conductor(deob_apply): platonic_intelligence_kumar decoder (43 terms tier-categorized, per pilot process improvement #2)

conductor/tracks/video_analysis_deob_apply_20260621/artifacts/platonic_intelligence_kumar/platonic_intelligence_kumar_decoder.md

@@ -0,0 +1,537 @@
+# platonic_intelligence_kumar — Per-Term Decoder (Tier-Categorized)
+
+**Source:** `conductor/tracks/video_analysis_platonic_intelligence_kumar_20260621/report.md` (1563 LOC)
+**Output:** This file is the **per-term decoder** for every term in the platonic_intelligence_kumar Pass 1 report that required de-obfuscation.
+**Method:** Per `lexicon.md` §2 (the 4 tiers) + §3 (the 6 noise-dedup maps) + §5 (form-anchor rule) + §6 (etymology rule).
+**Pilot process improvement #2 applied:** categorized by tier (Tier 1: Core concepts, Tier 2: Data-oriented pipeline, Tier 3: Type-theoretic primitives, Tier 4: AI-fuzzing tolerance) instead of by math section.
+**Date:** 2026-06-23
+
+> **Reading guide.** This is the **per-term decoder** for the platonic_intelligence_kumar Pass 1 report. Each entry has:
+> - **Original notation:** the Pass 1 form
+> - **Re-encoded:** the principled re-encoded form (per `lexicon.md` §2)
+> - **Form anchor:** the bounded form + projection (per Rule 2)
+> - **Etymology (1-line):** the origin
+> - **Definition history (1-line):** the first formalization
+> - **Source sections in original:** the Pass 1 §X.Y references
+>
+> **For the side-by-side table:** see `platonic_intelligence_kumar_translation.md` (36 rows).
+> **For the re-encoded report:** see `platonic_intelligence_kumar_deobfuscated.md`.
+
+---
+
+## Tier 1: Core concepts (foundational type-theoretic primitives)
+
+These are the principled type-theoretic primitives that appear in the de-obfuscation. Each maps to a Tier 1 entry in `lexicon.md` §2.1.
+
+### Term: forall (universal quantifier)
+
+- **Original notation:** `∀g ∈ G`, `∀x ∈ X`, `∀i`, `∀s ∈ S`, `∀σ ∈ A`, etc.
+- **Re-encoded:** `forall x : T, P(x) : Prop` (Tier 1 #1.2)
+- **Form anchor:** `forall x : T` (bounded form, universal over type T) → `P(x) : Prop` (projection)
+- **Etymology (1-line):** Latin *pro omnibus* ("for all")
+- **Definition history (1-line):** First formalized in modern logic by Frege 1879 (*Begriffsschrift*)
+- **Source sections in original:** §5.1, §5.2, §5.3, §5.6, §5.7, §5.8, §5.9, §5.12, App. C.1, C.6, C.8
+- **Used in de-obfuscation rows:** 1, 2, 3 (G-equivariance), 9 (inductive bias), 12 (activation → pattern), 15 (canalization), 16 (Waddington biological), 17 (UFR factorization), 19 (FER perturbation), 20 (dense Jacobian), 21 (basin), 25 (similarity), 26 (PRH convergence), 27 (single-weight ablation), 29 (causal intervention)
+
+### Term: exists (existential quantifier)
+
+- **Original notation:** `∃i`, `∃j ≠ i`, `∃ L`, `∃ δ`, `∃ α > 0`, etc.
+- **Re-encoded:** `exists x : T, P(x) : Prop` (Tier 1 #1.3)
+- **Form anchor:** `exists x : T` (bounded form, existential over type T) → `P(x) : Prop` (projection)
+- **Etymology (1-line):** Latin *existere* ("to stand out, to be")
+- **Definition history (1-line):** First formalized in modern logic by Frege 1879
+- **Source sections in original:** §5.7, §5.8, §5.12, App. C.6
+- **Used in de-obfuscation rows:** 17 (UFR factorization, ∃σ permutation), 19 (FER perturbation, ∃j ≠ i), 20 (dense Jacobian, ∃j ≠ i), 29 (causal intervention)
+
+### Term: and (logical conjunction)
+
+- **Original notation:** Used implicitly throughout (e.g., "and" in "a function f: X → Y is equivariant under G if ..., and ...").
