docs: use Proof as the product name, not The Proof

[tonyketcham]

Summary of changes

Proof is the product name. A leading "The" is not part of the brand. This drop it from user-facing copy that treated the product as "The Proof".

• README and positioning: sentences now start with Proof, not "The Proof"
• Packaged Proof skills (and the generated .agents/ copies): same fix, plus "in Proof" instead of "in the Proof"
• Bootstrap CLI: journal ignore message is now "The write journal for Proof at …"
• Explorer empty state no longer says "the Proof content root"
• Related article errors: "an Proof" → "a Proof" in explorer package copy

Phrases such as "the Proof skill" stay. There the article belongs to the noun after Proof.

Please don't delete this checklist! Before submitting the PR, please make sure you do the following:

• I added doc comments to any new public exports, and inline comments to any hard-to-understand areas
• My changes generate no new console errors locally
• If applicable, try to include a test that fails without this PR but passes with it

Does this introduce any non-backwards compatible changes?

• Yes
• No

The bootstrap journal-ignore string changed. That is operator-facing copy, not a config or API break.

Does this include any user config changes?

• Yes
• No

  

[cursor]

Approved. Cursor Bugbot passed and left no findings that need human review. No reviewers assigned.

  

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