\n Both questions here are disproved, by way of Erdős Problem 90. The source says so directly: this\nis a stronger form of the unit distance conjecture, so the disproof of that conjecture disproves\nthese too. See FormalConjectures.ErdosProblems.«90».
\nReference: erdosproblems.com/92
"},"constLinks":{"Erdos92.erdos_92.variants.strong":{"url":"/FormalConjectures/ErdosProblems/«92»/#Erdos92___erdos_92___variants___strong","anchor":"Erdos92___erdos_92___variants___strong","docHtml":"\n Or even $f(n) < n^{c/\\log\\log n}$ for some constant $c > 0$?
\n\n Also disproved, and by the weak form rather than separately: since $c/\\log\\log n \\to 0$, the bound\n$n^{c/\\log\\log n}$ is of the form $n^{o(1)}$, so this statement implies\nerdos_92.variants.weak and is false whenever that one is.
@[category research solved, AMS 52]\ntheorem erdos_92.variants.strong : answer(False) ↔\n∃ c > 0, ∀ᶠ n in atTop, (f n : ℝ) ≤ n^(c / (n : ℝ).log.log) := ⊢ False ↔ ∃ c > 0, ∀ᶠ (n : ℕ) in atTop, ↑(f n) ≤ ↑n ^ (c / Real.log (Real.log ↑n))\nAll goals completed! 🐙","hoverDocs":{"274":"`by tac` constructs a term of the expected type by running the tactic(s) `tac`. ","370":"The `sorry` tactic is a temporary placeholder for an incomplete tactic proof,\nclosing the main goal using `exact sorry`.\n\nThis is intended for stubbing-out incomplete parts of a proof while still having a syntactically correct proof skeleton.\nLean will give a warning whenever a proof uses `sorry`, so you aren't likely to miss it,\nbut you can double check if a theorem depends on `sorry` by looking for `sorryAx` in the output\nof the `#print axioms my_thm` command, the axiom used by the implementation of `sorry`.\n","476":"Nat : TypeThe natural numbers, starting at zero.\n\nThis type is special-cased by both the kernel and the compiler, and overridden with an efficient\nimplementation. Both use a fast arbitrary-precision arithmetic library (usually\n[GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.\n","477":"Iff (a b : Prop) : PropIf and only if, or logical bi-implication. `a ↔ b` means that `a` implies `b` and vice versa.\nBy `propext`, this implies that `a` and `b` are equal and hence any expression involving `a`\nis equivalent to the corresponding expression with `b` instead.\n\n\nConventions for notations in identifiers:\n\n * The recommended spelling of `↔` in identifiers is `iff`.\n\n * The recommended spelling of `<->` in identifiers is `iff` (prefer `↔` over `<->`).","852":"ℕ","884":"Real : TypeThe type `ℝ` of real numbers constructed as equivalence classes of Cauchy sequences of rational\nnumbers. ","886":"ℝ","892":"Filter.atTop.{u_3} {α : Type u_3} [Preorder α] : Filter α`atTop` is the filter representing the limit `→ ∞` on an ordered set.\nIt is generated by the collection of up-sets `{b | a ≤ b}`.\n(The preorder need not have a top element for this to be well defined,\nand indeed is trivial when a top element `x` exists, i.e., it coincides with `pure x`.) ","893":"LE.le.{u} {α : Type u} [self : LE α] : α → α → PropThe less-equal relation: `x ≤ y` \n\nConventions for notations in identifiers:\n\n * The recommended spelling of `≤` in identifiers is `le`.","953":"`f.Eventually p` or `∀ᶠ x in f, p x` mean that `{x | p x} ∈ f`. E.g., `∀ᶠ x in atTop, p x`\nmeans that `p` holds true for sufficiently large `x`. ","957":"Filter.Eventually.