@cite{beltrama-schwarz-2024}: Empirical Data

@cite{beltrama-schwarz-2024}

Experimental data from @cite{beltrama-schwarz-2024}, showing that speaker persona stereotypes affect imprecision resolution for round numerals.

Experiments

1. Experiment 1 (Covered Screen Task): Participants choose which of two phone screens (COVERED vs VISIBLE) a speaker was looking at when making a round-numeral statement. Both Nerdy and Chill personae significantly affect choice rates.

2. Experiment 2 (Truth-Value Judgment Task): Participants judge whether a speaker's round-numeral statement is RIGHT or WRONG given a visible phone screen. Only the Chill persona significantly affects judgments.

Key empirical generalization

Speaker persona stereotypes modulate imprecision resolution bi-directionally in inference tasks (Exp 1) but asymmetrically in judgment tasks (Exp 2): Chill speakers increase tolerance for imprecision in both tasks, but Nerdy speakers only increase exactness demands in the inference task.

inductive Phenomena.Imprecision.Studies.BeltramaSchwarz2024.PersonaCondition : Type

Speaker persona condition (between-subjects). Participants read a short vignette describing the speaker (§3.1).

• nerdy : PersonaCondition
• chill : PersonaCondition
• noPersona : PersonaCondition

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqPersonaCondition : DecidableEq PersonaCondition

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqPersonaCondition x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPersonaCondition : BEq PersonaCondition

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPersonaCondition = { beq := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPersonaCondition.beq }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPersonaCondition.beq : PersonaCondition → PersonaCondition → Bool

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPersonaCondition.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprPersonaCondition.repr : PersonaCondition → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprPersonaCondition : Repr PersonaCondition

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprPersonaCondition = { reprPrec := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprPersonaCondition.repr }

inductive Phenomena.Imprecision.Studies.BeltramaSchwarz2024.ScreenFit : Type

Screen fit condition (within-subjects, §3.1). Determines the relationship between the speaker's round-numeral statement and the amount shown on the VISIBLE phone screen.

• match_ : ScreenFit
• mismatch : ScreenFit
• imprecise : ScreenFit

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqScreenFit : DecidableEq ScreenFit

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqScreenFit x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqScreenFit.beq : ScreenFit → ScreenFit → Bool

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqScreenFit.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqScreenFit : BEq ScreenFit

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqScreenFit = { beq := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqScreenFit.beq }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprScreenFit.repr : ScreenFit → ℕ → Std.Format

Equations

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instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprScreenFit : Repr ScreenFit

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprScreenFit = { reprPrec := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprScreenFit.repr }

inductive Phenomena.Imprecision.Studies.BeltramaSchwarz2024.TaskType : Type

Experimental task type.

• coveredScreen : TaskType
• truthValueJudgment : TaskType

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqTaskType : DecidableEq TaskType

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqTaskType x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqTaskType.beq : TaskType → TaskType → Bool

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqTaskType.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqTaskType : BEq TaskType

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqTaskType = { beq := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqTaskType.beq }

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprTaskType : Repr TaskType

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprTaskType = { reprPrec := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprTaskType.repr }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprTaskType.repr : TaskType → ℕ → Std.Format

Equations

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def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.personaDescriptors : PersonaCondition → List String

The trait descriptors used for each persona condition. Each participant read: "Ryan is [descriptors]."

Equations

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• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.personaDescriptors Phenomena.Imprecision.Studies.BeltramaSchwarz2024.PersonaCondition.noPersona = []

structure Phenomena.Imprecision.Studies.BeltramaSchwarz2024.RegressionCoefficient : Type

A coefficient from a mixed-effects logistic regression model. Models fitted via glmer in R (lme4; @cite{bates-etal-2015}).

• predictor : String
• beta : ℚ

  Coefficient estimate (log-odds)

• se : ℚ

  Standard error

• significant : Bool

  Significant at p < 0.05?

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprRegressionCoefficient : Repr RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprRegressionCoefficient = { reprPrec := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprRegressionCoefficient.repr }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprRegressionCoefficient.repr : RegressionCoefficient → ℕ → Std.Format

Equations

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def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_n : ℕ

Experiment 1 sample size after exclusions (§4.1). 134 participants from 151 recruited.