+- **Re-encoded:** `P and Q : Prop` (Tier 1 #1.4)
+- **Form anchor:** `P and Q` (bounded form) → `Prop` (projection)
+- **Etymology (1-line):** Old English *and*
+- **Definition history (1-line):** Standard logical connective; formalized in modern logic by Boole 1847 (*The Mathematical Analysis of Logic*)
+- **Source sections in original:** §5.1, §5.7, §5.12 (where multiple conditions must hold)
+- **Used in de-obfuscation rows:** implicit in every row with multiple forall clauses
+
+### Term: or (logical disjunction)
+
+- **Original notation:** Used implicitly in `piecewise(matches, magnitude_heuristic, digit_combination)` (§5.10)
+- **Re-encoded:** `P or Q : Prop` (Tier 1 #1.5)
+- **Form anchor:** `P or Q` (bounded form) → `Prop` (projection)
+- **Etymology (1-line):** Old English *or*
+- **Definition history (1-line):** Standard logical connective
+- **Source sections in original:** §5.10 (piecewise function)
+- **Used in de-obfuscation rows:** 23 (piecewise function)
+
+### Term: not (logical negation)
+
+- **Original notation:** `≠ 0`, `≠ i`, `not in [0,1]`
+- **Re-encoded:** `not P : Prop` (Tier 1 #1.6)
+- **Form anchor:** `not P` (bounded form) → `Prop` (projection)
+- **Etymology (1-line):** Latin *non*
+- **Definition history (1-line):** Standard logical connective
+- **Source sections in original:** §5.7, §5.8, §5.11, §5.12
+- **Used in de-obfuscation rows:** 17 (j ≠ σ(i)), 19 (j ≠ i), 20 (j ≠ i), 25 (not in [0,1] check)
+
+### Term: implies (logical implication)
+
+- **Original notation:** Used implicitly in "if f is equivariant under G, then f(g·x) = g·f(x)"
+- **Re-encoded:** `P implies Q : Prop` (Tier 1 #1.7)
+- **Form anchor:** `P implies Q` (bounded form) → `Prop` (projection)
+- **Etymology (1-line):** Latin *implicare* ("to involve")
+- **Definition history (1-line):** Standard logical connective
+- **Source sections in original:** §5.1 (equivariance definition), §5.11 (PRH)
+- **Used in de-obfuscation rows:** 1, 2 (implications in the definitions)
+
+### Term: in (type ascription / set membership)
+
+- **Original notation:** `g ∈ G`, `x ∈ X`, `(x, y) ∈ [-1, 1]²`, `n ∈ ℝ⁺`
+- **Re-encoded:** `x : T` (Tier 1 #1.8 — re-encoded form for `x ∈ T`)
+- **Form anchor:** `x : T` (bounded form, type ascription) → `T` (projection)
+- **Etymology (1-line):** Latin *in*
+- **Definition history (1-line):** Russell/Whitehead 1910 (*Principia Mathematica*); modern constructive usage per Martin-Löf
+- **Source sections in original:** §5.1, §5.2, §5.4, §5.6, §5.7, App. C.3
+- **Used in de-obfuscation rows:** 1, 2, 3, 10, 17, 19, 20, 25, 26 (type ascriptions throughout)
+
+### Term: Bottom (empty type)
+
+- **Original notation:** Not used directly, but the "infeasible" basin of attraction in §5.3 could be re-encoded as `Bottom` (Tier 1 #1.10)
+- **Re-encoded:** `Bottom : type` (Tier 1 #1.10)
+- **Form anchor:** `Bottom` (bounded form) → `Type` (projection)
+- **Etymology (1-line):** Greek *βύσμα* via *boussomai* ("to stop up")
+- **Definition history (1-line):** First formalized in type theory by Per Martin-Löf 1972
+- **Source sections in original:** Not directly used (no zero-measure empty set claim)
+- **Used in de-obfuscation rows:** not used; reserved for future use
+
+### Term: concept (Notion, user-also-accepted)
+
+- **Original notation:** "Regularity," "pattern," "factor," "axis" — used informally throughout
+- **Re-encoded:** `concept : concept` (Tier 1 #1.11, user-also-accepted)
+- **Form anchor:** `concept` (bounded form) → `Type` (projection)
+- **Etymology (1-line):** Greek *ἔννοια* ("having in mind"); user's preferred form
+- **Definition history (1-line):** Per Cluster 7, `Notiones.txt`; the user's working definition of Type = "successful act of association"
+- **Source sections in original:** §2.1, §2.2, §2.4, §2.9, §2.14, §2.20 (all the conceptual claims)
+- **Used in de-obfuscation rows:** 1, 2, 3, 4, 17 (semantic_axis), 19, 20, 27, 28, 29
+
+---
+
+## Tier 2: Data-oriented pipeline (procedural/data-oriented primitives)
+
+These are the procedural primitives that appear in the de-obfuscation. Each maps to a Tier 2 entry in `lexicon.md` §2.2.
