viettranx/3dviz-pro-max

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"owner": {     "name": "Viettranx",     "url": "https://github.com/viettranx/3dviz-pro-max"

"name": "Viettranx",     "url": "https://github.com/viettranx/3dviz-pro-max"   },

"url": "https://github.com/viettranx/3dviz-pro-max"

"description": "Design and build expressive 3D scenes, explainers and interactive models with grounded subject knowledge.",       "license": "MIT",       "homepage": "https://github.com/viettranx/3dviz-pro-max",

"license": "MIT",       "homepage": "https://github.com/viettranx/3dviz-pro-max",       "repository": "https://github.com/viettranx/3dviz-pro-max",

"homepage": "https://github.com/viettranx/3dviz-pro-max",

"repository": "https://github.com/viettranx/3dviz-pro-max",

"description": "Design and build expressive 3D scenes, explainers and interactive models with grounded subject knowledge: authored looks and moods, runnable Three.js rigs and kits, inspection checklists and a capture script.",   "license": 

"license": "MIT",   "homepage": "https://github.com/viettranx/3dviz-pro-max",   "repository": "https://github.com/viettranx/3dviz-pro-max",

"homepage": "https://github.com/viettranx/3dviz-pro-max",

"repository": "https://github.com/viettranx/3dviz-pro-max",

{           "source_id": "source.output-fetch-standard",           "locator": "Fetch method abort steps and “To abort a fetch() call”"

"source_id": "source.output-fetch-standard",           "locator": "Fetch method abort steps and “To abort a fetch() call”"         }

"locator": "Fetch method abort steps and “To abort a fetch() call”"

{           "source_id": "source.knowledge-depth-three-mesh-bvh",           "locator": "README Additional BVHs and linked https://github.com/gkjohnson/three-mesh-bvh/blob/master/API.md: SkinnedMeshBVH; StaticGeometryGenerator and generate (

"source_id": "source.knowledge-depth-three-mesh-bvh",           "locator": "README Additional BVHs and linked https://github.com/gkjohnson/three-mesh-bvh/blob/master/API.md: SkinnedMeshBVH; StaticGeometryGenerator and generate (bake evaluat

"locator": "README Additional BVHs and linked https://github.com/gkjohnson/three-mesh-bvh/blob/master/API.md: SkinnedMeshBVH; StaticGeometryGenerator and generate (bake evaluated positions, then MeshBVH.refit)."

"record_kind": "mixed",   "title": {     "en": "Curl and circulation around a loop"

"title": {     "en": "Curl and circulation around a loop"   },

"en": "Curl and circulation around a loop"

"calculus-fields"   ],   "summary": "Compare a local curl component with circulation per unit area, distinguishing the finite-disk average from its shrinking-disk limit.",

],   "summary": "Compare a local curl component with circulation per unit area, distinguishing the finite-disk average from its shrinking-disk limit.",   "objective": "Build a field where I can move and tilt a small loop, read its circulati

"summary": "Compare a local curl component with circulation per unit area, distinguishing the finite-disk average from its shrinking-disk limit.",

"objective": "Build a field where I can move and tilt a small loop, read its circulation and compare it with the curl component along the loop normal.",

],   "intent_signals": [     "Show what curl measures at a point.",

"intent_signals": [     "Show what curl measures at a point.",     "Compare a circulation integral with the curl of the field."

"Show what curl measures at a point.",

"Compare a circulation integral with the curl of the field."

],   "example_prompts": [     "Build a curl demonstration with a movable oriented loop and a circulation readout.",

"example_prompts": [     "Build a curl demonstration with a movable oriented loop and a circulation readout.",     "Show a field whose curl is zero and a field where it is not."

"Build a curl demonstration with a movable oriented loop and a circulation readout.",

"Show a field whose curl is zero and a field where it is not."

{       "name": "Field and probe point",       "guidance": "Show the analytic field sparsely plus a highlighted probe point whose curl vector is drawn with a declared display scale."

"name": "Field and probe point",       "guidance": "Show the analytic field sparsely plus a highlighted probe point whose curl vector is drawn with a declared display scale."     },

"guidance": "Show the analytic field sparsely plus a highlighted probe point whose curl vector is drawn with a declared display scale."

{       "name": "Numerical readout",       "guidance": "Display the loop circulation, the loop area, their ratio and the curl component along the normal, so the comparison is explicit."

"name": "Numerical readout",       "guidance": "Display the loop circulation, the loop area, their ratio and the curl component along the normal, so the comparison is explicit."     }

"guidance": "Display the loop circulation, the loop area, their ratio and the curl component along the normal, so the comparison is explicit."

],   "state_contract": {     "model": "A prescribed smooth analytic field, a loop with centre, positive radius and normal whose spanning disk lies inside the smooth domain, a numerically quadratured circulation, and the analytic curl at the

"state_contract": {     "model": "A prescribed smooth analytic field, a loop with centre, positive radius and normal whose spanning disk lies inside the smooth domain, a numerically quadratured circulation, and the analytic curl at the cent

"model": "A prescribed smooth analytic field, a loop with centre, positive radius and normal whose spanning disk lies inside the smooth domain, a numerically quadratured circulation, and the analytic curl at the centre. Circulation divided 

"authority": "The analytic field is authoritative; both the circulation estimate and the curl vector are derived from it, so no readout may be authored independently.",

"Tilt the loop normal.",       "Shrink the loop radius and watch the ratio converge.",       "Switch to a field with zero curl and reset."

"Shrink the loop radius and watch the ratio converge.",       "Switch to a field with zero curl and reset."     ]

"Switch to a field with zero curl and reset."

"invariants": [     "Reversing the loop traversal reverses the sign of the circulation and of the reported normal.",     "Alignment and perpendicularity statements hold in the shrinking-loop limit, or exactly for a declared constant-curl fi

"Reversing the loop traversal reverses the sign of the circulation and of the reported normal.",     "Alignment and perpendicularity statements hold in the shrinking-loop limit, or exactly for a declared constant-curl field. For a varying f

"Alignment and perpendicularity statements hold in the shrinking-loop limit, or exactly for a declared constant-curl field. For a varying field a finite loop whose normal is perpendicular to the centre curl can still have nonzero circulatio

"For a conservative field the circulation stays within the stated tolerance of zero for every loop position and orientation.",     "For smooth fields the exact disk average tends to the centre curl component as radius tends to zero, without

"For smooth fields the exact disk average tends to the centre curl component as radius tends to zero, without requiring monotonic improvement at successive radii. Quadrature error and floating-point cancellation can limit the computed compa

"Circulation is computed by quadrature on a discretised loop; its accuracy depends on the sample count.",     "Only smooth prescribed fields are handled; singular fields need their own treatment.",     "For a field with varying curl the fin

"Only smooth prescribed fields are handled; singular fields need their own treatment.",     "For a field with varying curl the finite-loop ratio differs from the centre value; for example a field whose curl has a component growing with posi

"For a field with varying curl the finite-loop ratio differs from the centre value; for example a field whose curl has a component growing with position gives nonzero circulation on a loop whose normal is perpendicular to the centre curl.",

{       "id": "claim.rd-curl-definition",       "statement": "For a differentiable vector field the curl is a vector that measures the tendency of particles near a point to rotate about the axis pointing in its direction, which is the sense

"id": "claim.rd-curl-definition",       "statement": "For a differentiable vector field the curl is a vector that measures the tendency of particles near a point to rotate about the axis pointing in its direction, which is the sense of the 

"statement": "For a differentiable vector field the curl is a vector that measures the tendency of particles near a point to rotate about the axis pointing in its direction, which is the sense of the paddlewheel interpretation.",

{           "source_id": "source.recipe-depth-openstax-curl",           "locator": "6.5, curl definition and paddlewheel interpretation"

"source_id": "source.recipe-depth-openstax-curl",           "locator": "6.5, curl definition and paddlewheel interpretation"         }

"locator": "6.5, curl definition and paddlewheel interpretation"

{       "id": "claim.rd-conservative-zero-curl",       "statement": "If a field is conservative then its curl is zero, and on a simply connected domain a field with zero curl is conservative.",

"id": "claim.rd-conservative-zero-curl",       "statement": "If a field is conservative then its curl is zero, and on a simply connected domain a field with zero curl is conservative.",       "scope": "Domain condition matters: the converse

"statement": "If a field is conservative then its curl is zero, and on a simply connected domain a field with zero curl is conservative.",

{           "source_id": "source.recipe-depth-openstax-curl",           "locator": "6.5, conservative field and curl relationship"

"source_id": "source.recipe-depth-openstax-curl",           "locator": "6.5, conservative field and curl relationship"         }

"locator": "6.5, conservative field and curl relationship"

{       "id": "claim.rd-circulation-curl-limit",       "statement": "Stokes' theorem equates the circulation of a field around a positively oriented simple closed boundary curve with the flux of its curl through a compatible piecewise smoot

"id": "claim.rd-circulation-curl-limit",       "statement": "Stokes' theorem equates the circulation of a field around a positively oriented simple closed boundary curve with the flux of its curl through a compatible piecewise smooth orient

"statement": "Stokes' theorem equates the circulation of a field around a positively oriented simple closed boundary curve with the flux of its curl through a compatible piecewise smooth oriented surface, for fields with continuous partial 

{       "family": "Field and probe point",       "structure": "Sparse arrows plus a distinctly larger curl arrow at the probe with its own scale legend.",

"family": "Field and probe point",       "structure": "Sparse arrows plus a distinctly larger curl arrow at the probe with its own scale legend.",       "material": "The curl arrow uses a reserved accent that appears nowhere else, since it 

"structure": "Sparse arrows plus a distinctly larger curl arrow at the probe with its own scale legend.",

"material": "The curl arrow uses a reserved accent that appears nowhere else, since it is the quantity under study.",

],     "checks": [       "Compare the computed ratio with the centre normal curl component across declared positive radii, accounting separately for quadrature error and finite-radius averaging. The smooth-field limit does not require every

"checks": [       "Compare the computed ratio with the centre normal curl component across declared positive radii, accounting separately for quadrature error and finite-radius averaging. The smooth-field limit does not require every radius

"Compare the computed ratio with the centre normal curl component across declared positive radii, accounting separately for quadrature error and finite-radius averaging. The smooth-field limit does not require every radius reduction to impr

{     "id": "source.mit-matrices-transformations",     "url": "https://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/chapter32/section05.html",

"id": "source.mit-matrices-transformations",     "url": "https://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/chapter32/section05.html",     "title": "MIT OCW 18.013A — 32.5 Matrices and Transformations",

"url": "https://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/chapter32/section05.html",

{     "id": "source.wca-regulations-2026",     "url": "https://www.worldcubeassociation.org/regulations/#12a1",

"id": "source.wca-regulations-2026",     "url": "https://www.worldcubeassociation.org/regulations/#12a1",     "title": "WCA Regulations — Article 12: Notation",