{u_1} {α : Type u_1} (p : α → Prop) (f : Filter α) : Prop`f.Eventually p` or `∀ᶠ x in f, p x` mean that `{x | p x} ∈ f`. E.g., `∀ᶠ x in atTop, p x`\nmeans that `p` holds true for sufficiently large `x`. ","1199":"False : Prop`False` is the empty proposition. Thus, it has no introduction rules.\nIt represents a contradiction. `False` elimination rule, `False.rec`,\nexpresses the fact that anything follows from a contradiction.\nThis rule is sometimes called ex falso (short for ex falso sequitur quodlibet),\nor the principle of explosion.\nFor more information: [Propositional Logic](https://lean-lang.org/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)\n","1345":"HPow.hPow.{u, v, w} {α : Type u} {β : Type v} {γ : outParam (Type w)} [self : HPow α β γ] : α → β → γ`a ^ b` computes `a` to the power of `b`.\nThe meaning of this notation is type-dependent. \n\nConventions for notations in identifiers:\n\n * The recommended spelling of `^` in identifiers is `pow`.","1378":"Real.log (x : ℝ) : ℝThe real logarithm function, equal to the inverse of the exponential for `x > 0`,\nto `log |x|` for `x < 0`, and to `0` for `0`. We use this unconventional extension to\n`(-∞, 0]` as it gives the formula `log (x * y) = log x + log y` for all nonzero `x` and `y`, and\nthe derivative of `log` is `1/x` away from `0`. ","1504":"HDiv.hDiv.{u, v, w} {α : Type u} {β : Type v} {γ : outParam (Type w)} [self : HDiv α β γ] : α → β → γ`a / b` computes the result of dividing `a` by `b`.\nThe meaning of this notation is type-dependent.\n* For most types like `Nat`, `Int`, `Rat`, `Real`, `a / 0` is defined to be `0`.\n* For `Nat`, `a / b` rounds downwards.\n* For `Int`, `a / b` rounds downwards if `b` is positive or upwards if `b` is negative.\n It is implemented as `Int.ediv`, the unique function satisfying\n `a % b + b * (a / b) = a` and `0 ≤ a % b < natAbs b` for `b ≠ 0`.\n Other rounding conventions are available using the functions\n `Int.fdiv` (floor rounding) and `Int.tdiv` (truncation rounding).\n* For `Float`, `a / 0` follows the IEEE 754 semantics for division,\n usually resulting in `inf` or `nan`. \n\nConventions for notations in identifiers:\n\n * The recommended spelling of `/` in identifiers is `div`.","16516":"Erdos92.f (n : ℕ) : ℕLet $f(n)$ be maximal such that there exists a set $A$ of $n$ points in $\\mathbb^2$\nin which every $x \\in A$ has at least $f(n)$ points in $A$ equidistant from $x$.\n","16518":"Erdos92.erdos_92.variants.strong : False ↔ ∃ c > 0, ∀ᶠ (n : ℕ) in atTop, ↑(f n) ≤ ↑n ^ (c / Real.log (Real.log ↑n))Or even $f(n) < n^{c/\\log\\log n}$ for some constant $c > 0$?\n\nAlso disproved, and by the weak form rather than separately: since $c/\\log\\log n \\to 0$, the bound\n$n^{c/\\log\\log n}$ is of the form $n^{o(1)}$, so this statement implies\n`erdos_92.variants.weak` and is false whenever that one is.\n"}},"Erdos92.possible_f_values_BddAbove":{"url":"/FormalConjectures/ErdosProblems/«92»/#Erdos92___possible_f_values_BddAbove","anchor":"Erdos92___possible_f_values_BddAbove","docHtml":"\n A sanity check to ensure the set of possible f(n) values is bounded above. A trivial bound is\nn, since the points equidistant from any x form a subset of the other n - 1 points.\nThis ensures sSup is well-defined.