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_n = 134

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_intercept : RegressionCoefficient

Experiment 1, Model 1 (main effects only). DV: COVERED (1) vs VISIBLE (0). Reference levels: NoPersona, ScreenFit[Imprecise]. Table 1, Model 1 (§4.2).

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_intercept = { predictor := "Intercept", beta := 67 / 100, se := 18 / 100, significant := true }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_chill : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_chill = { predictor := "Chill", beta := -67 / 100, se := 13 / 100, significant := true }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_nerdy : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_nerdy = { predictor := "Nerdy", beta := 77 / 100, se := 14 / 100, significant := true }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_screenFitMatch : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_screenFitMatch = { predictor := "ScreenFit[Match]", beta := -447 / 100, se := 18 / 100, significant := true }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_screenFitMismatch : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_screenFitMismatch = { predictor := "ScreenFit[Mismatch]", beta := 248 / 100, se := 20 / 100, significant := true }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_model1 : List RegressionCoefficient

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_chillMatch : RegressionCoefficient

Experiment 1, Model 2 interaction terms (Table 1, Model 2). All Persona × ScreenFit interactions are non-significant (§4.2.2): persona effects are comparable across screen fit conditions.

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_chillMatch = { predictor := "Chill:Match", beta := -16 / 100, se := 37 / 100, significant := false }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_chillMismatch : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_chillMismatch = { predictor := "Chill:Mismatch", beta := 12 / 100, se := 40 / 100, significant := false }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_nerdyMatch : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_nerdyMatch = { predictor := "Nerdy:Match", beta := 11 / 100, se := 35 / 100, significant := false }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_nerdyMismatch : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_nerdyMismatch = { predictor := "Nerdy:Mismatch", beta := -22 / 100, se := 38 / 100, significant := false }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_interactions : List RegressionCoefficient

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_n : ℕ

Experiment 2 sample size after exclusions (§5.1). 132 participants from 150 recruited.

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_n = 132

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_intercept : RegressionCoefficient

Experiment 2, Model 1 (main effects only). DV: RIGHT (1) vs WRONG (0). Reference levels: NoPersona, ScreenFit[Imprecise]. Table 2, Model 1 (§5.2).

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_intercept = { predictor := "Intercept", beta := -78 / 100, se := 16 / 100, significant := true }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_chill : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_chill = { predictor := "Chill", beta := 104 / 100, se := 16 / 100, significant := true }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_nerdy : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_nerdy = { predictor := "Nerdy", beta := 2 / 100, se := 17 / 100, significant := false }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_screenFitMatch : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_screenFitMatch = { predictor := "ScreenFit[Match]", beta := 455 / 100, se := 20 / 100, significant := true }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_screenFitMismatch : RegressionCoefficient

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_screenFitMismatch = { predictor := "ScreenFit[Mismatch]", beta := -263 / 100, se := 18 / 100, significant := true }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_model1 : List RegressionCoefficient

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exampleStatedAmount : ℕ

All critical items use round dollar amounts. Example from §3.1: "The phone costs $200."

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exampleStatedAmount = 200

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exampleImpreciseAmount : ℕ

The imprecise screen shows a close-but-not-exact amount. Example from §3.1: visible screen shows $193 when statement says $200.

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exampleImpreciseAmount = 193

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.stimulus_is_round : Core.Roundness.roundnessGrade exampleStatedAmount = Core.Roundness.RoundnessGrade.high

Stimulus numerals are round: high roundness grade.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.imprecise_value_is_nonround : Core.Roundness.roundnessGrade exampleImpreciseAmount = Core.Roundness.RoundnessGrade.none

The imprecise value is non-round: zero roundness.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.roundness_gap : Core.Roundness.roundnessScore exampleStatedAmount = 6 ∧ Core.Roundness.roundnessScore exampleImpreciseAmount = 0

Roundness scores differ maximally: 6 vs 0.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_both_personae_significant : exp1_chill.significant = true ∧ exp1_nerdy.significant = true

Core finding: both persona conditions significantly affect Exp 1 (inference task).