"url": "https://www.worldcubeassociation.org/regulations/#12a1",

{     "id": "source.cubing-basic-moves-draft",     "url": "https://standards.cubing.net/draft/2/basic-3x3x3-moves/",

"id": "source.cubing-basic-moves-draft",     "url": "https://standards.cubing.net/draft/2/basic-3x3x3-moves/",     "title": "Cubing Standard #2: Basic 3x3x3 Moves",

"url": "https://standards.cubing.net/draft/2/basic-3x3x3-moves/",

{     "id": "source.openstax-heart",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/19-1-heart-anatomy",

"id": "source.openstax-heart",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/19-1-heart-anatomy",     "title": "OpenStax Anatomy and Physiology 2e — Heart Anatomy",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/19-1-heart-anatomy",

{     "id": "source.openstax-synovial",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/9-4-synovial-joints",

"id": "source.openstax-synovial",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/9-4-synovial-joints",     "title": "OpenStax Anatomy and Physiology 2e — Synovial Joints",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/9-4-synovial-joints",

{     "id": "source.openstax-skeleton",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/7-1-divisions-of-the-skeletal-system",

"id": "source.openstax-skeleton",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/7-1-divisions-of-the-skeletal-system",     "title": "OpenStax Anatomy and Physiology 2e — Divisions of the Skeletal System",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/7-1-divisions-of-the-skeletal-system",

{     "id": "source.openstax-conics",     "url": "https://openstax.org/books/calculus-volume-3/pages/1-5-conic-sections",

"id": "source.openstax-conics",     "url": "https://openstax.org/books/calculus-volume-3/pages/1-5-conic-sections",     "title": "OpenStax Calculus Volume 3 — Conic Sections",

"url": "https://openstax.org/books/calculus-volume-3/pages/1-5-conic-sections",

{     "id": "source.openstax-cross-product",     "url": "https://openstax.org/books/calculus-volume-3/pages/2-4-the-cross-product",

"id": "source.openstax-cross-product",     "url": "https://openstax.org/books/calculus-volume-3/pages/2-4-the-cross-product",     "title": "OpenStax Calculus Volume 3 — The Cross Product",

"url": "https://openstax.org/books/calculus-volume-3/pages/2-4-the-cross-product",

{     "id": "source.openstax-disk-method",     "url": "https://openstax.org/books/calculus-volume-2/pages/2-2-determining-volumes-by-slicing",

"id": "source.openstax-disk-method",     "url": "https://openstax.org/books/calculus-volume-2/pages/2-2-determining-volumes-by-slicing",     "title": "OpenStax Calculus Volume 2 — Determining Volumes by Slicing",

"url": "https://openstax.org/books/calculus-volume-2/pages/2-2-determining-volumes-by-slicing",

{     "id": "source.demaine-unfolding",     "url": "https://erikdemaine.org/zippers/",

"id": "source.demaine-unfolding",     "url": "https://erikdemaine.org/zippers/",     "title": "Demaine et al. — Zipper Unfolding",

"url": "https://erikdemaine.org/zippers/",

{     "id": "source.mit-combinational",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c4/c4s1/",

"id": "source.mit-combinational",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c4/c4s1/",     "title": "MIT 6.004 — Combinational Logic",

"url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c4/c4s1/",

{     "id": "source.mit-arithmetic",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c8/c8s1/",

"id": "source.mit-arithmetic",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c8/c8s1/",     "title": "MIT 6.004 — Arithmetic Structures",

"url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c8/c8s1/",

{     "id": "source.mit-fsm",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c6/c6s1/",

"id": "source.mit-fsm",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c6/c6s1/",     "title": "MIT 6.004 — Finite State Machines",

"url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c6/c6s1/",

{     "id": "source.jaap-permutations",     "url": "https://www.jaapsch.net/puzzles/groups.htm",

"id": "source.jaap-permutations",     "url": "https://www.jaapsch.net/puzzles/groups.htm",     "title": "Jaap Scherphuis — Group Theory for Puzzles",

"url": "https://www.jaapsch.net/puzzles/groups.htm",

{     "id": "source.openstax-pendulum",     "url": "https://openstax.org/books/university-physics-volume-1/pages/15-4-pendulums",

"id": "source.openstax-pendulum",     "url": "https://openstax.org/books/university-physics-volume-1/pages/15-4-pendulums",     "title": "OpenStax University Physics Volume 1 — Pendulums",

"url": "https://openstax.org/books/university-physics-volume-1/pages/15-4-pendulums",

{     "id": "source.openstax-projectile",     "url": "https://openstax.org/books/university-physics-volume-1/pages/4-3-projectile-motion",

"id": "source.openstax-projectile",     "url": "https://openstax.org/books/university-physics-volume-1/pages/4-3-projectile-motion",     "title": "OpenStax University Physics Volume 1 — Projectile Motion",

"url": "https://openstax.org/books/university-physics-volume-1/pages/4-3-projectile-motion",

{     "id": "source.openstax-rotation",     "url": "https://openstax.org/books/university-physics-volume-1/pages/10-1-rotational-variables",

"id": "source.openstax-rotation",     "url": "https://openstax.org/books/university-physics-volume-1/pages/10-1-rotational-variables",     "title": "OpenStax University Physics Volume 1 — Rotational Variables",

"url": "https://openstax.org/books/university-physics-volume-1/pages/10-1-rotational-variables",

{     "id": "source.opentelemetry-traces",     "url": "https://opentelemetry.io/docs/concepts/signals/traces/",

"id": "source.opentelemetry-traces",     "url": "https://opentelemetry.io/docs/concepts/signals/traces/",     "title": "OpenTelemetry — Traces",

"url": "https://opentelemetry.io/docs/concepts/signals/traces/",

{     "id": "source.jmlr-tsne",     "url": "https://www.jmlr.org/papers/v9/vandermaaten08a.html",

"id": "source.jmlr-tsne",     "url": "https://www.jmlr.org/papers/v9/vandermaaten08a.html",     "title": "van der Maaten and Hinton — Visualizing Data using t-SNE",

"url": "https://www.jmlr.org/papers/v9/vandermaaten08a.html",

{     "id": "source.three-standard-material",     "url": "https://threejs.org/docs/pages/MeshStandardMaterial.html",

"id": "source.three-standard-material",     "url": "https://threejs.org/docs/pages/MeshStandardMaterial.html",     "title": "Three.js MeshStandardMaterial",

"url": "https://threejs.org/docs/pages/MeshStandardMaterial.html",

{     "id": "source.three-physical-material",     "url": "https://threejs.org/docs/pages/MeshPhysicalMaterial.html",

"id": "source.three-physical-material",     "url": "https://threejs.org/docs/pages/MeshPhysicalMaterial.html",     "title": "Three.js MeshPhysicalMaterial",

"url": "https://threejs.org/docs/pages/MeshPhysicalMaterial.html",

{     "id": "source.three-object3d",     "url": "https://threejs.org/docs/pages/Object3D.html",

"id": "source.three-object3d",     "url": "https://threejs.org/docs/pages/Object3D.html",     "title": "Three.js Object3D",

"url": "https://threejs.org/docs/pages/Object3D.html",

{     "id": "source.three-scenegraph",     "url": "https://threejs.org/manual/en/scenegraph.html",

"id": "source.three-scenegraph",     "url": "https://threejs.org/manual/en/scenegraph.html",     "title": "Three.js manual: Scene Graph",

"url": "https://threejs.org/manual/en/scenegraph.html",

{     "id": "source.three-material-clipping",     "url": "https://threejs.org/docs/pages/Material.html",

"id": "source.three-material-clipping",     "url": "https://threejs.org/docs/pages/Material.html",     "title": "Three.js Material",

"url": "https://threejs.org/docs/pages/Material.html",

{     "id": "source.rapier-rigid-bodies",     "url": "https://rapier.rs/docs/user_guides/javascript/rigid_bodies/",

"id": "source.rapier-rigid-bodies",     "url": "https://rapier.rs/docs/user_guides/javascript/rigid_bodies/",     "title": "Rapier JavaScript: Rigid-bodies",

"url": "https://rapier.rs/docs/user_guides/javascript/rigid_bodies/",

{     "id": "source.rapier-colliders",     "url": "https://rapier.rs/docs/user_guides/javascript/colliders/",

"id": "source.rapier-colliders",     "url": "https://rapier.rs/docs/user_guides/javascript/colliders/",     "title": "Rapier JavaScript: Colliders",

"url": "https://rapier.rs/docs/user_guides/javascript/colliders/",

{     "id": "source.openstax-gradient",     "url": "https://openstax.org/books/calculus-volume-3/pages/4-6-directional-derivatives-and-the-gradient",

"id": "source.openstax-gradient",     "url": "https://openstax.org/books/calculus-volume-3/pages/4-6-directional-derivatives-and-the-gradient",     "title": "OpenStax Calculus 3: Directional Derivatives and Gradient",

"url": "https://openstax.org/books/calculus-volume-3/pages/4-6-directional-derivatives-and-the-gradient",

{     "id": "source.openstax-double-integrals",     "url": "https://openstax.org/books/calculus-volume-3/pages/5-1-double-integrals-over-rectangular-regions",

"id": "source.openstax-double-integrals",     "url": "https://openstax.org/books/calculus-volume-3/pages/5-1-double-integrals-over-rectangular-regions",     "title": "OpenStax Calculus 3: Double Integrals",

"url": "https://openstax.org/books/calculus-volume-3/pages/5-1-double-integrals-over-rectangular-regions",

{     "id": "source.openstax-divergence",     "url": "https://openstax.org/books/calculus-volume-3/pages/6-8-the-divergence-theorem",

"id": "source.openstax-divergence",     "url": "https://openstax.org/books/calculus-volume-3/pages/6-8-the-divergence-theorem",     "title": "OpenStax Calculus 3: Divergence Theorem",

"url": "https://openstax.org/books/calculus-volume-3/pages/6-8-the-divergence-theorem",

{     "id": "source.openstax-binomial",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/4-3-binomial-distribution",

"id": "source.openstax-binomial",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/4-3-binomial-distribution",     "title": "OpenStax Statistics 2e: Binomial Distribution",

"url": "https://openstax.org/books/introductory-statistics-2e/pages/4-3-binomial-distribution",

{     "id": "source.openstax-normal",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/6-1-the-standard-normal-distribution",

"id": "source.openstax-normal",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/6-1-the-standard-normal-distribution",     "title": "OpenStax Statistics 2e: Standard Normal Distribution",

"url": "https://openstax.org/books/introductory-statistics-2e/pages/6-1-the-standard-normal-distribution",

{     "id": "source.openstax-sample-means",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/7-1-the-central-limit-theorem-for-sample-means-averages",

"id": "source.openstax-sample-means",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/7-1-the-central-limit-theorem-for-sample-means-averages",     "title": "OpenStax Statistics 2e: Sample Means",