+
+### Term: procedure (function-as-procedure per Concatenative Map 3)
+
+- **Original notation:** `f: X → Y`, `f(x, y)`, `f(w)`, `image_coord`, `mutate(...)`, `user_select(...)`, `lookup_table(...)`, `magnitude_heuristic(...)`
+- **Re-encoded:** `procedure f (x : X) -> Y : body` (Tier 2 #2.1)
+- **Form anchor:** `procedure` (bounded form, procedure type) → `(arg) -> result` (projection)
+- **Etymology (1-line):** Latin *procedere* ("to proceed"); concatenative tradition
+- **Definition history (1-line):** Forth/colorForth/KYRA/CoSy tradition; Per Martin-Löf's typed lambda calculus
+- **Source sections in original:** §5.1, §5.2, §5.4, §5.5, §5.6, §5.9, §5.10, §5.11, §5.12, App. C.1, C.3, C.8
+- **Used in de-obfuscation rows:** all rows that define a procedure (5, 6, 7, 10, 14, 23, 24, 25, 27, 28, 29)
+
+### Term: argument (parameter)
+
+- **Original notation:** `(x, y)`, `theta`, `batch`, `eta_t`, `delta`, `i`, `a, b`, `(x, y) ∈ [-1, 1]²`
+- **Re-encoded:** `arg : T` (Tier 2 #2.2)
+- **Form anchor:** `arg` (bounded form, parameter type) → `T` (projection)
+- **Etymology (1-line):** Latin *argumentum* ("proof, evidence")
+- **Definition history (1-line):** Type-theoretic tradition; Curry-Howard correspondence
+- **Source sections in original:** §5.1, §5.2, §5.4, §5.5, §5.6, §5.7, §5.8, §5.10, §5.11, §5.12
+- **Used in de-obfuscation rows:** 1, 2, 5, 6, 7, 10, 14, 15, 17, 23, 24, 25, 27, 28, 29
+
+### Term: result (return value)
+
+- **Original notation:** Used implicitly throughout (the type after `->`)
+- **Re-encoded:** `result : T` (Tier 2 #2.3)
+- **Form anchor:** `result` (bounded form, return type) → `T` (projection)
+- **Etymology (1-line):** Latin *resultare* ("to spring back")
+- **Definition history (1-line):** Standard programming language usage
+- **Source sections in original:** every procedure definition
+- **Used in de-obfuscation rows:** every procedure
+
+### Term: formation (type formation)
+
+- **Original notation:** `Group`, `TranslationGroup`, `SymmetricGroup`, `Parameters`, `Population<CPPN>`, `Distribution`, `Vector`, `Matrix`, `Scalar`
+- **Re-encoded:** `formation T : kind` (Tier 2 #2.4 + Tier 3 #3.8)
+- **Form anchor:** `formation` (bounded form, type formation) → `T : kind` (projection)
+- **Etymology (1-line):** Latin *formatio* ("a forming")
+- **Definition history (1-line):** Per Martin-Löf 1972 (constructive type theory formation rule)
+- **Source sections in original:** §5.1, §5.2, §5.4, §5.5, App. C.3
+- **Used in de-obfuscation rows:** 3 (TranslationGroup formation), 4 (SymmetricGroup formation), 5 (DataDistribution), 7 (Parameters), 11 (ActivationAlphabet), 13 (Picbreeder kind), 14 (Population<CPPN>), 23 (Sum<LookupTable, MagnitudeHeuristic, DigitCombination>)
+
+### Term: arg (input abbreviation)
+
+- **Original notation:** Used in shorthand where the type ascription already conveys the meaning
+- **Re-encoded:** `arg : T` (Tier 2 #2.5)
+- **Form anchor:** `arg` (bounded form, input abbreviation) → `T` (projection)
+- **Etymology (1-line):** English (abbreviation)
+- **Definition history (1-line):** Standard programming abbreviation
+- **Source sections in original:** §5.4, §5.10, §5.12
+- **Used in de-obfuscation rows:** 14 (render), 23 (a, b), 25 (A, B)
+
+### Term: relation (equation / inequality)
+
+- **Original notation:** `=`, `<`, `>`, `≤`, `≥`, `≈`, `|x|`, `x²`, `δ·ε`, `x − x`
+- **Re-encoded:** `relation R : (T, T) -> Prop` (Tier 2 #2.6)
+- **Form anchor:** `relation` (bounded form, relation type) → `(T, T) -> Prop` (projection)
+- **Etymology (1-line):** Latin *relatio* ("a carrying back")
+- **Definition history (1-line):** Standard mathematical usage
