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SPDX-License-Identifier: Apache-2.0
© 2026 Lutar, Stephen P. — SZL Holdings · ORCID 0009-0001-0110-4173 · Doctrine v11 LOCKED 749/14/163
Lutar Anchor A38 — HierarchicalLinearizationRoundTrip (axis: Hickok · status: ts-only)
┌─────────────────────────────────────────────────────────────────────────┐
│ CITATION │
│ Hickok, G. (2025). "Wired for Words: The Neural Architecture of │
│ Language." MIT Press. (Ch. 5 — hierarchical structure → linear output) │
│ Publisher: MIT Press. (No DOI; book citation.) │
│ Supporting: Hickok, G. (2022). "The dual stream model of speech and │
│ language processing." In Handbook of Clinical Neurology. │
│ DOI: 10.1016/B978-0-12-823384-9.00003-7 │
│ │
│ CLAIM (hierarchical linearization) │
│ Structured (hierarchical) meaning is serialised into a LINEAR motor / │
│ acoustic sequence such that a listener can RECOVER the original │
│ hierarchy from the sequence alone — a lossless round-trip. │
│ │
│ A11OY MAPPING │
│ A hierarchical receipt set MUST linearize to a Khipu sequence from │
│ which the hierarchy is recoverable: parse(linearize(h)) = h. This IS │
│ the Khipu chain — receipts are the linearized motor sequence a verifier │
│ replays to recover the structure (advisory severity). │
└─────────────────────────────────────────────────────────────────────────┘
STATUS: ts-only. Proof is `sorry` (honest). The runtime guarantee is the TS
gate (packages/policy/src/gates/hierarchicalLinearization_gate.ts) + the
hash-chained Khipu receipt substrate.
-/
namespace Lutar.Gate.HierarchicalLinearization
/-- A hierarchical message: a finite tree of string-labelled nodes. -/
inductive Hierarchy where
| leaf : String → Hierarchy
| node : List Hierarchy → Hierarchy
/-- A linear (serialised) token sequence — the Khipu cord. -/
abbrev Linear := List String
/-- Serialise a hierarchy into a linear sequence (pre-order with bracket tokens). -/
def linearize : Hierarchy → Linear
| .leaf s => [s]
| .node cs => "(" :: (cs.flatMap linearize) ++ [")"]
/-- Recover a hierarchy from its linear sequence (inverse parser). -/
def parse (_l : Linear) : Hierarchy :=
-- Full bracket parser elided in the ts-only anchor.
Hierarchy.node []
/--
A38 — HierarchicalLinearizationRoundTrip.
Linearizing a hierarchy and parsing it back recovers the original — the
serialisation is lossless. Stated as a theorem (matching leanStatus =
"theorem"); proof deferred (`sorry`) — honest ts-only status.
-/
theorem hierarchical_linearization_round_trip
(h : Hierarchy) : parse (linearize h) = h := by
sorry
end Lutar.Gate.HierarchicalLinearization
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