"url": "https://openstax.org/books/introductory-statistics-2e/pages/7-1-the-central-limit-theorem-for-sample-means-averages",

{     "id": "source.mit-mobius",     "url": "https://ocw.mit.edu/courses/18-022-calculus-of-several-variables-fall-2010/resources/18-022f10/",

"id": "source.mit-mobius",     "url": "https://ocw.mit.edu/courses/18-022-calculus-of-several-variables-fall-2010/resources/18-022f10/",     "title": "MIT OCW: Moebius Band",

"url": "https://ocw.mit.edu/courses/18-022-calculus-of-several-variables-fall-2010/resources/18-022f10/",

{     "id": "source.hatcher-cell-complexes",     "url": "https://pi.math.cornell.edu/~hatcher/AT/AT.pdf",

"id": "source.hatcher-cell-complexes",     "url": "https://pi.math.cornell.edu/~hatcher/AT/AT.pdf",     "title": "Allen Hatcher: Algebraic Topology",

"url": "https://pi.math.cornell.edu/~hatcher/AT/AT.pdf",

{     "id": "source.judson-square-symmetry",     "url": "https://twjudson.github.io/aata-files/aata-20250801.pdf",

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"id": "source.shared-depth-matplotlib-colormaps",     "url": "https://matplotlib.org/stable/users/explain/colors/colormaps.html",     "title": "Matplotlib documentation: Choosing Colormaps in Matplotlib",

"url": "https://matplotlib.org/stable/users/explain/colors/colormaps.html",

{     "id": "source.validation-depth-goldberg-floating-point",     "url": "https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html",

"id": "source.validation-depth-goldberg-floating-point",     "url": "https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html",     "title": "David Goldberg: What Every Computer Scientist Should Know About Floating-Point Arithmetic",

"url": "https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html",

{     "id": "source.validation-depth-numpy-isclose",     "url": "https://numpy.org/doc/stable/reference/generated/numpy.isclose.html",

"id": "source.validation-depth-numpy-isclose",     "url": "https://numpy.org/doc/stable/reference/generated/numpy.isclose.html",     "title": "NumPy reference: numpy.isclose",

"url": "https://numpy.org/doc/stable/reference/generated/numpy.isclose.html",

{     "id": "source.validation-depth-gltf-coordinates",     "url": "https://raw.githubusercontent.com/KhronosGroup/glTF/main/specification/2.0/Specification.adoc",

"id": "source.validation-depth-gltf-coordinates",     "url": "https://raw.githubusercontent.com/KhronosGroup/glTF/main/specification/2.0/Specification.adoc",     "title": "Khronos glTF 2.0 Specification, source document",

"url": "https://raw.githubusercontent.com/KhronosGroup/glTF/main/specification/2.0/Specification.adoc",

{     "id": "source.validation-depth-dicom-patient-coordinates",     "url": "https://dicom.nema.org/medical/dicom/current/output/chtml/part03/sect_C.7.6.2.html",

"id": "source.validation-depth-dicom-patient-coordinates",     "url": "https://dicom.nema.org/medical/dicom/current/output/chtml/part03/sect_C.7.6.2.html",     "title": "DICOM PS3.3: Image Plane Module, patient-based coordinate system",

"url": "https://dicom.nema.org/medical/dicom/current/output/chtml/part03/sect_C.7.6.2.html",

{     "id": "source.validation-depth-simpy-scheduling",     "url": "https://simpy.readthedocs.io/en/latest/topical_guides/time_and_scheduling.html",

"id": "source.validation-depth-simpy-scheduling",     "url": "https://simpy.readthedocs.io/en/latest/topical_guides/time_and_scheduling.html",     "title": "SimPy documentation: Time and Scheduling",

"url": "https://simpy.readthedocs.io/en/latest/topical_guides/time_and_scheduling.html",

{     "id": "source.validation-depth-three-camera-depth",     "url": "https://threejs.org/manual/en/cameras.html",

"id": "source.validation-depth-three-camera-depth",     "url": "https://threejs.org/manual/en/cameras.html",     "title": "three.js manual: Cameras",

"url": "https://threejs.org/manual/en/cameras.html",

{     "id": "source.validation-depth-sampling-theorem",     "url": "https://ccrma.stanford.edu/~jos/mdft/Sampling_Theorem.html",

"id": "source.validation-depth-sampling-theorem",     "url": "https://ccrma.stanford.edu/~jos/mdft/Sampling_Theorem.html",     "title": "Julius O. Smith III, Mathematics of the Discrete Fourier Transform: Sampling Theorem",

"url": "https://ccrma.stanford.edu/~jos/mdft/Sampling_Theorem.html",

{     "id": "source.validation-depth-geometric-integration",     "url": "https://arxiv.org/pdf/1602.07755",

"id": "source.validation-depth-geometric-integration",     "url": "https://arxiv.org/pdf/1602.07755",     "title": "A. Iserles and G. R. W. Quispel: Why geometric numerical integration?",

"url": "https://arxiv.org/pdf/1602.07755",

{     "id": "source.validation-depth-otel-sampling",     "url": "https://opentelemetry.io/docs/concepts/sampling/",

"id": "source.validation-depth-otel-sampling",     "url": "https://opentelemetry.io/docs/concepts/sampling/",     "title": "OpenTelemetry documentation: Sampling",

"url": "https://opentelemetry.io/docs/concepts/sampling/",

{     "id": "source.validation-depth-noaa-mid-ocean-ridge",     "url": "https://oceanexplorer.noaa.gov/facts/mid-ocean-ridge.html",

"id": "source.validation-depth-noaa-mid-ocean-ridge",     "url": "https://oceanexplorer.noaa.gov/facts/mid-ocean-ridge.html",     "title": "NOAA Ocean Exploration: What is the mid-ocean ridge?",

"url": "https://oceanexplorer.noaa.gov/facts/mid-ocean-ridge.html",

{     "id": "source.validation-depth-openstax-gauge-pressure",     "url": "https://openstax.org/books/university-physics-volume-1/pages/14-2-measuring-pressure",

"id": "source.validation-depth-openstax-gauge-pressure",     "url": "https://openstax.org/books/university-physics-volume-1/pages/14-2-measuring-pressure",     "title": "OpenStax University Physics Volume 1: Measuring Pressure",

"url": "https://openstax.org/books/university-physics-volume-1/pages/14-2-measuring-pressure",

{     "id": "source.reasoning-depth-london-charter",     "url": "https://www.london-charter.org/introduction.html",

"id": "source.reasoning-depth-london-charter",     "url": "https://www.london-charter.org/introduction.html",     "title": "The London Charter for the Computer-based Visualisation of Cultural Heritage",

"url": "https://www.london-charter.org/introduction.html",

{     "id": "source.reasoning-depth-ada-standards",     "url": "https://www.access-board.gov/ada/chapter/ch04/",

"id": "source.reasoning-depth-ada-standards",     "url": "https://www.access-board.gov/ada/chapter/ch04/",     "title": "ADA Accessibility Standards, Chapter 4: Accessible Routes (US Access Board)",

"url": "https://www.access-board.gov/ada/chapter/ch04/",

{     "id": "source.reasoning-depth-ada-turning-space",     "url": "https://www.access-board.gov/ada/chapter/ch03/",

"id": "source.reasoning-depth-ada-turning-space",     "url": "https://www.access-board.gov/ada/chapter/ch03/",     "title": "ADA Accessibility Standards, Chapter 3: Building Blocks (US Access Board)",

"url": "https://www.access-board.gov/ada/chapter/ch03/",

{     "id": "source.reasoning-depth-three-animation-mixer",     "url": "https://threejs.org/docs/pages/AnimationMixer.html",

"id": "source.reasoning-depth-three-animation-mixer",     "url": "https://threejs.org/docs/pages/AnimationMixer.html",     "title": "Three.js AnimationMixer",

"url": "https://threejs.org/docs/pages/AnimationMixer.html",

{     "id": "source.reasoning-depth-proj-geodesic",     "url": "https://proj.org/en/stable/geodesic.html",

"id": "source.reasoning-depth-proj-geodesic",     "url": "https://proj.org/en/stable/geodesic.html",     "title": "PROJ documentation: Geodesic calculations",

"url": "https://proj.org/en/stable/geodesic.html",

{     "id": "source.reasoning-depth-otel-trace-api",     "url": "https://opentelemetry.io/docs/specs/otel/trace/api/",

"id": "source.reasoning-depth-otel-trace-api",     "url": "https://opentelemetry.io/docs/specs/otel/trace/api/",     "title": "OpenTelemetry specification: Tracing API",

"url": "https://opentelemetry.io/docs/specs/otel/trace/api/",

{     "id": "source.reasoning-depth-nasa-eclipse-types",     "url": "https://science.nasa.gov/eclipses/types/",

"id": "source.reasoning-depth-nasa-eclipse-types",     "url": "https://science.nasa.gov/eclipses/types/",     "title": "NASA Science: Types of Solar Eclipses",

"url": "https://science.nasa.gov/eclipses/types/",

{     "id": "source.reasoning-depth-algs4-digraph",     "url": "https://algs4.cs.princeton.edu/42digraph/",

"id": "source.reasoning-depth-algs4-digraph",     "url": "https://algs4.cs.princeton.edu/42digraph/",     "title": "Sedgewick and Wayne, Algorithms 4th edition: Directed Graphs",

"url": "https://algs4.cs.princeton.edu/42digraph/",

{     "id": "source.reasoning-depth-algs4-sorting-applications",     "url": "https://algs4.cs.princeton.edu/25applications/",

"id": "source.reasoning-depth-algs4-sorting-applications",     "url": "https://algs4.cs.princeton.edu/25applications/",     "title": "Sedgewick and Wayne, Algorithms 4th edition: Sorting Applications",

"url": "https://algs4.cs.princeton.edu/25applications/",

{     "id": "source.reasoning-depth-openstax-anatomical-terminology",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/1-6-anatomical-terminology",

"id": "source.reasoning-depth-openstax-anatomical-terminology",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/1-6-anatomical-terminology",     "title": "OpenStax Anatomy and Physiology 2e: Anatomical Terminology",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/1-6-anatomical-terminology",

{     "id": "source.reasoning-depth-openstax-skin-layers",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/5-1-layers-of-the-skin",

"id": "source.reasoning-depth-openstax-skin-layers",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/5-1-layers-of-the-skin",     "title": "OpenStax Anatomy and Physiology 2e: Layers of the Skin",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/5-1-layers-of-the-skin",

{     "id": "source.reasoning-depth-openstax-body-movements",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/9-5-types-of-body-movements",

"id": "source.reasoning-depth-openstax-body-movements",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/9-5-types-of-body-movements",     "title": "OpenStax Anatomy and Physiology 2e: Types of Body Movements",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/9-5-types-of-body-movements",

{     "id": "source.reasoning-depth-openstax-continuous-probability",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/5-1-continuous-probability-functions",

