Proof Path Theory: Proof fields and certificates

Part I Proof fields and certificates

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A completed proof occupies only part of its surrounding field. Keep the successful deduction, but do not confuse its unused alternatives with either errors in that deduction or proofs of impossibility.

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Figure 2. A declared proof field retains three different statuses. The solid route certifies the target. The upper branch has an unresolved obligation. The lower branch has a scoped refutation. Neither the open branch nor the refuted step invalidates the certified route.

The governing distinction

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A proof field preserves more than a proof needs. Its failed and unresolved records remain available to inquiry without acquiring the force of certified deductions.

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Source and conversion record

Source SHA-256: ce05e88b439e9fd55ef6eb04da708a63ce02e6627424e6daac0dca4177b8ab51

Unsupported prose commands stop the build. The mathematical expression sequence is checked against the source, with manuscript macros expanded for display.

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Part I Proof fields and certificates

The governing distinction