+- **Source sections in original:** §5.1, §5.2, §5.6, §5.7, §5.8, §5.11
+- **Used in de-obfuscation rows:** 1, 2 (equality), 15 (|<|, <), 17 (=), 19 (|.| > 0), 25 (∈ [0,1])
+
+### Term: property (mathematical property / predicate)
+
+- **Original notation:** `Prop`, predicate symbols like `is_FER`, `is_UFR`, `is_canalyzed`, `is_a_satisfies`, `is_basal_G`
+- **Re-encoded:** `property : T -> Prop` (Tier 2 #2.7)
+- **Form anchor:** `property` (bounded form, predicate type) → `T -> Prop` (projection)
+- **Etymology (1-line):** Latin *proprietas* ("a peculiarity")
+- **Definition history (1-line):** Standard type-theoretic usage
+- **Source sections in original:** §5.1, §5.3, §5.6, §5.7, §5.8, §5.9, §5.11, §5.12
+- **Used in de-obfuscation rows:** 1, 2, 8, 9, 12, 15, 16, 17, 18, 20, 21, 22, 25, 27, 28, 29
+
+### Term: construction (proof-as-program per Curry-Howard Map 1)
+
+- **Original notation:** "Proof" of a property, the existence of a UFR
+- **Re-encoded:** `construction : T : Prop` (Tier 2 #2.9)
+- **Form anchor:** `construction` (bounded form, proof/program) → `T : Prop` (projection)
+- **Etymology (1-line):** Latin *constructio* ("a building")
+- **Definition history (1-line):** Curry-Howard correspondence (1969); constructive type theory
+- **Source sections in original:** §5.3 (existence of UFR), §5.9 (basin argument), §5.12 (proving UFR vs FER)
+- **Used in de-obfuscation rows:** implicit in every row that asserts a Prop
+
+### Term: instance (witness / example)
+
+- **Original notation:** "Example," "instance of a CPPN," "instance of UFR"
+- **Re-encoded:** `instance : T` (Tier 2 #2.10)
+- **Form anchor:** `instance` (bounded form, value of a type) → `T` (projection)
+- **Etymology (1-line):** Latin *instantia* ("presence")
+- **Definition history (1-line):** Standard type-theoretic usage
+- **Source sections in original:** §5.7 (Picbreeder skull instance), §5.8 (SGD skull instance), §5.10 (Claude arithmetic instance)
+- **Used in de-obfuscation rows:** 17 (cppn : CPPN), 19 (sgd_mlp : MLP), 23 (claude_arithmetic)
+
+### Term: attribute (user-also-accepted — extrinsic property)
+
+- **Original notation:** "External property," "annotation"
+- **Re-encoded:** `attribute : T -> Prop` (Tier 2 #2.11, user-also-accepted)
+- **Form anchor:** `attribute` (bounded form, extrinsic property) → `T -> Prop` (projection)
+- **Etymology (1-line):** Latin *attributus* ("assigned to")
+- **Definition history (1-line):** Per Cluster 7, `Notiones.txt`; the 4 elements (Notion/Attribute/Property/Type)
+- **Source sections in original:** §2.4 (architectural inductive bias — extrinsic), §5.11 (representation similarity — extrinsic metric)
+- **Used in de-obfuscation rows:** 9 (ArchitecturalInductiveBias), 25 (SimilarityMetric)
+
+### Term: kind (Type/Genus, user-also-accepted)
+
+- **Original notation:** `Group`, `TranslationGroup`, `SymmetricGroup`, `Parameters`, `Distribution`, `Vector`, `Matrix`, `CPPN`
+- **Re-encoded:** `kind T` (Tier 2 #2.13, user-also-accepted; same as Tier 3 #3.1 principled)
+- **Form anchor:** `kind` (bounded form, meta-type) → `T` (projection)
+- **Etymology (1-line):** Old English *cynd*; Greek *γένος*; Latin *genus*; Sanskrit *जनस्*
+- **Definition history (1-line):** Per Cluster 7, `Notiones.txt`; the user's preferred term for the meta-type
+- **Source sections in original:** §5.1, §5.2, §5.4, §5.5, App. C.3
+- **Used in de-obfuscation rows:** 3, 4, 5, 7, 11, 13, 14
+
+---
+
+## Tier 3: Type-theoretic primitives (constructive type theory operators)
+
+These are the constructive type theory operators that appear in the de-obfuscation. Each maps to a Tier 3 entry in `lexicon.md` §2.3.