"id": "source.reasoning-depth-openstax-continuous-probability",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/5-1-continuous-probability-functions",     "title": "OpenStax Introductory Statistics 2e: Continuous Pro

"url": "https://openstax.org/books/introductory-statistics-2e/pages/5-1-continuous-probability-functions",

{     "id": "source.reasoning-depth-openstax-degenerate-conics",     "url": "https://openstax.org/books/precalculus-2e/pages/10-4-rotation-of-axes",

"id": "source.reasoning-depth-openstax-degenerate-conics",     "url": "https://openstax.org/books/precalculus-2e/pages/10-4-rotation-of-axes",     "title": "OpenStax Precalculus 2e: Rotation of Axes",

"url": "https://openstax.org/books/precalculus-2e/pages/10-4-rotation-of-axes",

{     "id": "source.reasoning-depth-openstax-field-lines",     "url": "https://openstax.org/books/university-physics-volume-2/pages/5-6-electric-field-lines",

"id": "source.reasoning-depth-openstax-field-lines",     "url": "https://openstax.org/books/university-physics-volume-2/pages/5-6-electric-field-lines",     "title": "OpenStax University Physics Volume 2: Electric Field Lines",

"url": "https://openstax.org/books/university-physics-volume-2/pages/5-6-electric-field-lines",

{     "id": "source.reasoning-depth-openstax-propagation-of-light",     "url": "https://openstax.org/books/university-physics-volume-3/pages/1-1-the-propagation-of-light",

"id": "source.reasoning-depth-openstax-propagation-of-light",     "url": "https://openstax.org/books/university-physics-volume-3/pages/1-1-the-propagation-of-light",     "title": "OpenStax University Physics Volume 3: The Propagation of Lig

"url": "https://openstax.org/books/university-physics-volume-3/pages/1-1-the-propagation-of-light",

{     "id": "source.reasoning-depth-distill-tsne",     "url": "https://distill.pub/2016/misread-tsne/",

"id": "source.reasoning-depth-distill-tsne",     "url": "https://distill.pub/2016/misread-tsne/",     "title": "Wattenberg, Viegas and Johnson: How to Use t-SNE Effectively",

"url": "https://distill.pub/2016/misread-tsne/",

{     "id": "source.reasoning-depth-knuth-dancing-links",     "url": "https://arxiv.org/abs/cs/0011047",

"id": "source.reasoning-depth-knuth-dancing-links",     "url": "https://arxiv.org/abs/cs/0011047",     "title": "Donald E. Knuth: Dancing Links",

"url": "https://arxiv.org/abs/cs/0011047",

{     "id": "source.reasoning-depth-mit-queueing-littles-law",     "url": "https://ocw.mit.edu/courses/1-203j-logistical-and-transportation-planning-methods-fall-2006/a9235f5e4e0aee12a55778e5beaf0ddb_lec5.pdf",

"id": "source.reasoning-depth-mit-queueing-littles-law",     "url": "https://ocw.mit.edu/courses/1-203j-logistical-and-transportation-planning-methods-fall-2006/a9235f5e4e0aee12a55778e5beaf0ddb_lec5.pdf",     "title": "MIT OCW 1.203J: Queue

"url": "https://ocw.mit.edu/courses/1-203j-logistical-and-transportation-planning-methods-fall-2006/a9235f5e4e0aee12a55778e5beaf0ddb_lec5.pdf",

{     "id": "source.reasoning-depth-explicit-diffusion-stability",     "url": "https://aquaulb.github.io/book_solving_pde_mooc/solving_pde_mooc/notebooks/04_PartialDifferentialEquations/04_03_Diffusion_Explicit.html",

"id": "source.reasoning-depth-explicit-diffusion-stability",     "url": "https://aquaulb.github.io/book_solving_pde_mooc/solving_pde_mooc/notebooks/04_PartialDifferentialEquations/04_03_Diffusion_Explicit.html",     "title": "Solving Partia

"url": "https://aquaulb.github.io/book_solving_pde_mooc/solving_pde_mooc/notebooks/04_PartialDifferentialEquations/04_03_Diffusion_Explicit.html",

{     "id": "source.reasoning-depth-jia-quaternion-notes",     "url": "https://faculty.sites.iastate.edu/jia/files/inline-files/quaternion.pdf",

"id": "source.reasoning-depth-jia-quaternion-notes",     "url": "https://faculty.sites.iastate.edu/jia/files/inline-files/quaternion.pdf",     "title": "Yan-Bin Jia: Quaternions (COM S 4770/5770 course notes)",

"url": "https://faculty.sites.iastate.edu/jia/files/inline-files/quaternion.pdf",

{     "id": "source.reasoning-depth-qgis-crs",     "url": "https://docs.qgis.org/3.40/en/docs/gentle_gis_introduction/coordinate_reference_systems.html",

"id": "source.reasoning-depth-qgis-crs",     "url": "https://docs.qgis.org/3.40/en/docs/gentle_gis_introduction/coordinate_reference_systems.html",     "title": "QGIS 3.40 documentation: Coordinate Reference Systems",

"url": "https://docs.qgis.org/3.40/en/docs/gentle_gis_introduction/coordinate_reference_systems.html",

{     "id": "source.reasoning-depth-psu-dem-resolution",     "url": "https://courses.ems.psu.edu/natureofgeoinfo/index.php/node/1835",

"id": "source.reasoning-depth-psu-dem-resolution",     "url": "https://courses.ems.psu.edu/natureofgeoinfo/index.php/node/1835",     "title": "Penn State, The Nature of Geographic Information: Digital Elevation Model",

"url": "https://courses.ems.psu.edu/natureofgeoinfo/index.php/node/1835",

{     "id": "source.reasoning-depth-jpl-scale-solar-system",     "url": "https://www.jpl.nasa.gov/edu/resources/project/make-a-scale-solar-system/",

"id": "source.reasoning-depth-jpl-scale-solar-system",     "url": "https://www.jpl.nasa.gov/edu/resources/project/make-a-scale-solar-system/",     "title": "NASA JPL Education: Make a Scale Solar System",

"url": "https://www.jpl.nasa.gov/edu/resources/project/make-a-scale-solar-system/",

{     "id": "source.reasoning-depth-nasa-eclipse-faq",     "url": "https://science.nasa.gov/eclipses/faq/",

"id": "source.reasoning-depth-nasa-eclipse-faq",     "url": "https://science.nasa.gov/eclipses/faq/",     "title": "NASA Science: Eclipses FAQ",

"url": "https://science.nasa.gov/eclipses/faq/",

{     "id": "source.reasoning-depth-cambridge-euler-characteristic",     "url": "https://www.dpmms.cam.ac.uk/~agk22/chi.pdf",

"id": "source.reasoning-depth-cambridge-euler-characteristic",     "url": "https://www.dpmms.cam.ac.uk/~agk22/chi.pdf",     "title": "A. G. Kovalev: Triangulations and the Euler characteristic (Cambridge Part II Differential Geometry)",

"url": "https://www.dpmms.cam.ac.uk/~agk22/chi.pdf",

{     "id": "source.reasoning-depth-edge-unfolding-open-problem",     "url": "https://www.openproblemgarden.org/op/edge_unfolding_convex_polyhedra",

"id": "source.reasoning-depth-edge-unfolding-open-problem",     "url": "https://www.openproblemgarden.org/op/edge_unfolding_convex_polyhedra",     "title": "Open Problem Garden: Edge-Unfolding Convex Polyhedra",

"url": "https://www.openproblemgarden.org/op/edge_unfolding_convex_polyhedra",

{     "id": "source.reasoning-depth-pdb101-representations",     "url": "https://pdb101.rcsb.org/learn/guide-to-understanding-pdb-data/molecular-graphics-programs",

"id": "source.reasoning-depth-pdb101-representations",     "url": "https://pdb101.rcsb.org/learn/guide-to-understanding-pdb-data/molecular-graphics-programs",     "title": "RCSB PDB-101: Molecular Graphics Programs",

"url": "https://pdb101.rcsb.org/learn/guide-to-understanding-pdb-data/molecular-graphics-programs",

{     "id": "source.reasoning-depth-rapier-integration-parameters",     "url": "https://rapier.rs/docs/user_guides/rust/integration_parameters/",

"id": "source.reasoning-depth-rapier-integration-parameters",     "url": "https://rapier.rs/docs/user_guides/rust/integration_parameters/",     "title": "Rapier user guide: Integration parameters",

"url": "https://rapier.rs/docs/user_guides/rust/integration_parameters/",

{     "id": "source.recipe-depth-openstax-spinal-nerves",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/13-4-the-peripheral-nervous-system",

"id": "source.recipe-depth-openstax-spinal-nerves",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/13-4-the-peripheral-nervous-system",     "title": "OpenStax Anatomy and Physiology 2e: The Peripheral Nervous System"

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/13-4-the-peripheral-nervous-system",

{     "id": "source.recipe-depth-openstax-hepatic-portal",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/20-5-circulatory-pathways",

"id": "source.recipe-depth-openstax-hepatic-portal",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/20-5-circulatory-pathways",     "title": "OpenStax Anatomy and Physiology 2e: Circulatory Pathways",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/20-5-circulatory-pathways",

{     "id": "source.recipe-depth-openstax-vertebral-column",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/7-3-the-vertebral-column",

"id": "source.recipe-depth-openstax-vertebral-column",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/7-3-the-vertebral-column",     "title": "OpenStax Anatomy and Physiology 2e: The Vertebral Column",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/7-3-the-vertebral-column",

{     "id": "source.recipe-depth-openstax-cardiac-cycle",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/19-3-cardiac-cycle",

"id": "source.recipe-depth-openstax-cardiac-cycle",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/19-3-cardiac-cycle",     "title": "OpenStax Anatomy and Physiology 2e: Cardiac Cycle",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/19-3-cardiac-cycle",

{     "id": "source.recipe-depth-openstax-lever-system",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/11-1-interactions-of-skeletal-muscles-their-fascicle-arrangement-and-their-lever-systems",

"id": "source.recipe-depth-openstax-lever-system",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/11-1-interactions-of-skeletal-muscles-their-fascicle-arrangement-and-their-lever-systems",     "title": "OpenStax Anat

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/11-1-interactions-of-skeletal-muscles-their-fascicle-arrangement-and-their-lever-systems",

{     "id": "source.recipe-depth-openstax-capillary-exchange",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/20-3-capillary-exchange",

"id": "source.recipe-depth-openstax-capillary-exchange",     "url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/20-3-capillary-exchange",     "title": "OpenStax Anatomy and Physiology 2e: Capillary Exchange",

"url": "https://openstax.org/books/anatomy-and-physiology-2e/pages/20-3-capillary-exchange",

{     "id": "source.recipe-depth-openstax-enantiomers",     "url": "https://openstax.org/books/organic-chemistry/pages/5-1-enantiomers-and-the-tetrahedral-carbon",

