypersurface singularities with bounded mean curvature",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatStolarski2023"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-cohomogeneity-one-lagrangian-singularities",
      "title": "Lagrangian singularities with prescribed orbit models",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatMadnickWood2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-network-spoon",
      "title": "Brakke spoon",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChang2026",
        "CatChenGuo2007"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-network-lens",
      "title": "Shrinking lens network",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChang2026",
        "CatChenGuo2007"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-network-fish",
      "title": "Shrinking fish network",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChang2026",
        "CatChenGuo2007"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-network-three-ray",
      "title": "Three-ray shrinking star",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChang2026",
        "CatChenGuo2007"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-network-four-ray",
      "title": "Four-ray shrinking star",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChang2026",
        "CatChenGuo2007"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-network-five-ray",
      "title": "Five-ray shrinking star",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChang2026",
        "CatChenGuo2007"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-network-rocket",
      "title": "Shrinking rocket network",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChang2026",
        "CatChenGuo2007"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-network-cisgeminate-eye",
      "title": "Cisgeminate-eye shrinker",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChangLue2019"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-shrinking-lens-cluster",
      "title": "Lens-shaped shrinking surface clusters",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBaldiHausMantegazza2019"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-rotational-trumpet-ends",
      "title": "Rotational shrinking trumpet ends",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatKleeneMoller2014"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-isoparametric-shrinking-ends",
      "title": "Shrinking ends asymptotic to isoparametric cones",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChangSpruck2017"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-park-birotational-ends",
      "title": "Park bi-rotational shrinking ends",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatPark2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-expanding-cycle-networks",
      "title": "Expanding planar networks with a bounded cell",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatChenGuo2007"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-multiphase-expander-report",
      "title": "Reported multiphase expanding surface constructions",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatLiao2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-free-boundary-ancient-balls",
      "title": "Convex ancient free-boundary flows in balls",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBourniLangford2023",
        "CatBourniLangford2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-free-boundary-convex-domains",
      "title": "Ancient free-boundary curves in convex domains",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBourniBurnsCatron2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-mixed-boundary-ancient-curves",
      "title": "Ancient curves with mixed boundary conditions",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatLangfordLiuMcNamara2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-unstable-free-boundary-ancient",
      "title": "Ancient flows from unstable free-boundary minimal hypersurfaces",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBourniFranz2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-yamamoto-cone-shrinkers",
      "title": "Yamamoto Lagrangian shrinkers in Calabi--Yau cones",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatYamamoto2012"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-hyperbolic-product-rotational-translators",
      "title": "Rotational translators in the hyperbolic-plane product",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBueno2018"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-hyperbolic-product-grim-reapers",
      "title": "Grim reapers in the hyperbolic-plane product",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBuenoLopez2024"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-hyperbolic-product-helicoidal",
      "title": "Helicoidal rotators-translators in the hyperbolic-plane product",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatLimaRamosSantos2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-hyperbolic-killing-catenoids",
      "title": "Hyperbolic Killing translators and catenoids",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatLimaRamosSantos2026",
        "CatLimaRamos2026"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-hyperbolic-parabolic-grims",
      "title": "Parabolic Killing grim reapers in hyperbolic space",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatBuenoLopez2024a"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-nil-invariant-translators",
      "title": "Invariant translators in the Heisenberg group",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatPipoli2018"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-sol-invariant-translators",
      "title": "Invariant translators in Sol geometry",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatPipoli2019"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-sl2-invariant-translators",
      "title": "Invariant translators in the special linear group",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatLopezMunteanu2024"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-compact-symmetric-product-translators",
      "title": "Graphical translators over compact symmetric spaces",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatFujii2024",
        "CatFujiiKoike2023"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-hyperbolic-curve-solitons",
      "title": "Isometric curve-shortening solitons in the hyperbolic plane",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatWoolgarXie2022"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-perturbed-sphere-eternal-tori",
      "title": "Eternal tori in perturbations of the round three-sphere",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatMaganoSmith2020"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-lotay-oliveira-neck-pinches",
      "title": "Finite-time Lagrangian neck pinches with circle symmetry",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatLotayOliveira2023"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-jlt-mixed-periodic-shrinkers",
      "title": "Noncompact periodic Lagrangian shrinkers",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatJoyceLeeTsui2010"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-jlt-mixed-periodic-expanders",
      "title": "Noncompact periodic Lagrangian expanders",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatJoyceLeeTsui2010"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-sun-wang-prescribed-ends",
      "title": "Translators with general closed-shrinker ends",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatSunWang2025"
      ],
      "dependencies": [],
      "formal_verification": "none"
    },
    {
      "label": "ex:catalogue-immersed-ancient-grim-chains",
      "title": "Immersed ancient curves from grim-reaper chains",
      "kind": "example",
      "file": "catalogue-literature.tex",
      "status": "cited-example",
      "citations": [
        "CatAY18"
      ],
      "dependencies": [],
      "formal_verification": "none"
    }
  ],
  "external_proof_dependencies": [
    "Existence, classification, stability, and asymptotic results cited in the catalogue retain the proofs in their identified source papers. Numerical figures do not constitute existence proofs."
  ],
  "next_development": [
    "Add special solutions on request within the four categories, with precise sources, properties, formulas where available, and illustrations."
  ]
}