+
+### Term: kind (Type, the meta-type)
+
+- **Original notation:** `Group`, `kind`, `Group`, `Population<CPPN>`
+- **Re-encoded:** `kind T` (Tier 3 #3.1)
+- **Form anchor:** `kind` (bounded form) → `Kind` (projection)
+- **Etymology (1-line):** Old English *cynd* (also Tier 1 #1.1 + Tier 2 #2.13)
+- **Definition history (1-line):** Per Martin-Löf 1972; type-theoretic tradition
+- **Source sections in original:** §5.1, §5.2, §5.4, §5.5
+- **Used in de-obfuscation rows:** 3, 4, 7, 11, 13, 14 (kind formations)
+
+### Term: Kind (Type of types)
+
+- **Original notation:** Not used directly; the `Group`, `Parameters`, etc. are kinds, but no explicit `Kind` meta-type is used
+- **Re-encoded:** `Kind` (Tier 3 #3.2)
+- **Form anchor:** `Kind` (bounded form) → `Type` (projection)
+- **Etymology (1-line):** Old English *cynd* + meta
+- **Definition history (1-line):** Per Martin-Löf 1972; type-theoretic tradition
+- **Source sections in original:** Not used directly
+- **Used in de-obfuscation rows:** implicit in kind formations
+
+### Term: intro / construct (constructor)
+
+- **Original notation:** `Zero | Succ(Nat)`, `LookupTable | MagnitudeHeuristic | DigitCombination`, `Sin | Cos | Gaussian | Sigmoid | Abs | Linear`
+- **Re-encoded:** `intro` / `construct` (Tier 3 #3.3)
+- **Form anchor:** `intro` (bounded form, value constructor) → `T -> T` (projection)
+- **Etymology (1-line):** Latin *introductio* ("a leading in")
+- **Definition history (1-line):** Per Martin-Löf 1972; introduction rule of type theory
+- **Source sections in original:** §5.4 (activation alphabet), §5.10 (piecewise function cases)
+- **Used in de-obfuscation rows:** 11 (Sum<Sin, Cos, ...>), 23 (piecewise with LookupTable, MagnitudeHeuristic, DigitCombination)
+
+### Term: elim / eliminate (eliminator)
+
+- **Original notation:** Not used directly; the de-obfuscation uses apply + match instead of explicit elim
+- **Re-encoded:** `elim` / `eliminate` (Tier 3 #3.4)
+- **Form anchor:** `elim` (bounded form, type eliminator) → `(T, C) -> C` (projection)
+- **Etymology (1-line):** Latin *eliminatio* ("a driving out")
+- **Definition history (1-line):** Per Martin-Löf 1972; elimination rule of type theory
+- **Source sections in original:** not directly used (could apply to `Sum<>` cases)
+- **Used in de-obfuscation rows:** implicit in piecewise (row 23)
+
+### Term: comp (computation rule, value-level)
+
+- **Original notation:** Implicit in `sgn`, `nearest_multiple_of_10`, `matmul`, `apply`
+- **Re-encoded:** `comp` (Tier 3 #3.5)
+- **Form anchor:** `comp` (bounded form, β-reduction) → `β-reduction` (projection)
+- **Etymology (1-line):** Latin *computatio* ("a reckoning")
+- **Definition history (1-line):** Per Martin-Löf 1972; computation rule of type theory
+- **Source sections in original:** implicit in every procedure body
+- **Used in de-obfuscation rows:** implicit in every procedure
+
+### Term: getType (type-level computation)
+
+- **Original notation:** Not used directly; the de-obfuscation uses type ascriptions instead of explicit getType
+- **Re-encoded:** `getType(...) === T` (Tier 3 #3.6)
+- **Form anchor:** `getType` (bounded form, type check) → `type check` (projection)
+- **Etymology (1-line):** User coinage (per Cluster 3, Pattern 4)
+- **Definition history (1-line):** User-specific; per Cluster 3
+- **Source sections in original:** not used
+- **Used in de-obfuscation rows:** not used; reserved for future formalization
+
+### Term: uniq (uniqueness rule)
+
+- **Original notation:** Not used directly
+- **Re-encoded:** `uniq` (Tier 3 #3.7)
+- **Form anchor:** `uniq` (bounded form, canonical form) → `canonical form` (projection)
+- **Etymology (1-line):** Latin *unicitas* ("oneness")
+- **Definition history (1-line):** Per Martin-Löf 1972; uniqueness rule
+- **Source sections in original:** not used
+- **Used in de-obfuscation rows:** not used; reserved for future formalization
+
+### Term: Pair<A, B> (Sigma type / product type)
+
+- **Original notation:** `(x, y)`, `Pair<x, y>`, `(a, b)`, `(W, b)`, `[x, y]`, `(A, B)`
+- **Re-encoded:** `Pair<A, B> = (A, B)` with `Build<A>`, `Build<B>` projections (Tier 3 #3.12)
+- **Form anchor:** `Pair<A, B>` (bounded form, product type) → `(A, B)` (projection)
+- **Etymology (1-line):** Latin *par* ("equal")
+- **Definition history (1-line):** Per Martin-Löf 1972; sigma type
+- **Source sections in original:** §5.1 (Pair<float64, float64> for translation group), §5.4 ([x, y] for image coord), §5.10 ((a, b) for addends)
+- **Used in de-obfuscation rows:** 3 (Pair<quantity, quantity>), 10 (Pair<float64, float64>), 23 ((a, b))
+
+### Term: Dependent<x : A>(B) (Pi type / dependent function)
+
+- **Original notation:** Not used directly; could re-encode "for each weight index i, a procedure that depends on i"
+- **Re-encoded:** `Dependent<x : A>(B)` (Tier 3 #3.14)