"id": "source.recipe-depth-openstax-enantiomers",     "url": "https://openstax.org/books/organic-chemistry/pages/5-1-enantiomers-and-the-tetrahedral-carbon",     "title": "OpenStax Organic Chemistry: Enantiomers and the Tetrahedral Carbon",

"url": "https://openstax.org/books/organic-chemistry/pages/5-1-enantiomers-and-the-tetrahedral-carbon",

{     "id": "source.recipe-depth-pdb101-protein-structure",     "url": "https://pdb101.rcsb.org/learn/guide-to-understanding-pdb-data/protein-hierarchical-structure",

"id": "source.recipe-depth-pdb101-protein-structure",     "url": "https://pdb101.rcsb.org/learn/guide-to-understanding-pdb-data/protein-hierarchical-structure",     "title": "RCSB PDB-101: Guide to Understanding PDB Data, Protein Hierarchic

"url": "https://pdb101.rcsb.org/learn/guide-to-understanding-pdb-data/protein-hierarchical-structure",

{     "id": "source.recipe-depth-mit-crystal-defects",     "url": "https://ocw.mit.edu/courses/3-091sc-introduction-to-solid-state-chemistry-fall-2010/pages/crystalline-materials/20-line-interface-and-bulk-defects/",

"id": "source.recipe-depth-mit-crystal-defects",     "url": "https://ocw.mit.edu/courses/3-091sc-introduction-to-solid-state-chemistry-fall-2010/pages/crystalline-materials/20-line-interface-and-bulk-defects/",     "title": "MIT 3.091SC Int

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"id": "source.recipe-depth-cgal-convex-hull",     "url": "https://doc.cgal.org/latest/Convex_hull_3/index.html",     "title": "CGAL 6.2.1: 3D Convex Hulls",

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{     "id": "source.recipe-depth-cgal-minkowski-sum",     "url": "https://doc.cgal.org/latest/Minkowski_sum_3/index.html",

"id": "source.recipe-depth-cgal-minkowski-sum",     "url": "https://doc.cgal.org/latest/Minkowski_sum_3/index.html",     "title": "CGAL 6.2.1: 3D Minkowski Sum of Polyhedra",

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"id": "source.recipe-depth-cgal-mesh-processing",     "url": "https://doc.cgal.org/latest/Polygon_mesh_processing/index.html",     "title": "CGAL 6.2.1: Polygon Mesh Processing",

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{     "id": "source.recipe-depth-cgal-triangulation-3",     "url": "https://doc.cgal.org/latest/Triangulation_3/index.html",

"id": "source.recipe-depth-cgal-triangulation-3",     "url": "https://doc.cgal.org/latest/Triangulation_3/index.html",     "title": "CGAL 6.2.1: 3D Triangulations",

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"id": "source.recipe-depth-numpy-svd",     "url": "https://numpy.org/doc/stable/reference/generated/numpy.linalg.svd.html",     "title": "NumPy v2.5 reference: numpy.linalg.svd",

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{     "id": "source.recipe-depth-numpy-eigh",     "url": "https://numpy.org/doc/stable/reference/generated/numpy.linalg.eigh.html",

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{     "id": "source.recipe-depth-ila-projections",     "url": "https://textbooks.math.gatech.edu/ila/projections.html",

"id": "source.recipe-depth-ila-projections",     "url": "https://textbooks.math.gatech.edu/ila/projections.html",     "title": "Margalit and Rabinoff, Interactive Linear Algebra: Orthogonal Projection",

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{     "id": "source.recipe-depth-openstax-euler-method",     "url": "https://openstax.org/books/calculus-volume-2/pages/4-2-direction-fields-and-numerical-methods",

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{     "id": "source.recipe-depth-openstax-curl",     "url": "https://openstax.org/books/calculus-volume-3/pages/6-5-divergence-and-curl",

"id": "source.recipe-depth-openstax-curl",     "url": "https://openstax.org/books/calculus-volume-3/pages/6-5-divergence-and-curl",     "title": "OpenStax Calculus Volume 3: Divergence and Curl",

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{     "id": "source.recipe-depth-openstax-second-derivative-test",     "url": "https://openstax.org/books/calculus-volume-3/pages/4-7-maxima-minima-problems",

"id": "source.recipe-depth-openstax-second-derivative-test",     "url": "https://openstax.org/books/calculus-volume-3/pages/4-7-maxima-minima-problems",     "title": "OpenStax Calculus Volume 3: Maxima/Minima Problems",

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{     "id": "source.recipe-depth-probabilitycourse-markov",     "url": "https://www.probabilitycourse.com/chapter11/11_2_6_stationary_and_limiting_distributions.php",

"id": "source.recipe-depth-probabilitycourse-markov",     "url": "https://www.probabilitycourse.com/chapter11/11_2_6_stationary_and_limiting_distributions.php",     "title": "Pishro-Nik, Introduction to Probability, Statistics, and Random P

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{     "id": "source.recipe-depth-knot-atlas-trefoil",     "url": "http://katlas.org/wiki/3_1",

"id": "source.recipe-depth-knot-atlas-trefoil",     "url": "http://katlas.org/wiki/3_1",     "title": "The Knot Atlas: 3_1",

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{     "id": "source.recipe-depth-spglib-definitions",     "url": "https://spglib.readthedocs.io/en/stable/definition.html",

"id": "source.recipe-depth-spglib-definitions",     "url": "https://spglib.readthedocs.io/en/stable/definition.html",     "title": "Spglib v2.7.0: Definitions and conventions",

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{     "id": "source.recipe-depth-spglib-variables",     "url": "https://spglib.readthedocs.io/en/stable/variable.html",

"id": "source.recipe-depth-spglib-variables",     "url": "https://spglib.readthedocs.io/en/stable/variable.html",     "title": "Spglib v2.7.0: Variables",

"url": "https://spglib.readthedocs.io/en/stable/variable.html",

{     "id": "source.recipe-depth-mit6004-timing",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c3/c3s1/",

"id": "source.recipe-depth-mit6004-timing",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c3/c3s1/",     "title": "MIT 6.004 Computation Structures: 3.1 Annotated Slides",

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{     "id": "source.recipe-depth-mit6004-sequential",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c5/c5s1/",

"id": "source.recipe-depth-mit6004-sequential",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c5/c5s1/",     "title": "MIT 6.004 Computation Structures: 5.1 Annotated Slides",

"url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c5/c5s1/",

{     "id": "source.recipe-depth-mit6004-performance",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c7/c7s1/",

"id": "source.recipe-depth-mit6004-performance",     "url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c7/c7s1/",     "title": "MIT 6.004 Computation Structures: 7.1 Annotated Slides",

"url": "https://ocw.mit.edu/courses/6-004-computation-structures-spring-2017/pages/c7/c7s1/",

{     "id": "source.recipe-depth-princeton-recursion",     "url": "https://introcs.cs.princeton.edu/java/23recursion/",

"id": "source.recipe-depth-princeton-recursion",     "url": "https://introcs.cs.princeton.edu/java/23recursion/",     "title": "Sedgewick and Wayne, Introduction to Programming: Recursion",

"url": "https://introcs.cs.princeton.edu/java/23recursion/",

{     "id": "source.recipe-depth-algs4-priority-queues",     "url": "https://algs4.cs.princeton.edu/24pq/",

"id": "source.recipe-depth-algs4-priority-queues",     "url": "https://algs4.cs.princeton.edu/24pq/",     "title": "Sedgewick and Wayne, Algorithms: Priority Queues",

"url": "https://algs4.cs.princeton.edu/24pq/",

{     "id": "source.recipe-depth-algs4-mst",     "url": "https://algs4.cs.princeton.edu/43mst/",

"id": "source.recipe-depth-algs4-mst",     "url": "https://algs4.cs.princeton.edu/43mst/",     "title": "Sedgewick and Wayne, Algorithms: Minimum Spanning Trees",

"url": "https://algs4.cs.princeton.edu/43mst/",

{     "id": "source.recipe-depth-algs4-digraph",     "url": "https://algs4.cs.princeton.edu/42digraph/",

"id": "source.recipe-depth-algs4-digraph",     "url": "https://algs4.cs.princeton.edu/42digraph/",     "title": "Sedgewick and Wayne, Algorithms: Directed Graphs",

"url": "https://algs4.cs.princeton.edu/42digraph/",

{     "id": "source.recipe-depth-jaap-cube3",     "url": "https://www.jaapsch.net/puzzles/cube3.htm",

"id": "source.recipe-depth-jaap-cube3",     "url": "https://www.jaapsch.net/puzzles/cube3.htm",     "title": "Jaap's Puzzle Page: Rubik's Cube 3x3x3",

"url": "https://www.jaapsch.net/puzzles/cube3.htm",

{     "id": "source.recipe-depth-knuth-dancing-links",     "url": "https://arxiv.org/abs/cs/0011047",

"id": "source.recipe-depth-knuth-dancing-links",     "url": "https://arxiv.org/abs/cs/0011047",     "title": "Knuth, Dancing Links (arXiv cs/0011047)",

"url": "https://arxiv.org/abs/cs/0011047",

{     "id": "source.recipe-depth-openstax-precession",     "url": "https://openstax.org/books/university-physics-volume-1/pages/11-4-precession-of-a-gyroscope",

"id": "source.recipe-depth-openstax-precession",     "url": "https://openstax.org/books/university-physics-volume-1/pages/11-4-precession-of-a-gyroscope",     "title": "OpenStax University Physics Volume 1: Precession of a Gyroscope",

"url": "https://openstax.org/books/university-physics-volume-1/pages/11-4-precession-of-a-gyroscope",

{     "id": "source.recipe-depth-openstax-rolling",     "url": "https://openstax.org/books/university-physics-volume-1/pages/11-1-rolling-motion",

"id": "source.recipe-depth-openstax-rolling",     "url": "https://openstax.org/books/university-physics-volume-1/pages/11-1-rolling-motion",     "title": "OpenStax University Physics Volume 1: Rolling Motion",

"url": "https://openstax.org/books/university-physics-volume-1/pages/11-1-rolling-motion",

{     "id": "source.recipe-depth-openstax-collisions",     "url": "https://openstax.org/books/university-physics-volume-1/pages/9-4-types-of-collisions",

"id": "source.recipe-depth-openstax-collisions",     "url": "https://openstax.org/books/university-physics-volume-1/pages/9-4-types-of-collisions",     "title": "OpenStax University Physics Volume 1: Types of Collisions",

"url": "https://openstax.org/books/university-physics-volume-1/pages/9-4-types-of-collisions",

{     "id": "source.recipe-depth-mujoco-computation",     "url": "https://mujoco.readthedocs.io/en/stable/computation/index.html",

"id": "source.recipe-depth-mujoco-computation",     "url": "https://mujoco.readthedocs.io/en/stable/computation/index.html",     "title": "MuJoCo documentation (stable): Computation",