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp2_chill_only : exp2_chill.significant = true ∧ exp2_nerdy.significant = false

Key asymmetry: in Exp 2 (judgment task), only Chill is significant.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.chill_reduces_exactness_exp1 : exp1_chill.beta < 0

Chill decreases COVERED rate (negative β): Chill persona leads listeners to favor the VISIBLE screen, treating the round numeral as imprecise (§4.2.2).

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.nerdy_increases_exactness_exp1 : exp1_nerdy.beta > 0

Nerdy increases COVERED rate (positive β): Nerdy persona leads listeners to favor the COVERED screen, treating the round numeral as exact (§4.2.2).

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.chill_increases_tolerance_exp2 : exp2_chill.beta > 0

Chill increases RIGHT rate (positive β on RIGHT DV), i.e., increases tolerance for imprecision in truth-value judgments (§5.2.2).

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.nerdy_null_in_exp2 : exp2_nerdy.significant = false

Nerdy has no significant effect on truth-value judgments (§5.2.2).

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.exp1_no_interactions : exp1_chillMatch.significant = false ∧ exp1_chillMismatch.significant = false ∧ exp1_nerdyMatch.significant = false ∧ exp1_nerdyMismatch.significant = false

No significant Persona × ScreenFit interactions in Exp 1 (§4.2.2): persona effects are comparable across all screen fit conditions.

This absence (while main effects ARE significant) implies that persona modulates a global interpretive parameter — the precision threshold — rather than a local disambiguation strategy that operates only in ambiguous contexts.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.chill_effect_larger_in_exp2 : exp2_chill.beta > -exp1_chill.beta

The Chill effect is larger in Exp 2 (|β| = 1.04) than in Exp 1 (|β| = 0.67).

inductive Phenomena.Imprecision.Studies.BeltramaSchwarz2024.PrecisionVariant : Type

Precision variants for numeral use.

• exact : PrecisionVariant
• approximate : PrecisionVariant

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqPrecisionVariant : DecidableEq PrecisionVariant

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqPrecisionVariant x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPrecisionVariant.beq : PrecisionVariant → PrecisionVariant → Bool

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPrecisionVariant.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPrecisionVariant : BEq PrecisionVariant

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPrecisionVariant = { beq := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqPrecisionVariant.beq }

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprPrecisionVariant : Repr PrecisionVariant

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprPrecisionVariant = { reprPrec := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprPrecisionVariant.repr }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprPrecisionVariant.repr : PrecisionVariant → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.precisionField : Core.SocialMeaning.IndexicalField PrecisionVariant Sociolinguistics.SCM.SocialDimension

The indexical field for numeral precision.

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.personaPrecision : PersonaCondition → Option PrecisionVariant

The precision variant favored by a given persona condition.

Equations

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• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.personaPrecision Phenomena.Imprecision.Studies.BeltramaSchwarz2024.PersonaCondition.noPersona = none

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.personaDimension : PersonaCondition → Option Sociolinguistics.SCM.SocialDimension

Persona conditions mapped to SCM social dimensions.

Equations

• One or more equations did not get rendered due to their size.
• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.personaDimension Phenomena.Imprecision.Studies.BeltramaSchwarz2024.PersonaCondition.chill = some Sociolinguistics.SCM.SocialDimension.warmth
• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.personaDimension Phenomena.Imprecision.Studies.BeltramaSchwarz2024.PersonaCondition.noPersona = none

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.bidirectionality (p : PersonaCondition) (d : Sociolinguistics.SCM.SocialDimension) (v : PrecisionVariant) (hd : personaDimension p = some d) (hv : personaPrecision p = some v) : precisionField.indexes v d

Bidirectionality theorem: production and comprehension mappings cohere.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.scm_coherence_nerdy : precisionField.indexes PrecisionVariant.exact Sociolinguistics.SCM.SocialDimension.competence

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.scm_coherence_chill : precisionField.indexes PrecisionVariant.approximate Sociolinguistics.SCM.SocialDimension.warmth

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.opposite_directions (d : Sociolinguistics.SCM.SocialDimension) : precisionField.association PrecisionVariant.exact d = -precisionField.association PrecisionVariant.approximate d

Exact and approximate use have opposite associations with every dimension.

inductive Phenomena.Imprecision.Studies.BeltramaSchwarz2024.ResponseShift : Type

• towardRejection : ResponseShift
• towardAcceptance : ResponseShift

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqResponseShift : DecidableEq ResponseShift