n:ℕk:ℕpoints:Finset ℝ²hcard:points.card = nhall:∀ x ∈ points, k ≤ maxEquidistantPointsAt x pointsx:ℝ²hx:x ∈ pointsm:ℕhm:∃ a ∈ Finset.image (dist x) (points.erase x), {p ∈ points.erase x | dist x p = a}.card = m⊢ m ≤ n\nn:ℕk:ℕpoints:Finset ℝ²hcard:points.card = nhall:∀ x ∈ points, k ≤ maxEquidistantPointsAt x pointsx:ℝ²hx:x ∈ pointsd:ℝhd:d ∈ Finset.image (dist x) (points.erase x)⊢ {p ∈ points.erase x | dist x p = d}.card ≤ n\ncalc ((points.erase x).filter fun p => dist x p = d).card\n≤ (points.erase x).card := Finset.card_filter_le _ _\n_ ≤ points.card := Finset.card_erase_le\n_ = n := hcard","hoverDocs":{"274":"`by tac` constructs a term of the expected type by running the tactic(s) `tac`. ","476":"Nat : TypeThe natural numbers, starting at zero.\n\nThis type is special-cased by both the kernel and the compiler, and overridden with an efficient\nimplementation. Both use a fast arbitrary-precision arithmetic library (usually\n[GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.\n","479":"Eq.{u_1} {α : Sort u_1} : α → α → PropThe equality relation. It has one introduction rule, `Eq.refl`.\nWe use `a = b` as notation for `Eq a b`.\nA fundamental property of equality is that it is an equivalence relation.\n```\nvariable (α : Type) (a b c d : α)\nvariable (hab : a = b) (hcb : c = b) (hcd : c = d)\n\nexample : a = d :=\n Eq.trans (Eq.trans hab (Eq.symm hcb)) hcd\n```\nEquality is much more than an equivalence relation, however. It has the important property that every assertion\nrespects the equivalence, in the sense that we can substitute equal expressions without changing the truth value.\nThat is, given `h1 : a = b` and `h2 : p a`, we can construct a proof for `p b` using substitution: `Eq.subst h1 h2`.\nExample:\n```\nexample (α : Type) (a b : α) (p : α → Prop)\n (h1 : a = b) (h2 : p a) : p b :=\n Eq.subst h1 h2\n\nexample (α : Type) (a b : α) (p : α → Prop)\n (h1 : a = b) (h2 : p a) : p b :=\n h1 ▸ h2\n```\nThe triangle in the second presentation is a macro built on top of `Eq.subst` and `Eq.symm`, and you can enter it by typing `\\t`.\nFor more information: [Equality](https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#equality)\n\n\nConventions for notations in identifiers:\n\n * The recommended spelling of `=` in identifiers is `eq`.","852":"ℕ","884":"Real : TypeThe type `ℝ` of real numbers constructed as equivalence classes of Cauchy sequences of rational\nnumbers. ","886":"ℝ","893":"LE.le.{u} {α : Type u} [self : LE α] : α → α → PropThe less-equal relation: `x ≤ y` \n\nConventions for notations in identifiers:\n\n * The recommended spelling of `≤` in identifiers is `le`.","900":"`rw` is like `rewrite`, but also tries to close the goal by \"cheap\" (reducible) `rfl` afterwards.\n","913":"Finset.{u_4} (α : Type u_4) : Type u_4`Finset α` is the type of finite sets of elements of `α`. It is implemented\nas a multiset (a list up to permutation) which has no duplicate elements. ","930":"Membership.mem.{u, v} {α : outParam (Type u)} {γ : Type v} [self : Membership α γ] : γ → α → PropThe membership relation `a ∈ s : Prop` where `a : α`, `s : γ`. \n\nConventions for notations in identifiers:\n\n * The recommended spelling of `∈` in identifiers is `mem`.","936":"`refine e` behaves like `exact e`, except that named (`?x`) or unnamed (`?_`)\nholes in `e` that are not solved by unification with the main goal's target type\nare converted into new goals, using the hole's name, if any, as the goal case name.\n","963":"The `obtain` tactic is a combination of `have` and `rcases`. See `rcases` for\na description of supported patterns.\n\n```lean\nobtain ⟨patt⟩ : type := proof\n```\nis equivalent to\n```lean\nhave h : type := proof\nrcases h with ⟨patt⟩\n```\n\nIf `⟨patt⟩` is omitted, `rcases` will try to infer the pattern.\n\nIf `type` is omitted, `:= proof` is required.\n","1195":"Finset.card.{u_1} {α : Type u_1} (s : Finset α) : ℕ`s.card` is the number of elements of `s`, aka its cardinality.