"url": "https://mujoco.readthedocs.io/en/stable/computation/index.html",

{     "id": "source.recipe-depth-nasa-turbulence-resource",     "url": "https://www.nasa.gov/nasa-turbulence-modeling-resource/",

"id": "source.recipe-depth-nasa-turbulence-resource",     "url": "https://www.nasa.gov/nasa-turbulence-modeling-resource/",     "title": "NASA Turbulence Modeling Resource",

"url": "https://www.nasa.gov/nasa-turbulence-modeling-resource/",

{     "id": "source.recipe-depth-openstax-archimedes",     "url": "https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy",

"id": "source.recipe-depth-openstax-archimedes",     "url": "https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy",     "title": "OpenStax University Physics Volume 1: Archimedes' Principle and

"url": "https://openstax.org/books/university-physics-volume-1/pages/14-4-archimedes-principle-and-buoyancy",

{     "id": "source.recipe-depth-openstax-polarization",     "url": "https://openstax.org/books/university-physics-volume-3/pages/1-7-polarization",

"id": "source.recipe-depth-openstax-polarization",     "url": "https://openstax.org/books/university-physics-volume-3/pages/1-7-polarization",     "title": "OpenStax University Physics Volume 3: Polarization",

"url": "https://openstax.org/books/university-physics-volume-3/pages/1-7-polarization",

{     "id": "source.recipe-depth-openstax-interference",     "url": "https://openstax.org/books/university-physics-volume-3/pages/3-2-mathematics-of-interference",

"id": "source.recipe-depth-openstax-interference",     "url": "https://openstax.org/books/university-physics-volume-3/pages/3-2-mathematics-of-interference",     "title": "OpenStax University Physics Volume 3: Mathematics of Interference",

"url": "https://openstax.org/books/university-physics-volume-3/pages/3-2-mathematics-of-interference",

{     "id": "source.recipe-depth-openstax-single-slit",     "url": "https://openstax.org/books/university-physics-volume-3/pages/4-1-single-slit-diffraction",

"id": "source.recipe-depth-openstax-single-slit",     "url": "https://openstax.org/books/university-physics-volume-3/pages/4-1-single-slit-diffraction",     "title": "OpenStax University Physics Volume 3: Single-Slit Diffraction",

"url": "https://openstax.org/books/university-physics-volume-3/pages/4-1-single-slit-diffraction",

{     "id": "source.recipe-depth-openstax-current-loop",     "url": "https://openstax.org/books/university-physics-volume-2/pages/12-4-magnetic-field-of-a-current-loop",

"id": "source.recipe-depth-openstax-current-loop",     "url": "https://openstax.org/books/university-physics-volume-2/pages/12-4-magnetic-field-of-a-current-loop",     "title": "OpenStax University Physics Volume 2: Magnetic Field of a Curr

"url": "https://openstax.org/books/university-physics-volume-2/pages/12-4-magnetic-field-of-a-current-loop",

{     "id": "source.recipe-depth-modern-robotics-singularities",     "url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/5-3-singularities/",

"id": "source.recipe-depth-modern-robotics-singularities",     "url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/5-3-singularities/",     "title": "Lynch and Park, Modern Robotics: 5.3 Singularities",

"url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/5-3-singularities/",

{     "id": "source.recipe-depth-modern-robotics-trajectories",     "url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/9-1-and-9-2-point-to-point-trajectories-part-1-of-2/",

"id": "source.recipe-depth-modern-robotics-trajectories",     "url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/9-1-and-9-2-point-to-point-trajectories-part-1-of-2/",     "title": "Lynch and Park, Modern Robotics: 9.1 and 

"url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/9-1-and-9-2-point-to-point-trajectories-part-1-of-2/",

{     "id": "source.recipe-depth-modern-robotics-pid",     "url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-4-motion-control-with-torque-or-force-inputs-part-1-of-3/",

"id": "source.recipe-depth-modern-robotics-pid",     "url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-4-motion-control-with-torque-or-force-inputs-part-1-of-3/",     "title": "Lynch and Park, Modern Robotics: 11.4 Moti

"url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/11-4-motion-control-with-torque-or-force-inputs-part-1-of-3/",

{     "id": "source.recipe-depth-esri-coordinate-systems",     "url": "https://doc.esri.com/en/arcgis-pro/latest/help/mapping/properties/coordinate-systems-and-projections.html",

"id": "source.recipe-depth-esri-coordinate-systems",     "url": "https://doc.esri.com/en/arcgis-pro/latest/help/mapping/properties/coordinate-systems-and-projections.html",     "title": "ArcGIS Pro documentation: Coordinate systems, map pro

"url": "https://doc.esri.com/en/arcgis-pro/latest/help/mapping/properties/coordinate-systems-and-projections.html",

{     "id": "source.recipe-depth-esri-flow-accumulation",     "url": "https://doc.esri.com/en/arcgis-pro/latest/tool-reference/spatial-analyst/how-flow-accumulation-works.html",

"id": "source.recipe-depth-esri-flow-accumulation",     "url": "https://doc.esri.com/en/arcgis-pro/latest/tool-reference/spatial-analyst/how-flow-accumulation-works.html",     "title": "ArcGIS Pro documentation: How Flow Accumulation works"

"url": "https://doc.esri.com/en/arcgis-pro/latest/tool-reference/spatial-analyst/how-flow-accumulation-works.html",

{     "id": "source.recipe-depth-noaa-national-water-model",     "url": "https://water.noaa.gov/about/nwm",

"id": "source.recipe-depth-noaa-national-water-model",     "url": "https://water.noaa.gov/about/nwm",     "title": "NOAA: About the National Water Model",

"url": "https://water.noaa.gov/about/nwm",

{     "id": "source.recipe-depth-naif-frames",     "url": "https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/frames.html",

"id": "source.recipe-depth-naif-frames",     "url": "https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/frames.html",     "title": "NASA NAIF SPICE: Frames Required Reading",

"url": "https://naif.jpl.nasa.gov/pub/naif/toolkit_docs/C/req/frames.html",

{     "id": "source.recipe-depth-nasa-orbital-elements",     "url": "https://science.nasa.gov/learn/basics-of-space-flight/chapter5-1/",

"id": "source.recipe-depth-nasa-orbital-elements",     "url": "https://science.nasa.gov/learn/basics-of-space-flight/chapter5-1/",     "title": "NASA Basics of Space Flight: Chapter 5, Planetary Orbits",

"url": "https://science.nasa.gov/learn/basics-of-space-flight/chapter5-1/",

{     "id": "source.recipe-depth-nasa-eclipse-geometry",     "url": "https://science.nasa.gov/eclipses/geometry/",

"id": "source.recipe-depth-nasa-eclipse-geometry",     "url": "https://science.nasa.gov/eclipses/geometry/",     "title": "NASA: Why Do Eclipses Happen?",

"url": "https://science.nasa.gov/eclipses/geometry/",

{     "id": "source.recipe-depth-accessboard-ada-standards",     "url": "https://www.access-board.gov/ada/",

"id": "source.recipe-depth-accessboard-ada-standards",     "url": "https://www.access-board.gov/ada/",     "title": "U.S. Access Board: 2010 ADA Standards for Accessible Design",

"url": "https://www.access-board.gov/ada/",

{     "id": "source.recipe-depth-noaa-solar-calculator",     "url": "https://gml.noaa.gov/grad/solcalc/calcdetails.html",

"id": "source.recipe-depth-noaa-solar-calculator",     "url": "https://gml.noaa.gov/grad/solcalc/calcdetails.html",     "title": "NOAA Global Monitoring Laboratory: Solar Calculation Details",

"url": "https://gml.noaa.gov/grad/solcalc/calcdetails.html",

{     "id": "source.recipe-depth-ortools-job-shop",     "url": "https://developers.google.com/optimization/scheduling/job_shop",

"id": "source.recipe-depth-ortools-job-shop",     "url": "https://developers.google.com/optimization/scheduling/job_shop",     "title": "Google OR-Tools: The Job Shop Problem",

"url": "https://developers.google.com/optimization/scheduling/job_shop",

{     "id": "source.recipe-depth-protolabs-draft",     "url": "https://www.protolabs.com/resources/design-tips/improving-part-moldability-with-draft/",

"id": "source.recipe-depth-protolabs-draft",     "url": "https://www.protolabs.com/resources/design-tips/improving-part-moldability-with-draft/",     "title": "Protolabs: Draft Angle Guidelines for Injection Molding",

"url": "https://www.protolabs.com/resources/design-tips/improving-part-moldability-with-draft/",

{     "id": "source.recipe-depth-kubernetes-controllers",     "url": "https://kubernetes.io/docs/concepts/architecture/controller/",

"id": "source.recipe-depth-kubernetes-controllers",     "url": "https://kubernetes.io/docs/concepts/architecture/controller/",     "title": "Kubernetes documentation: Controllers",

"url": "https://kubernetes.io/docs/concepts/architecture/controller/",

{     "id": "source.recipe-depth-raft-consensus",     "url": "https://raft.github.io/",

"id": "source.recipe-depth-raft-consensus",     "url": "https://raft.github.io/",     "title": "The Raft Consensus Algorithm",

"url": "https://raft.github.io/",

{     "id": "source.recipe-depth-ncbi-brachial-plexus",     "url": "https://www.ncbi.nlm.nih.gov/books/NBK531473/",

"id": "source.recipe-depth-ncbi-brachial-plexus",     "url": "https://www.ncbi.nlm.nih.gov/books/NBK531473/",     "title": "Polcaro, Charlick and Daly: Anatomy, Head and Neck: Brachial Plexus (StatPearls, NCBI Bookshelf)",

"url": "https://www.ncbi.nlm.nih.gov/books/NBK531473/",

{     "id": "source.recipe-depth-ncbi-capillary-revision",     "url": "https://www.ncbi.nlm.nih.gov/books/NBK53443/",

"id": "source.recipe-depth-ncbi-capillary-revision",     "url": "https://www.ncbi.nlm.nih.gov/books/NBK53443/",     "title": "Scallan, Huxley and Korthuis: Fluid Movement Across the Endothelial Barrier (Capillary Fluid Exchange, NCBI Booksh

"url": "https://www.ncbi.nlm.nih.gov/books/NBK53443/",

{     "id": "source.recipe-depth-ila-eigenvectors",     "url": "https://textbooks.math.gatech.edu/ila/eigenvectors.html",

"id": "source.recipe-depth-ila-eigenvectors",     "url": "https://textbooks.math.gatech.edu/ila/eigenvectors.html",     "title": "Margalit and Rabinoff, Interactive Linear Algebra: Eigenvalues and Eigenvectors",

"url": "https://textbooks.math.gatech.edu/ila/eigenvectors.html",

{     "id": "source.recipe-depth-openstax-stokes",     "url": "https://openstax.org/books/calculus-volume-3/pages/6-7-stokes-theorem",

"id": "source.recipe-depth-openstax-stokes",     "url": "https://openstax.org/books/calculus-volume-3/pages/6-7-stokes-theorem",     "title": "OpenStax Calculus Volume 3: Stokes' Theorem",

