Foundation Seam Bridge Bridge Coverage Tag

The coverage ledger

CoverageTag is a three-state classification used by the framework's internal audit system. The three states are transported, posited, and unclassified. Transported means a module's theorems follow from a derivation bridge rooted in distinction, the framework's basic notion of difference. Posited means the module rests on a named extra commitment beyond distinction. Unclassified means the module has not yet been classified, a state the framework's standing commitment forbids at completion.

The tag belongs to the framework's ledger, a discrete record of recognition events that the framework uses to track what has been derived and what has been assumed. The tag itself is a simple inductive type with three constructors. The posited constructor carries a string, the name of the extra commitment. This makes the classification honest: a module cannot quietly rely on an unnamed assumption. The name must be stated in the code itself.

In Recognition Science, the tag works with a derivation bridge, a map from a delta-side carrier to a theory carrier that preserves a source operation into a genuine theory operation. The framework proves that such a bridge transports every iterate of the delta-side operation to the matching iterate of the theory operation. A fixed point of the delta-side operation maps to a fixed point of the theory operation. These are machine-checked theorems in the framework's library of formal theorems.

The tag does not claim that any particular module is transported or posited. It does not prove that a bridge exists for any given theory. It does not say what the extra commitments are, only that they must be named. The tag is a bookkeeping device, not a derivation. Its purpose is to make the ledger honest, so that a reader can see at a glance which results are derived from distinction and which rest on additional assumptions.

What this changes for a reader: the tag turns the framework's coverage into a visible contract. A module labeled transported carries a promise that its theorems follow from the delta-rooted bridge. A module labeled posited carries a named debt. The unclassified state is a red flag that the standing commitment forbids at completion. The tag gives the framework a way to say, in code, exactly where each result comes from.

/-- The honest per-module classification used by the coverage ledger.
`transported` means the module's theorems follow from a derivation bridge rooted
in distinction; `posited name` means the module rests on the named extra
commitment beyond delta; `unclassified` is the only state the standing commitment
forbids at completion. -/
inductive CoverageTag where
  /-- Theorems follow from a delta-rooted bridge. -/
  | transported
  /-- Rests on a named extra commitment beyond distinction. -/
  | posited (name : String)
  /-- Not yet classified (forbidden at completion). -/
  | unclassified
  deriving DecidableEq, Repr

/-- The honest per-module classification used by the coverage ledger.
`transported` means the module's theorems follow from a derivation bridge rooted
in distinction; `posited name` means the module rests on the named extra
commitment beyond delta; `unclassified` is the only state the standing commitment
forbids at completion. -/
inductive CoverageTag where
  /-- Theorems follow from a delta-rooted bridge. -/
  | transported
  /-- Rests on a named extra commitment beyond distinction. -/
  | posited (name : String)
  /-- Not yet classified (forbidden at completion). -/
  | unclassified
  deriving DecidableEq, Repr

/-- The honest per-module classification used by the coverage ledger.
`transported` means the module's theorems follow from a derivation bridge rooted
in distinction; `posited name` means the module rests on the named extra
commitment beyond delta; `unclassified` is the only state the standing commitment
forbids at completion. -/
inductive CoverageTag where
  /-- Theorems follow from a delta-rooted bridge. -/
  | transported
  /-- Rests on a named extra commitment beyond distinction. -/
  | posited (name : String)
  /-- Not yet classified (forbidden at completion). -/
  | unclassified
  deriving DecidableEq, Repr

/-- The transport core. A derivation bridge carries every iterate of the
delta-side operation to the matching iterate of the theory operation. Any theorem
of the theory phrased about iterated dynamics therefore transports to a statement
about the delta-rooted object: it suffices to read the theory's `tgtOp^[n]`
behaviour off the delta side's `srcOp^[n]`. -/
theorem transport_iterate (s : Src) :
    ∀ n : ℕ, B.carrier (B.srcOp^[n] s) = B.tgtOp^[n] (B.carrier s) := by
  intro n
  induction n generalizing s with
  | zero => simp
  | succ k ih =>
    rw [Function.iterate_succ_apply, Function.iterate_succ_apply, ih (B.srcOp s),
        B.preserves s]

/-- Corollary: a fixed point of the delta-side operation maps to a fixed point of
the theory operation. (A representative transported theorem: any "stationary
state" result of the theory holds for the delta image of a delta-side fixed
point.) -/
theorem transport_fixedPoint (s : Src) (hs : B.srcOp s = s) :
    B.tgtOp (B.carrier s) = B.carrier s := by
  have := B.preserves s
  rw [hs] at this
  exact this.symm

What this page does not claim

No claim that any particular module is transported or posited. No claim that a derivation bridge exists for any given theory. No claim about what the extra commitments are beyond the requirement that they be named.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Foundation/SeamBridge/Bridge.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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