\n\nThe notation `#s` can be accessed in the `Finset` locale. ","1204":"Step-wise reasoning over transitive relations.\n```\ncalc\n a = b := pab\n b = c := pbc\n ...\n y = z := pyz\n```\nproves `a = z` from the given step-wise proofs. `=` can be replaced with any\nrelation implementing the typeclass `Trans`. Instead of repeating the right-\nhand sides, subsequent left-hand sides can be replaced with `_`.\n```\ncalc\n a = b := pab\n _ = c := pbc\n ...\n _ = z := pyz\n```\nIt is also possible to write the *first* relation as `<lhs>\\n _ = <rhs> :=\n<proof>`. This is useful for aligning relation symbols, especially on longer\nidentifiers:\n```\ncalc abc\n _ = bce := pabce\n _ = cef := pbcef\n ...\n _ = xyz := pwxyz\n```\n\n`calc` works as a term, as a tactic or as a `conv` tactic.\n\nSee [Theorem Proving in Lean 4][tpil4] for more information.\n\n[tpil4]: https://lean-lang.org/theorem_proving_in_lean4/quantifiers_and_equality.html#calculational-proofs\n","1227":"Exists.intro.{u} {α : Sort u} {p : α → Prop} (w : α) (h : p w) : Exists pExistential introduction. If `a : α` and `h : p a`,\nthen `⟨a, h⟩` is a proof that `∃ x : α, p x`. ","1295":"Location specifications are used by many tactics that can operate on either the\nhypotheses or the goal. It can have one of the forms:\n* 'empty' is not actually present in this syntax, but most tactics use\n `(location)?` matchers. It means to target the goal only.\n* `at h₁ ... hₙ`: target the hypotheses `h₁`, ..., `hₙ`\n* `at h₁ h₂ ⊢`: target the hypotheses `h₁` and `h₂`, and the goal\n* `at *`: target all hypotheses and the goal\n","1394":"Finset.mem_coe.{u_1} {α : Type u_1} {a : α} {s : Finset α} : a ∈ ↑s ↔ a ∈ s","1518":"Finset.filter.{u_1} {α : Type u_1} (p : α → Prop) [DecidablePred p] (s : Finset α) : Finset α`Finset.filter p s` is the set of elements of `s` that satisfy `p`.\n\nFor example, one can use `s.filter (· ∈ t)` to get the intersection of `s` with `t : Set α`\nas a `Finset α` (when a `DecidablePred (· ∈ t)` instance is available). ","1647":"* `unfold id` unfolds all occurrences of definition `id` in the target.\n* `unfold id1 id2 ...` is equivalent to `unfold id1; unfold id2; ...`.\n* `unfold id at h` unfolds at the hypothesis `h`.\n\nDefinitions can be either global or local definitions.\n\nFor non-recursive global definitions, this tactic is identical to `delta`.\nFor recursive global definitions, it uses the \"unfolding lemma\" `id.eq_def`,\nwhich is generated for each recursive definition, to unfold according to the recursive definition given by the user.\nOnly one level of unfolding is performed, in contrast to `simp only [id]`, which unfolds definition `id` recursively.\n","1659":"LE.le.trans.{u_1} {α : Type u_1} [Preorder α] {a b c : α} : a ≤ b → b ≤ c → a ≤ c**Alias** of `le_trans`.","1681":"Finset.image.{u_1, u_2} {α : Type u_1} {β : Type u_2} [DecidableEq β] (f : α → β) (s : Finset α) : Finset β`image f s` is the forward image of `s` under `f`. ","1952":"EuclideanSpace.{u_7, u_8} (𝕜 : Type u_7) (n : Type u_8) : Type (max u_7 u_8)The standard real/complex Euclidean space, functions on a finite type. For an `n`-dimensional\nspace use `EuclideanSpace 𝕜 (Fin n)`.\n\nFor the case when `n = Fin _`, there is `!₂[x, y, ...]` notation for building elements of this type,\nanalogous to `![x, y, ...]` notation. ","1989":"ℝ²","1992":"Finset ℝ²","2144":"SupSet.sSup.{u_1} {α : Type u_1} [self : SupSet α] : Set α → αSupremum of a set ","2152":"Dist.dist.{u_3} {α : Type u_3} [self : Dist α] : α → α → ℝDistance between two points ","2173":"Finset.erase.{u_1} {α : Type u_1} [DecidableEq α] (s : Finset α) (a : α) : Finset α`erase s a` is the set `s - {a}`, that is, the elements of `s` which are\nnot equal to `a`. ","2195":"Finset.mem_image.{u_1, u_2} {α : Type u_1} {β : Type u_2} [DecidableEq β] {f : α → β} {s : Finset α} {b : β} :\n b ∈ Finset.image f s ↔ ∃ a ∈ s, f a = b","3686":"BddAbove.{u_1} {α : Type u_1} [LE α] (s : Set α) : PropA set is bounded above if there exists an upper bound. ","15567":"csSup_le'.