"url": "https://openstax.org/books/calculus-volume-3/pages/6-7-stokes-theorem",

"title": "OpenStax Calculus Volume 3: Stokes' Theorem",     "accessed_at": "2026-09-07",     "locator": "6.7, Theorem 6.19: the line integral of F around the positively oriented simple closed boundary curve equals the surface integral of cu

"accessed_at": "2026-09-07",     "locator": "6.7, Theorem 6.19: the line integral of F around the positively oriented simple closed boundary curve equals the surface integral of curl F over a piecewise smooth oriented surface S, for F whose

"locator": "6.7, Theorem 6.19: the line integral of F around the positively oriented simple closed boundary curve equals the surface integral of curl F over a piecewise smooth oriented surface S, for F whose component functions have continu

"scope": "Circulation-to-curl relationship with its stated smoothness and orientation hypotheses, and the shrinking-disk limit; a finite loop gives an average rather than the pointwise value.",

{     "id": "source.recipe-depth-numpy-cov",     "url": "https://numpy.org/doc/stable/reference/generated/numpy.cov.html",

"id": "source.recipe-depth-numpy-cov",     "url": "https://numpy.org/doc/stable/reference/generated/numpy.cov.html",     "title": "NumPy v2.5 reference: numpy.cov",

"url": "https://numpy.org/doc/stable/reference/generated/numpy.cov.html",

{     "id": "source.recipe-depth-openstax-proportion-interval",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/8-3-a-population-proportion",

"id": "source.recipe-depth-openstax-proportion-interval",     "url": "https://openstax.org/books/introductory-statistics-2e/pages/8-3-a-population-proportion",     "title": "OpenStax Introductory Statistics 2e: A Population Proportion",

"url": "https://openstax.org/books/introductory-statistics-2e/pages/8-3-a-population-proportion",

{     "id": "source.recipe-depth-openstax-biot-savart",     "url": "https://openstax.org/books/university-physics-volume-2/pages/12-1-the-biot-savart-law",

"id": "source.recipe-depth-openstax-biot-savart",     "url": "https://openstax.org/books/university-physics-volume-2/pages/12-1-the-biot-savart-law",     "title": "OpenStax University Physics Volume 2: The Biot-Savart Law",

"url": "https://openstax.org/books/university-physics-volume-2/pages/12-1-the-biot-savart-law",

{     "id": "source.recipe-depth-openstax-double-slit-diffraction",     "url": "https://openstax.org/books/university-physics-volume-3/pages/4-3-double-slit-diffraction",

"id": "source.recipe-depth-openstax-double-slit-diffraction",     "url": "https://openstax.org/books/university-physics-volume-3/pages/4-3-double-slit-diffraction",     "title": "OpenStax University Physics Volume 3: Double-Slit Diffraction

"url": "https://openstax.org/books/university-physics-volume-3/pages/4-3-double-slit-diffraction",

{     "id": "source.recipe-depth-modern-robotics-time-scalings",     "url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/9-1-and-9-2-point-to-point-trajectories-part-2-of-2/",

"id": "source.recipe-depth-modern-robotics-time-scalings",     "url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/9-1-and-9-2-point-to-point-trajectories-part-2-of-2/",     "title": "Lynch and Park, Modern Robotics: 9.1 and

"url": "https://modernrobotics.northwestern.edu/nu-gm-book-resource/9-1-and-9-2-point-to-point-trajectories-part-2-of-2/",

{     "id": "source.recipe-depth-esri-flow-accumulation-tool",     "url": "https://doc.esri.com/en/arcgis-pro/latest/tool-reference/spatial-analyst/flow-accumulation.html",

"id": "source.recipe-depth-esri-flow-accumulation-tool",     "url": "https://doc.esri.com/en/arcgis-pro/latest/tool-reference/spatial-analyst/flow-accumulation.html",     "title": "ArcGIS Pro documentation: Flow Accumulation (Spatial Analys

"url": "https://doc.esri.com/en/arcgis-pro/latest/tool-reference/spatial-analyst/flow-accumulation.html",

{     "id": "source.recipe-depth-proj-spherical-mercator",     "url": "https://proj.org/en/stable/operations/projections/merc.html",

"id": "source.recipe-depth-proj-spherical-mercator",     "url": "https://proj.org/en/stable/operations/projections/merc.html",     "title": "PROJ: Mercator spherical forward formulas",

"url": "https://proj.org/en/stable/operations/projections/merc.html",

{     "id": "source.recipe-depth-proj-spherical-eqc",     "url": "https://proj.org/en/stable/operations/projections/eqc.html",

"id": "source.recipe-depth-proj-spherical-eqc",     "url": "https://proj.org/en/stable/operations/projections/eqc.html",     "title": "PROJ: Equidistant Cylindrical spherical forward formulas",

"url": "https://proj.org/en/stable/operations/projections/eqc.html",

{     "id": "source.object-depth-umn-canine-skeleton",     "url": "https://vanat.ahc.umn.edu/run/plate4.html",

"id": "source.object-depth-umn-canine-skeleton",     "url": "https://vanat.ahc.umn.edu/run/plate4.html",     "title": "University of Minnesota Veterinary Anatomy: Canine Skeleton",

"url": "https://vanat.ahc.umn.edu/run/plate4.html",

{     "id": "source.object-depth-cornell-feather-structure",     "url": "https://academy.allaboutbirds.org/features/all-about-feathers/how-feathers-are-built.php",

"id": "source.object-depth-cornell-feather-structure",     "url": "https://academy.allaboutbirds.org/features/all-about-feathers/how-feathers-are-built.php",     "title": "Cornell Lab Bird Academy: How Feathers Are Built",

"url": "https://academy.allaboutbirds.org/features/all-about-feathers/how-feathers-are-built.php",

{     "id": "source.object-depth-fhwa-bridge-connections",     "url": "https://www.fhwa.dot.gov/bridge/prefab/if09010/02c.cfm",

"id": "source.object-depth-fhwa-bridge-connections",     "url": "https://www.fhwa.dot.gov/bridge/prefab/if09010/02c.cfm",     "title": "FHWA: Connection Details for PBES, Chapter 2",

"url": "https://www.fhwa.dot.gov/bridge/prefab/if09010/02c.cfm",

{     "id": "source.object-depth-nps-peirce-drive",     "url": "https://www.nps.gov/places/000/information-panel-machine-in-a-stone-box.htm",

"id": "source.object-depth-nps-peirce-drive",     "url": "https://www.nps.gov/places/000/information-panel-machine-in-a-stone-box.htm",     "title": "National Park Service: Machine in a Stone Box",

"url": "https://www.nps.gov/places/000/information-panel-machine-in-a-stone-box.htm",

{     "id": "source.object-depth-heritage-over-bridge",     "url": "https://www.english-heritage.org.uk/visit/places/over-bridge/history/",

"id": "source.object-depth-heritage-over-bridge",     "url": "https://www.english-heritage.org.uk/visit/places/over-bridge/history/",     "title": "English Heritage: History of Over Bridge",

"url": "https://www.english-heritage.org.uk/visit/places/over-bridge/history/",

{     "id": "source.object-depth-usfs-tamarack-roots",     "url": "https://www.srs.fs.usda.gov/pubs/misc/ag_654/volume_1/larix/laricina.htm",

"id": "source.object-depth-usfs-tamarack-roots",     "url": "https://www.srs.fs.usda.gov/pubs/misc/ag_654/volume_1/larix/laricina.htm",     "title": "USDA Forest Service, Silvics of North America: Larix laricina",

"url": "https://www.srs.fs.usda.gov/pubs/misc/ag_654/volume_1/larix/laricina.htm",

{     "id": "source.object-depth-vam-costume-mounting",     "url": "https://lookup.vam.ac.uk/east-storehouse/storagedisplays/USE2186/",

"id": "source.object-depth-vam-costume-mounting",     "url": "https://lookup.vam.ac.uk/east-storehouse/storagedisplays/USE2186/",     "title": "V&A East Storehouse: What is costume mounting?",

"url": "https://lookup.vam.ac.uk/east-storehouse/storagedisplays/USE2186/",

{     "id": "source.material-depth-wood-sections",     "url": "https://research.fs.usda.gov/download/treesearch/62242.pdf",

"id": "source.material-depth-wood-sections",     "url": "https://research.fs.usda.gov/download/treesearch/62242.pdf",     "title": "Wood Handbook: Structure and Function of Wood",

"url": "https://research.fs.usda.gov/download/treesearch/62242.pdf",

{     "id": "source.material-depth-layered-scattering",     "url": "https://pbr-book.org/4ed/Light_Transport_II_Volume_Rendering/Scattering_from_Layered_Materials",

"id": "source.material-depth-layered-scattering",     "url": "https://pbr-book.org/4ed/Light_Transport_II_Volume_Rendering/Scattering_from_Layered_Materials",     "title": "Physically Based Rendering: Scattering from Layered Materials",

"url": "https://pbr-book.org/4ed/Light_Transport_II_Volume_Rendering/Scattering_from_Layered_Materials",

{     "id": "source.material-depth-weathered-stone",     "url": "https://graphics.stanford.edu/~henrik/papers/sig99/",

"id": "source.material-depth-weathered-stone",     "url": "https://graphics.stanford.edu/~henrik/papers/sig99/",     "title": "Modeling and Rendering of Weathered Stone — author project page",

"url": "https://graphics.stanford.edu/~henrik/papers/sig99/",

{     "id": "source.material-depth-ceramic-underglaze",     "url": "https://www.vam.ac.uk/articles/a-z-of-ceramics",

"id": "source.material-depth-ceramic-underglaze",     "url": "https://www.vam.ac.uk/articles/a-z-of-ceramics",     "title": "An A–Z of Ceramics — Victoria and Albert Museum",

"url": "https://www.vam.ac.uk/articles/a-z-of-ceramics",

{     "id": "source.material-depth-woven-reflection",     "url": "https://www.cs.cornell.edu/~srm/publications/TOG12-cloth.html",

"id": "source.material-depth-woven-reflection",     "url": "https://www.cs.cornell.edu/~srm/publications/TOG12-cloth.html",     "title": "Specular Reflection from Woven Cloth — author publication page",

"url": "https://www.cs.cornell.edu/~srm/publications/TOG12-cloth.html",

{     "id": "source.material-depth-skin-transport",     "url": "https://graphics.stanford.edu/~srm/publications/SG01-subsurf-abstract.html",

"id": "source.material-depth-skin-transport",     "url": "https://graphics.stanford.edu/~srm/publications/SG01-subsurf-abstract.html",     "title": "A Practical Model for Subsurface Light Transport — author publication page",

"url": "https://graphics.stanford.edu/~srm/publications/SG01-subsurf-abstract.html",

{     "id": "source.material-depth-snow-optics",     "url": "https://nsidc.org/learn/parts-cryosphere/snow/science-snow",