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableEqResponseShift x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqResponseShift : BEq ResponseShift

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqResponseShift = { beq := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqResponseShift.beq }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqResponseShift.beq : ResponseShift → ResponseShift → Bool

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instBEqResponseShift.beq x✝ y✝ = (x✝.ctorIdx == y✝.ctorIdx)

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprResponseShift : Repr ResponseShift

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprResponseShift = { reprPrec := Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprResponseShift.repr }

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instReprResponseShift.repr : ResponseShift → ℕ → Std.Format

Equations

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def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.shiftDirection : PrecisionVariant → ResponseShift

Equations

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def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.rejectionIsPrejudicial : TaskType → Prop

Equations

• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.rejectionIsPrejudicial Phenomena.Imprecision.Studies.BeltramaSchwarz2024.TaskType.coveredScreen = False
• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.rejectionIsPrejudicial Phenomena.Imprecision.Studies.BeltramaSchwarz2024.TaskType.truthValueJudgment = True

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableRejectionIsPrejudicial (t : TaskType) : Decidable (rejectionIsPrejudicial t)

Equations

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• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableRejectionIsPrejudicial Phenomena.Imprecision.Studies.BeltramaSchwarz2024.TaskType.truthValueJudgment = isTrue trivial

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.shiftManifests (shift : ResponseShift) (task : TaskType) : Prop

Equations

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• Phenomena.Imprecision.Studies.BeltramaSchwarz2024.shiftManifests Phenomena.Imprecision.Studies.BeltramaSchwarz2024.ResponseShift.towardAcceptance task = True

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.personaEffectPredicted (persona : PersonaCondition) (task : TaskType) : Prop

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theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.acceptance_never_blocked (task : TaskType) : shiftManifests ResponseShift.towardAcceptance task

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.rejection_manifests_in_cst : shiftManifests ResponseShift.towardRejection TaskType.coveredScreen

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.rejection_blocked_in_tvjt : ¬shiftManifests ResponseShift.towardRejection TaskType.truthValueJudgment

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.cst_both_manifest : personaEffectPredicted PersonaCondition.nerdy TaskType.coveredScreen ∧ personaEffectPredicted PersonaCondition.chill TaskType.coveredScreen

Both personae's effects manifest in CST.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.tvjt_chill_only : personaEffectPredicted PersonaCondition.chill TaskType.truthValueJudgment ∧ ¬personaEffectPredicted PersonaCondition.nerdy TaskType.truthValueJudgment

Only Chill's effect manifests in TVJT.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.noPersona_no_effect (task : TaskType) : ¬personaEffectPredicted PersonaCondition.noPersona task

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.task_asymmetry_derived : (personaEffectPredicted PersonaCondition.nerdy TaskType.coveredScreen ∧ personaEffectPredicted PersonaCondition.chill TaskType.coveredScreen) ∧ (personaEffectPredicted PersonaCondition.chill TaskType.truthValueJudgment ∧ ¬personaEffectPredicted PersonaCondition.nerdy TaskType.truthValueJudgment) ∧ (exp1_nerdy.significant = true ∧ exp1_chill.significant = true) ∧ exp2_chill.significant = true ∧ exp2_nerdy.significant = false

Combined task asymmetry matches empirical significance pattern.

def Phenomena.Imprecision.Studies.BeltramaSchwarz2024.impreciseReadingAvailable (n : ℕ) : Prop

Whether imprecise readings are available for a numeral.

Equations

• One or more equations did not get rendered due to their size.

instance Phenomena.Imprecision.Studies.BeltramaSchwarz2024.instDecidableImpreciseReadingAvailable (n : ℕ) : Decidable (impreciseReadingAvailable n)

Equations

• One or more equations did not get rendered due to their size.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.roundness_gates_persona : impreciseReadingAvailable exampleStatedAmount ∧ ¬impreciseReadingAvailable exampleImpreciseAmount

Roundness gates persona effects: $200 supports imprecision, $193 does not.

theorem Phenomena.Imprecision.Studies.BeltramaSchwarz2024.div10_enables_imprecision (n : ℕ) (h10 : n % 10 = 0) : impreciseReadingAvailable n

Multiples of 10 always have imprecise readings.