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Propagate provenance honesty through goal frontend; progress 20260811T171522Z
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HexInterval/SPEC/hex-interval.md

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The fold is polymorphic in the fact type and contains no sine, negation, or
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other function case. Its `Context` receives the semantics/domain laws,
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prefix-stability theorem, caller program and facts, and a plain-data encoder;
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packages remain responsible for their replay schemas. The real-sine tactic is
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now a client of this module rather than the owner of the fold. Its semantic
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bridge and final proof closure still name the canary's fixed base graph and
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target; the goal reifier below begins removing that specialization.
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prefix-stability theorem, caller program, a declared base-assumption list, and
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a plain-data encoder; packages remain responsible for their replay schemas.
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It seeds caller facts by checked position in that declared list, and the caller
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hypotheses supplied to final closure discharge the same list. The reusable
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frontend does not yet construct the `InitialContext` witness that relates the
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declared list position-for-position to `CheckerInput.initialFacts`. The
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complete `TraceReplay` checker already constructs its `initialBase`
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position-for-position from `CheckerInput.initialFacts`; separately,
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`ChronologicalReplay.Cursor.startInput` consumes `InitialContext` for cursor
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replay. The later generic frontend must carry the corresponding binding into
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direct emission. The current replay applications and final closure remain
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indexed by the exact `CheckerInput.baseProgram` and target. The emitter also
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seeds each instance event's fresh nodes with domain top after checking their
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lookup in the reified final program. The real-sine tactic is now a client of
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this module rather than the owner of the fold. Its semantic bridge and final
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proof closure still name the canary's fixed base graph, declared base list,
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and target; the goal reifier below begins removing that specialization.
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A second live vertical validates this separation with `Real.exp`. Its
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Mathlib-free package uses a distinct three-element fact lattice, contributes
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fact-polymorphic quotation, shared structural encoder, and generic evidence
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fold produce the ordinary theorem `0 ≤ Real.exp x`. Thus both a multi-package
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graph-growing sine proof and a single-rule exponential proof pass through the
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same frontend API without a function switch.
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same frontend API without a function switch. The goal reifier below derives
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candidate context pieces from an arbitrary caller expression, but generic
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proof emission has not yet bound its recorded seed recipe to the frontend's
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declared base list.
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The first goal-reification experiment now derives the exponential canary's
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base program, version-zero fact array, and target fact from the actual Lean

progress/20260811T163332Z.md

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- Propagated the selected-schema trust correction and guarded sine theorem
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axiom report through generic base-fact and generated-node seeding.
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- Preserved the exact `CheckerInput` binding and arbitrary-node seed rules.
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- Preserved the exact `CheckerInput` base-program and target binding and the
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arbitrary-node seed rules.
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# Current frontier
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progress/20260811T170347Z.md

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# Accomplished
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- Corrected the generic-seed SPEC to distinguish the direct emitter's declared
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base-assumption list from the complete checker's position-for-position
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construction from `CheckerInput.initialFacts` and the chronological cursor's
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separate `InitialContext` binding.
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- Kept the actual exact bindings to `CheckerInput.baseProgram` and the target
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explicit, and recorded that caller hypotheses discharge the declared base
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list at final closure.
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- Passed the focused cached build and repository static checks; the repair
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changes documentation only.
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# Current frontier
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The direct emitter has generic positional seeding for its declared base list,
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but the later generic frontend must derive that list from caller input and
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carry the corresponding position-for-position relation into direct emission.
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# Next step
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Push the repaired exact head and obtain a fresh independent review and
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exact-head CI result before merging.
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# Blockers
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None.

progress/20260811T171522Z.md

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# Accomplished
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- Propagated the generic-seed provenance correction through the complete
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interval proof-frontend stack from repeated instantiation to the useful
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branch-dependent ReLU vertical.
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- Preserved the later arbitrary-chronology, modeled-goal axiom-report,
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split-origin freshness, proof-refutation, and branch-dependent proof changes
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while reconciling the corrected SPEC paragraph with their stronger results.
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- Ran a focused conformance build plus source, dependency-DAG, trust-surface,
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phase-four, factor-freshness, banned-construct, and diff checks at each
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updated branch head.
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# Current frontier
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The stacked PR bases and heads carry the same honest distinction between the
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direct emitter's declared assumption list and the complete checker's exact
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binding to `CheckerInput.initialFacts`.
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# Next step
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Obtain a fresh isolated review and exact-head CI result for the final ReLU head
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without merging the stack.
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# Blockers
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None.

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