{u_1} {α : Type u_1} [ConditionallyCompleteLinearOrderBot α] {s : Set α} {a : α} (h : a ∈ upperBounds s) :\n sSup s ≤ a","15925":"Finset.card_filter_le.{u_1} {α : Type u_1} (s : Finset α) (p : α → Prop) [DecidablePred p] :\n (Finset.filter p s).card ≤ s.card","16502":"Erdos92.maxEquidistantPointsAt (x : ℝ²) (points : Finset ℝ²) : ℕFor a given point `x` and a set of other points, this function finds the maximum number of points\nthat lie on a single circle centered at `x`. It does this by grouping the other points by their\ndistance to `x` and finding the size of the largest group.\n","16504":"Erdos92.possible_f_values (n : ℕ) : Set ℕThe set of all possible values `k` for which there exists a set of `n` points\nsatisfying the `hasMinEquidistantProperty k`. The function `f(n)` will be the supremum of this set.\n","16505":"Erdos92.possible_f_values_BddAbove (n : ℕ) : BddAbove (possible_f_values n)A sanity check to ensure the set of possible `f(n)` values is bounded above. A trivial bound is\n`n`, since the points equidistant from any `x` form a subset of the other `n - 1` points.\nThis ensures `sSup` is well-defined.\n","16506":"k ∈ possible_f_values n","16507":"points.card = n","16508":"x ∈ points","16509":"∀ x ∈ points, k ≤ maxEquidistantPointsAt x points","16510":"m ∈ ↑(Finset.image (fun d ↦ {p ∈ points.erase x | dist x p = d}.card) (Finset.image (dist x) (points.erase x)))","16511":"m ∈ Finset.image (fun d ↦ {p ∈ points.erase x | dist x p = d}.card) (Finset.image (dist x) (points.erase x))","16512":"∃ a ∈ Finset.image (dist x) (points.erase x), {p ∈ points.erase x | dist x p = a}.card = m","16513":"d ∈ Finset.image (dist x) (points.erase x)","16514":"{p ∈ points.erase x | dist x p = d}.card = m","16515":"Finset.card_erase_le.{u_1} {α : Type u_1} {s : Finset α} {a : α} [DecidableEq α] : (s.erase a).card ≤ s.card"}},"Erdos92.erdos_92.variants.weak":{"url":"/FormalConjectures/ErdosProblems/«92»/#Erdos92___erdos_92___variants___weak","anchor":"Erdos92___erdos_92___variants___weak","docHtml":"\n Is it true that $f(n)\\leq n^{o(1)}$?
\n\n The source records this as disproved: \"This is a stronger form of the unit distance conjecture\n(see [90]). As such the recent disproof of [90] also disproves this.\" That disproof is\nErdos90.erdos_90, which this repository already records as research solved with the answer\nFalse.
@[category research solved, AMS 52]\ntheorem erdos_92.variants.weak : answer(False) ↔ ∃ o : ℕ → ℝ,\no =o[atTop] (1 : ℕ → ℝ) ∧ ∀ n, (f n : ℝ) ≤ n^(o n) := ⊢ False ↔ ∃ o, o =o[atTop] 1 ∧ ∀ (n : ℕ), ↑(f n) ≤ ↑n ^ o n\nAll goals completed! 🐙","hoverDocs":{"274":"`by tac` constructs a term of the expected type by running the tactic(s) `tac`. ","370":"The `sorry` tactic is a temporary placeholder for an incomplete tactic proof,\nclosing the main goal using `exact sorry`.\n\nThis is intended for stubbing-out incomplete parts of a proof while still having a syntactically correct proof skeleton.\nLean will give a warning whenever a proof uses `sorry`, so you aren't likely to miss it,\nbut you can double check if a theorem depends on `sorry` by looking for `sorryAx` in the output\nof the `#print axioms my_thm` command, the axiom used by the implementation of `sorry`.\n","381":"And (a b : Prop) : Prop`And a b`, or `a ∧ b`, is the conjunction of propositions. It can be\nconstructed and destructed like a pair: if `ha : a` and `hb : b` then\n`⟨ha, hb⟩ : a ∧ b`, and if `h : a ∧ b` then `h.left : a` and `h.right : b`.\n\n\nConventions for notations in identifiers:\n\n * The recommended spelling of `∧` in identifiers is `and`.","476":"Nat : TypeThe natural numbers, starting at zero.\n\nThis type is special-cased by both the kernel and the compiler, and overridden with an efficient\nimplementation. Both use a fast arbitrary-precision arithmetic library (usually\n[GMP](https://gmplib.org/)); at runtime, `Nat` values that are sufficiently small are unboxed.\n","477":"Iff (a b : Prop) : PropIf and only if, or logical bi-implication. `a ↔ b` means that `a` implies `b` and vice versa.