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Anything pointy can be considered a "dagger" according to California law. Since basically every citizen owns, uses, and often carries something pointy, this makes the entire population criminals subject to arrest at the whim of the police. Good luck with that.
If carried "concealed upon his or her person," yes it could, subject to officer and prosecutorial discretion of course.Icepicks are included in that. A sharpened stick would be included in that.