+- **Form anchor:** `Dependent<x : A>(B)` (bounded form, Pi type) → `forall x : A, B(x)` (projection)
+- **Etymology (1-line):** User coinage (per Cluster 3, Phase 1)
+- **Definition history (1-line):** Per Martin-Löf 1972 (dependent function type); Cluster 3 Phase 1
+- **Source sections in original:** implicit in `forall i, ...` patterns
+- **Used in de-obfuscation rows:** implicit in rows 17, 19, 20
+
+### Term: lambda.x.M (lambda abstraction)
+
+- **Original notation:** Not used directly; could re-encode `procedures` more formally as `lambda x. body`
+- **Re-encoded:** `lambda.x.M` (Tier 3 #3.15)
+- **Form anchor:** `lambda.x.M` (bounded form, function abstraction) → `M` (projection)
+- **Etymology (1-line):** Greek letter *λ* (Church's notation)
+- **Definition history (1-line):** Church 1932 (*A Set of Postulates for the Foundation of Logic*)
+- **Source sections in original:** implicit in every procedure
+- **Used in de-obfuscation rows:** implicit in every procedure
+
+### Term: Sum (Disjoint Sum, A + B)
+
+- **Original notation:** `Sum<Sin, Cos, Gaussian, Sigmoid, Abs, Linear, ...>`, `piecewise(matches, magnitude_heuristic, digit_combination)`
+- **Re-encoded:** `A + B` with `inl`/`inr` injections (Tier 3 #3.17)
+- **Form anchor:** `A + B` (bounded form, sum type) → sum type (projection)
+- **Etymology (1-line):** Latin *summa*
+- **Definition history (1-line):** Per Martin-Löf 1972; disjoint sum type
+- **Source sections in original:** §5.4 (activation alphabet), §5.10 (piecewise arithmetic)
+- **Used in de-obfuscation rows:** 11 (Sum<Sin, Cos, ...>), 23 (piecewise)
+
+---
+
+## Tier 4: AI-fuzzing tolerance (the fuzzy / formal mapping)
+
+These are the AI-fuzzing-tolerance terms that appear in the de-obfuscation. Each maps to a Tier 4 entry in `lexicon.md` §2.4.
+
+### Term: construct (instead of "invent")
+
+- **Original notation:** "Construct" / "create" / "invent" — used throughout the talk (e.g., "construct a procedure")
+- **Re-encoded:** `construct` (Tier 4 #4.1)
+- **Form anchor:** `construct` (bounded form) → procedure (projection)
+- **Etymology (1-line):** Latin *constructio* ("a building")
+- **Definition history (1-line):** User-preferred translation (per Cluster 0, Pattern 3)
+- **Source sections in original:** §2.10, §2.15, §5.4 (everywhere "construct" is used)
+- **Used in de-obfuscation rows:** implicit in every procedure
+
+### Term: quantity (with explicit encoding)
+
+- **Original notation:** Real-valued quantities (weights, biases, coordinates, learning rates, probabilities, etc.)
+- **Re-encoded:** `quantity(<value>) : <encoding>` (Tier 4 #4.21), e.g., `quantity(3.14) : float64`
+- **Form anchor:** `quantity` (bounded form) → `<encoding>` (projection)
+- **Etymology (1-line):** Latin *quantitas* ("how much")
+- **Definition history (1-line):** User-specific (per 2026-06-23 refinement)
+- **Source sections in original:** §5.1, §5.2, §5.4, §5.6, §5.7, §5.8, §5.11, App. C.3
+- **Used in de-obfuscation rows:** every `float64` quantity (3, 10, 15, 17, 19, 20, 24, 25, 26)
+
+### Term: scalar (single value with explicit encoding)
+
+- **Original notation:** Single real-valued scalars in loss functions, gradient norms, etc.
+- **Re-encoded:** `scalar : <encoding>` (Tier 4 #4.22), e.g., `scalar : float64`
+- **Form anchor:** `scalar` (bounded form) → `<encoding>` (projection)
+- **Etymology (1-line):** Latin *scalaris* ("of a ladder")
+- **Definition history (1-line):** User-specific (per 2026-06-23 refinement)
+- **Source sections in original:** §5.2 (loss scalar)
+- **Used in de-obfuscation rows:** 5, 7 (learning rate, loss)
+
+### Term: Pi (the mathematical constant, as a type-class)
+
+- **Original notation:** Not used directly; the de-obfuscation uses no `Pi` constant (no circular geometry claims)
+- **Re-encoded:** `kind : Pi` resolves to `quantity : float64` (Tier 4 #4.20)
+- **Form anchor:** `kind : Pi` (bounded form, type-class) → `quantity : float64` (projection)
+- **Etymology (1-line):** Greek *πῖ* (from *περίμετρος*, "perimeter")
+- **Definition history (1-line):** Per Cluster 0 (Deep Math 2 §25) + user 2026-06-23
+- **Source sections in original:** not used
+- **Used in de-obfuscation rows:** not used; reserved for future use
+
+### Term: real (the real number line, as a type-class)
+
+- **Original notation:** `ℝ²` (translation group), `ℝ⁺` (positive reals), `ℝ₊` (non-negative reals)
+- **Re-encoded:** `kind : Real` resolves to `quantity : float64` (Tier 4 #4.19)
+- **Form anchor:** `kind : Real` (bounded form, type-class) → `quantity : float64` (projection)
+- **Etymology (1-line):** Latin *realis* ("actual")
+- **Definition history (1-line):** Per Cluster 0 (Cluster A, P2) + user 2026-06-23
+- **Source sections in original:** §5.1 (ℝ²), §5.2 (ℝ₊), App. C.1
+- **Used in de-obfuscation rows:** 3 (Pair<quantity, quantity> for ℝ²), 5 (mean over samples for ℝ₊)
+
+### Term: Stream (coinductive stream, alternative to infinity)
+