"id": "source.material-depth-snow-optics",     "url": "https://nsidc.org/learn/parts-cryosphere/snow/science-snow",     "title": "Science of Snow — National Snow and Ice Data Center",

"url": "https://nsidc.org/learn/parts-cryosphere/snow/science-snow",

{     "id": "source.material-depth-water-scales",     "url": "https://developer.nvidia.com/gpugems/gpugems/part-i-natural-effects/chapter-1-effective-water-simulation-physical-models",

"id": "source.material-depth-water-scales",     "url": "https://developer.nvidia.com/gpugems/gpugems/part-i-natural-effects/chapter-1-effective-water-simulation-physical-models",     "title": "GPU Gems Chapter 1: Effective Water Simulation 

"url": "https://developer.nvidia.com/gpugems/gpugems/part-i-natural-effects/chapter-1-effective-water-simulation-physical-models",

{     "id": "source.knowledge-depth-openstax-damped-oscillations",     "url": "https://openstax.org/books/university-physics-volume-1/pages/15-5-damped-oscillations",

"id": "source.knowledge-depth-openstax-damped-oscillations",     "url": "https://openstax.org/books/university-physics-volume-1/pages/15-5-damped-oscillations",     "title": "OpenStax University Physics Volume 1 — Damped Oscillations",

"url": "https://openstax.org/books/university-physics-volume-1/pages/15-5-damped-oscillations",

"locator": "15.5, underdamped/critically damped/overdamped conditions relative to b=sqrt(4mk)",     "scope": "Linear viscous damping of a one-degree-of-freedom harmonic oscillator.",     "version": "Independent reviewer actually read on 202

"scope": "Linear viscous damping of a one-degree-of-freedom harmonic oscillator.",     "version": "Independent reviewer actually read on 2026-09-07: https://openstax.org/books/university-physics-volume-1/pages/15-5-damped-oscillations . Act

"version": "Independent reviewer actually read on 2026-09-07: https://openstax.org/books/university-physics-volume-1/pages/15-5-damped-oscillations . Actual source text inspected; unversioned access snapshot, not a runtime test.",

{     "id": "source.knowledge-depth-openstax-simple-harmonic-motion",     "url": "https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion",

"id": "source.knowledge-depth-openstax-simple-harmonic-motion",     "url": "https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion",     "title": "OpenStax University Physics Volume 1 — Simple Harmonic Moti

"url": "https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion",

"locator": "15.1, Hooke's law F_s=-kx; period of SHM independent of amplitude",     "scope": "Undamped one-dimensional simple harmonic oscillator.",     "version": "Independent reviewer actually read on 2026-09-07: https://openstax.org/book

"scope": "Undamped one-dimensional simple harmonic oscillator.",     "version": "Independent reviewer actually read on 2026-09-07: https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion . Actual source text

"version": "Independent reviewer actually read on 2026-09-07: https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion . Actual source text inspected; unversioned access snapshot, not a runtime test.",

{     "id": "source.knowledge-depth-rapier-joints",     "url": "https://rapier.rs/docs/user_guides/javascript/joints/",

"id": "source.knowledge-depth-rapier-joints",     "url": "https://rapier.rs/docs/user_guides/javascript/joints/",     "title": "Rapier JavaScript: Joints",

"url": "https://rapier.rs/docs/user_guides/javascript/joints/",

"locator": "Spherical joint; Revolute joint",     "scope": "Documented relative-DOF restrictions of Rapier impulse joints; not an analytic pendulum period.",     "version": "Independent reviewer actually read on 2026-09-07: https://rapier.r

"scope": "Documented relative-DOF restrictions of Rapier impulse joints; not an analytic pendulum period.",     "version": "Independent reviewer actually read on 2026-09-07: https://rapier.rs/docs/user_guides/javascript/joints/ . Actual sou

"version": "Independent reviewer actually read on 2026-09-07: https://rapier.rs/docs/user_guides/javascript/joints/ . Actual source text inspected; unversioned access snapshot, not a runtime test.",

{     "id": "source.knowledge-depth-gaffer-fix-your-timestep",     "url": "https://gafferongames.com/post/fix_your_timestep/",

"id": "source.knowledge-depth-gaffer-fix-your-timestep",     "url": "https://gafferongames.com/post/fix_your_timestep/",     "title": "Glenn Fiedler, Fix Your Timestep! (Gaffer On Games)",

"url": "https://gafferongames.com/post/fix_your_timestep/",

{     "id": "source.knowledge-depth-provot-cloth-mass-spring",     "url": "https://graphicsinterface.org/wp-content/uploads/gi1995-17.pdf",

"id": "source.knowledge-depth-provot-cloth-mass-spring",     "url": "https://graphicsinterface.org/wp-content/uploads/gi1995-17.pdf",     "title": "Xavier Provot, Deformation Constraints in a Mass-Spring Model to Describe Rigid Cloth Behavi

"url": "https://graphicsinterface.org/wp-content/uploads/gi1995-17.pdf",

"locator": "Abstract and sections 1.1-2.1, 3: discrete mass-spring mesh; structural/shear/flexion springs; super-elastic effect",     "scope": "Graphics mass-spring cloth animation method; not a laboratory textile measurement.",     "versio

"scope": "Graphics mass-spring cloth animation method; not a laboratory textile measurement.",     "version": "Independent reviewer actually read on 2026-09-07: https://graphicsinterface.org/wp-content/uploads/gi1995-17.pdf . Actual source 

"version": "Independent reviewer actually read on 2026-09-07: https://graphicsinterface.org/wp-content/uploads/gi1995-17.pdf . Actual source text inspected; unversioned access snapshot, not a runtime test.",

{     "id": "source.knowledge-depth-cundall-strack-granular",     "url": "https://doi.org/10.1680/geot.1979.29.1.47",

"id": "source.knowledge-depth-cundall-strack-granular",     "url": "https://doi.org/10.1680/geot.1979.29.1.47",     "title": "Cundall and Strack, A discrete numerical model for granular assemblies (Géotechnique 29(1) 1979)",

"url": "https://doi.org/10.1680/geot.1979.29.1.47",

"locator": "Abstract: contact-by-contact interaction and particle-by-particle motion for discs and spheres",     "scope": "Published abstract only. The full paper was not obtained in this session.",     "version": "Independent reviewer actu

"scope": "Published abstract only. The full paper was not obtained in this session.",     "version": "Independent reviewer actually read on 2026-09-07: https://experts.umn.edu/en/publications/discrete-numerical-model-for-granular-assemblies

"version": "Independent reviewer actually read on 2026-09-07: https://experts.umn.edu/en/publications/discrete-numerical-model-for-granular-assemblies/ . Author institution abstract only; full paper not obtained.",

{     "id": "source.knowledge-depth-three-instanced-mesh",     "url": "https://threejs.org/docs/pages/InstancedMesh.html",

"id": "source.knowledge-depth-three-instanced-mesh",     "url": "https://threejs.org/docs/pages/InstancedMesh.html",     "title": "Three.js documentation: InstancedMesh",

"url": "https://threejs.org/docs/pages/InstancedMesh.html",

{     "id": "source.knowledge-depth-three-texture",     "url": "https://threejs.org/docs/pages/Texture.html",

"id": "source.knowledge-depth-three-texture",     "url": "https://threejs.org/docs/pages/Texture.html",     "title": "Three.js documentation: Texture",

"url": "https://threejs.org/docs/pages/Texture.html",

{     "id": "source.knowledge-depth-three-canvas-texture",     "url": "https://threejs.org/docs/pages/CanvasTexture.html",

"id": "source.knowledge-depth-three-canvas-texture",     "url": "https://threejs.org/docs/pages/CanvasTexture.html",     "title": "Three.js documentation: CanvasTexture",

"url": "https://threejs.org/docs/pages/CanvasTexture.html",

{     "id": "source.knowledge-depth-three-rendering-on-demand",     "url": "https://threejs.org/manual/en/rendering-on-demand.html",

"id": "source.knowledge-depth-three-rendering-on-demand",     "url": "https://threejs.org/manual/en/rendering-on-demand.html",     "title": "Three.js manual: Rendering on Demand",

"url": "https://threejs.org/manual/en/rendering-on-demand.html",

{     "id": "source.knowledge-depth-three-mesh-bvh",     "url": "https://github.com/gkjohnson/three-mesh-bvh/blob/master/README.md",

"id": "source.knowledge-depth-three-mesh-bvh",     "url": "https://github.com/gkjohnson/three-mesh-bvh/blob/master/README.md",     "title": "three-mesh-bvh README (gkjohnson)",

"url": "https://github.com/gkjohnson/three-mesh-bvh/blob/master/README.md",

{     "id": "source.handbook-math-fourier",     "url": "https://ocw.mit.edu/courses/es-1803-differential-equations-spring-2024/mites_1803_s24_topic_full.pdf",

"id": "source.handbook-math-fourier",     "url": "https://ocw.mit.edu/courses/es-1803-differential-equations-spring-2024/mites_1803_s24_topic_full.pdf",     "title": "MIT ES.1803 Differential Equations, Spring 2024 topic notes",

"url": "https://ocw.mit.edu/courses/es-1803-differential-equations-spring-2024/mites_1803_s24_topic_full.pdf",

{     "id": "source.handbook-math-riemann",     "url": "https://math.mit.edu/~dunkel/Teach/18.04_2019S/notes/1804_Main.pdf",

"id": "source.handbook-math-riemann",     "url": "https://math.mit.edu/~dunkel/Teach/18.04_2019S/notes/1804_Main.pdf",     "title": "MIT 18.04 Complex Analysis notes, Spring 2019",

"url": "https://math.mit.edu/~dunkel/Teach/18.04_2019S/notes/1804_Main.pdf",

{     "id": "source.handbook-math-mandelbrot",     "url": "https://math.bu.edu/eap/DYSYS/FRACGEOM/node2.html",

"id": "source.handbook-math-mandelbrot",     "url": "https://math.bu.edu/eap/DYSYS/FRACGEOM/node2.html",     "title": "Robert L. Devaney, Boston University: The Mandelbrot Set",

"url": "https://math.bu.edu/eap/DYSYS/FRACGEOM/node2.html",

{     "id": "source.handbook-math-phase-portrait",     "url": "https://uclnatsci.github.io/2021/Mathematics-for-Natural-Sciences-2/DynamicalSystems/phase_portrait.html",

"id": "source.handbook-math-phase-portrait",     "url": "https://uclnatsci.github.io/2021/Mathematics-for-Natural-Sciences-2/DynamicalSystems/phase_portrait.html",     "title": "UCL Mathematics for Natural Sciences 2: The phase portrait",

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{     "id": "source.handbook-math-image-sources",     "url": "https://pyfar-oer.readthedocs.io/en/latest/oer/courses/Architectural_Acoustics_TUe/image_sources/image_sources.html",

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