\nBy `propext`, this implies that `a` and `b` are equal and hence any expression involving `a`\nis equivalent to the corresponding expression with `b` instead.\n\n\nConventions for notations in identifiers:\n\n * The recommended spelling of `↔` in identifiers is `iff`.\n\n * The recommended spelling of `<->` in identifiers is `iff` (prefer `↔` over `<->`).","852":"ℕ","883":"ℕ → ℝ","884":"Real : TypeThe type `ℝ` of real numbers constructed as equivalence classes of Cauchy sequences of rational\nnumbers. ","892":"Filter.atTop.{u_3} {α : Type u_3} [Preorder α] : Filter α`atTop` is the filter representing the limit `→ ∞` on an ordered set.\nIt is generated by the collection of up-sets `{b | a ≤ b}`.\n(The preorder need not have a top element for this to be well defined,\nand indeed is trivial when a top element `x` exists, i.e., it coincides with `pure x`.) ","893":"LE.le.{u} {α : Type u} [self : LE α] : α → α → PropThe less-equal relation: `x ≤ y` \n\nConventions for notations in identifiers:\n\n * The recommended spelling of `≤` in identifiers is `le`.","1199":"False : Prop`False` is the empty proposition. Thus, it has no introduction rules.\nIt represents a contradiction. `False` elimination rule, `False.rec`,\nexpresses the fact that anything follows from a contradiction.\nThis rule is sometimes called ex falso (short for ex falso sequitur quodlibet),\nor the principle of explosion.\nFor more information: [Propositional Logic](https://lean-lang.org/theorem_proving_in_lean4/propositions_and_proofs.html#propositional-logic)\n","1345":"HPow.hPow.{u, v, w} {α : Type u} {β : Type v} {γ : outParam (Type w)} [self : HPow α β γ] : α → β → γ`a ^ b` computes `a` to the power of `b`.\nThe meaning of this notation is type-dependent. \n\nConventions for notations in identifiers:\n\n * The recommended spelling of `^` in identifiers is `pow`.","8132":"Asymptotics.IsLittleO.{u_18, u_19, u_20} {α : Type u_18} {E : Type u_19} {F : Type u_20} [Norm E] [Norm F]\n (l : Filter α) (f : α → E) (g : α → F) : PropThe Landau notation `f =o[l] g` where `f` and `g` are two functions on a type `α` and `l` is\na filter on `α`, means that eventually for `l`, `‖f‖` is bounded by an arbitrarily small constant\nmultiple of `‖g‖`. In other words, `‖f‖ / ‖g‖` tends to `0` along `l`, modulo division by zero\nissues that are avoided by this definition. ","16516":"Erdos92.f (n : ℕ) : ℕLet $f(n)$ be maximal such that there exists a set $A$ of $n$ points in $\\mathbb^2$\nin which every $x \\in A$ has at least $f(n)$ points in $A$ equidistant from $x$.\n","16517":"Erdos92.erdos_92.variants.weak : False ↔ ∃ o, o =o[atTop] 1 ∧ ∀ (n : ℕ), ↑(f n) ≤ ↑n ^ o nIs it true that $f(n)\\leq n^{o(1)}$?\n\nThe source records this as disproved: \"This is a stronger form of the unit distance conjecture\n(see [90]). As such the recent disproof of [90] also disproves this.\" That disproof is\n`Erdos90.erdos_90`, which this repository already records as `research solved` with the answer\n`False`.\n"}}},"contributors":[{"name":"Moritz Firsching","login":"mo271","profileUrl":"https://github.com/mo271","avatarUrl":"https://avatars.githubusercontent.com/u/3491627?v=4","commitCount":4,"firstCommitDate":"2025-09-25","lastCommitDate":"2026-01-11","originalAuthor":true},{"name":"Anton Kukushkin","login":"kukushking","profileUrl":"https://github.com/kukushking","avatarUrl":"https://avatars.githubusercontent.com/u/3997468?v=4","commitCount":1,"firstCommitDate":"2026-07-22","lastCommitDate":"2026-07-22","originalAuthor":false},{"name":"Will Blair","login":"williamjblair","profileUrl":"https://github.com/williamjblair","avatarUrl":"https://avatars.githubusercontent.com/u/85643015?v=4","commitCount":1,"firstCommitDate":"2026-08-14","lastCommitDate":"2026-08-14","originalAuthor":false},{"name":"Yaël Dillies","login":"YaelDillies","profileUrl":"https://github.com/YaelDillies","avatarUrl":"https://avatars.githubusercontent.com/u/14090593?v=4","commitCount":1,"firstCommitDate":"2026-07-17","lastCommitDate":"2026-07-17","originalAuthor":false}]}