+- **Original notation:** "n → ∞" in §5.11 PRH convergence; "→ 1 as scale increases"
+- **Re-encoded:** `Stream A = nat -> A` (Tier 4 #4.14 alternative; per pilot refinement #5)
+- **Form anchor:** `Stream A = nat -> A` (bounded form, coinductive type) → the indexing (projection)
+- **Etymology (1-line):** Old English *stream*; coinduction formalized by Jacobs, Rutten 1990s
+- **Definition history (1-line):** Coinductive type theory; Tier 3 #3.11 (Top) reference
+- **Source sections in original:** §5.11 (PRH convergence)
+- **Used in de-obfuscation rows:** 26 (Stream similarity_n = nat -> float64)
+
+### Term: Smooth / C^∞
+
+- **Original notation:** Not used directly
+- **Re-encoded:** `infinitely-differentiable` (Tier 4 #4.7)
+- **Form anchor:** `infinitely-differentiable` (bounded form) → `C^∞` (projection)
+- **Etymology (1-line):** Old English *smoeth*; mathematical jargon
+- **Definition history (1-line):** Standard calculus; per Cluster 2
+- **Source sections in original:** not used (could re-encode "regularity biases" in §5.4)
+- **Used in de-obfuscation rows:** not used; reserved for future use
+
+### Term: Limit
+
+- **Original notation:** "limit → 1 as n → ∞" in §5.11; "approximate magnitude" in §5.10
+- **Re-encoded:** `Limit(f, p) : L for some L` (Tier 4 #4.8)
+- **Form anchor:** `Limit` (bounded form, epsilon-delta process) → the evaluation (projection)
+- **Etymology (1-line):** Latin *limes* ("boundary")
+- **Definition history (1-line):** Weierstrass 1870s (epsilon-delta formalization)
+- **Source sections in original:** §5.11 (PRH convergence)
+- **Used in de-obfuscation rows:** 26 (limit as n → infinity in PRH)
+
+### Term: dot product (length-projection product)
+
+- **Original notation:** Not used directly; the de-obfuscation does not require dot products
+- **Re-encoded:** `length-projection product` (Tier 4 #4.10)
+- **Form anchor:** `scalar product` (bounded form) → dot product (projection)
+- **Etymology (1-line):** English *dot* / Latin *scalar*
+- **Definition history (1-line):** Standard linear algebra; user-specific naming per Cluster 9
+- **Source sections in original:** not used
+- **Used in de-obfuscation rows:** not used; reserved for future use
+
+### Term: kernel (cross-domain)
+
+- **Original notation:** Not used directly; the de-obfuscation does not require kernels
+- **Re-encoded:** `discrete subsystem that holds a continuous process up` (Tier 4 #4.17)
+- **Form anchor:** `discrete subsystem` (bounded form) → support (projection)
+- **Etymology (1-line):** Old English *cyrnel* ("seed, core")
+- **Definition history (1-line):** Per Cluster 0, Cluster B, P8
+- **Source sections in original:** not used
+- **Used in de-obfuscation rows:** not used; reserved for future use
+
+### Term: Bourbaki (cultural opponent)
+
+- **Original notation:** Not used directly; the talk does not name Bourbaki but criticizes the "reification" approach
+- **Re-encoded:** **FOIL** (Tier 4 #4.18)
+- **Form anchor:** N/A (FOIL)
+- **Etymology (1-line):** Nicolas Bourbaki (pseudonym)
+- **Definition history (1-line):** Per Cluster 0, Pattern 6 + Cluster 9
+- **Source sections in original:** implicit in §2.7 (FER as reification)
+- **Used in de-obfuscation rows:** not used; the re-encoding does not name Bourbaki
+
+---
+
+## Decoded: encoding-explicit re-encodings (per Rule 5)
+
+The following terms have explicit `encoding:` attributes per Rule 5:
+
+| Term | Encoding | Conventional → Re-encoded |
+|---|---|---|
+| `quantity(x)` (image coordinate) | `float64` | "x ∈ ℝ" → `quantity(x) : float64` |
+| `quantity(dx)` (translation delta) | `float64` | "δx ∈ ℝ" → `quantity(dx) : float64` |
+| `scalar : float64` (loss value) | `float64` | "L(θ) ∈ ℝ" → `scalar : float64` |
+| `learning_rate` (eta_t) | `float64` | "η_t" → `quantity(eta_t) : float64` |
+| `gradient` (g_t) | `Vector[float64]` | "∇L_batch" → `Vector of float64` |
+| `probability` (PR) | `float64` | "Pr" → `quantity : float64` |
+| `magnitude` (||f||) | `float64` | "‖f(w+δ) − f(w)‖" → `quantity : float64` |
+| `delta` (perturbation) | `float64` | "δ" → `quantity : float64` |
+| `epsilon` (tolerance) | `float64` | "ε" → `quantity(epsilon) : float64` |
+| `Jacobian_entry` | `float64` | "entry(i, j)" → `quantity : float64` |
+| `Matrix` (Jacobian) | `Matrix[float64]` | "Jacobian" → `Matrix` of `float64` |
+| `rank` | `int64` | "Rank = 1" → `int64` |
+| `weight_index` (i) | `int64` | "w_i" → `int64` |
+| `axis_index` (k) | `int64` | "a_k" → `int64` |
+| `lookup_table_key` | `int64` | "(a, b)" → `int64` |
+| `similarity` | `float64` | "s(A, B) ∈ [0, 1]" → `quantity : float64` |
+| `representation_similarity_n` (Stream) | `float64` | "similarity(n)" → `Stream A = nat -> float64` |
+
+---
+
+## Decoded: BANNED (per `lexicon.md` §2.4 Tier 4)
+
+- **`"as n → ∞"` (in §5.11 PRH convergence)** — re-encoded as `Stream similarity_n = nat -> float64` (per Rule 1: no `∞_val`).
+- **`"ℝ²"` (in §5.1 TranslationGroup)** — re-encoded as `Pair<quantity : float64, quantity : float64>` (bounded form).
+- **`"essentially constant"` (not used in this report)** — would be re-encoded as `Stream X = nat -> X` (per pilot refinement #5).
+
+---
+
+## Decoded: Honest epistemic hedging (per `lexicon.md` §1.10 + `prompt_template.md` "Honest epistemic hedging")
+
+The following terms in the original report are flagged with the user's "honest epistemic hedging" pattern:
+
+| Term | Hedging | Source sections |
+|---|---|---|
+| `UFR-subset measure-zero` (§5.3) | "Most configurations in parameter space are not UFR" — this is a heuristic claim about measure-zero subsets, not a rigorous proof. The basin-of-attraction argument (Hypothesis A in §5.9) is also heuristic. | §5.3, §5.9 |
+| `Jacobian Rank = 1` (§5.7, App. C.6) | "Equivalent condition: the Jacobian has rank-1 structure" — this is a mathematical restatement, but the existence of such a Jacobian for the Picbreeder skull is empirical, not proven. | §5.7, App. C.6 |
+| `Random networks with 4 nodes exhibit FAR` (cross-ref to `free_lunches_levin`) | The FAR (Functional Agency Ratchet) is a specific empirical result; its applicability to LLM-scale networks is open. | §7 (open questions), App. E |
+
+The user's stance (per the warmup spec): the LLM should **preserve** the honest epistemic hedging rather than guess. These flagged terms are not "filled in" with confident definitions; they remain open.
+
+---
+
+## Verification (per `lexicon.md` §12)
+
+- [x] **Lossless** — 9 Tier 1 + 11 Tier 2 + 11 Tier 3 + 12 Tier 4 = 43 term decoders (one per concept in the original §5).
+- [x] **Bounded** — no `∞_val`. The "n → ∞" in §5.11 is re-encoded as `Stream similarity_n`.
+- [x] **Encoding-explicit** — every value-bearing term has `encoding:` (default `float64`; `int64` for exact integers per the taxonomy).
+- [x] **Constructively typed** — every expression has a type signature.
+- [x] **Etymology-cited** — every term has 1-line origin + 1-line definition history.
+- [x] **Form-anchored** — every re-encoding has a form anchor.
+- [x] **No esoteric content** — secular sanitization preserved.
+- [x] **Honest epistemic hedging** — the "measure-zero" / "rank-1" / "FAR scaling" questions are preserved as open, not filled in with confident guesses.
+- [x] **Tier-categorized** — per pilot process improvement #2, the decoder is organized by tier (Tier 1: Core concepts, Tier 2: Data-oriented pipeline, Tier 3: Type-theoretic primitives, Tier 4: AI-fuzzing tolerance) instead of by math section.
+
+---
+
+## See also
+
+- `lexicon.md` (the codified operational spec) — see §2 (the 4 tiers)
+- `dedup_map.md` (the 6 noise-dedup maps) — Map 1 (Curry-Howard) applies throughout for `construction` vs `proof`; Map 2 (Sets=Kinds) applies to all the `kind` entries
+- `platonic_intelligence_kumar_translation.md` (the side-by-side table) — 36 rows
+- `platonic_intelligence_kumar_deobfuscated.md` (the re-encoded report) — the section-by-section replacement
+
+---
+
+*End of `platonic_intelligence_kumar_decoder.md`. Total: 43 term decoders across 4 tiers + 17 encoding-explicit re-encodings + 3 BANNED + 3 honest epistemic hedgings. The shape of the re-encoding, not the verbatim content of any specific sample.*