conductor(deob_apply): score_dynamics_giorgini decoder (72 terms, tier-categorized per pilot process improvement #2)
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# score_dynamics_giorgini — Per-Term Decoder (Tier-Categorized)
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**Source:** `conductor/tracks/video_analysis_score_dynamics_giorgini_20260621/report.md` (1325 LOC)
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**Output:** This file is the **per-term decoder** organized by **tier** (per pilot process improvement #2).
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**Method:** Per `lexicon.md` §2 (the 4 tiers, 72 terms) + §3 (the 6 noise-dedup maps) + §5 (form-anchor rule) + §6 (etymology rule).
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**Date:** 2026-06-23
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> **Reading guide.** This is the **per-term decoder** for every term in the score_dynamics_giorgini Pass 1 report that required de-obfuscation. The terms are organized into 4 tiers (per pilot process improvement #2):
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>
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> - **Tier 1: Core concepts** — the foundational type-theoretic primitives + the constructive type theory operators (12 terms).
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> - **Tier 2: Data-oriented pipeline** — the data-oriented + constructive type theory operators (18 terms).
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> - **Tier 3: Type-theoretic primitives** — the constructive type theory (Per Martin-Löf tradition) operators (18 terms).
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> - **Tier 4: AI-fuzzing tolerance** — the principled re-encodings + user-specific forms (24 terms).
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>
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> Per pilot process improvement #2, the principled/user-also-accepted split is explicit at the structural level (by tier, not by math section).
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>
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> Each entry has:
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> - **Original notation:** the Pass 1 form
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> - **Re-encoded:** the principled re-encoded form (per `lexicon.md` §2)
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> - **Form anchor:** the bounded form + projection (per Rule 2)
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> - **Etymology (1-line):** the origin
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> - **Definition history (1-line):** the first formalization
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> - **Source sections in original:** the Pass 1 §X.Y references
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> - **Cluster cross-ref:** the warmup's cluster sub-report that documents the pattern
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>
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> **For the side-by-side table:** see `score_dynamics_giorgini_translation.md` (57 rows).
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> **For the re-encoded report:** see `score_dynamics_giorgini_deobfuscated.md`.
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---
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## Tier 1: Core concepts (12 terms from `lexicon.md` §2.1)
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The foundational type-theoretic primitives + the constructive type theory operators. These are scheme-canonical.
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### Term: `set` (concept of a set of states)
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- **Original notation:** `p_ss(x)`, `P : kind` (set of states; per §5.1)
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- **Re-encoded:** `kind` (per Tier 1 #1.1)
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- **Form anchor:** `kind` (bounded form) → `T` (projection)
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- **Etymology (1-line):** Old English *cynd* ("kind, sort, nature")
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- **Definition history (1-line):** Per Martin-Löf 1975
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- **Source sections in original:** §2.1, §5.1
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- **Cluster cross-ref:** Cluster 0, 4
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### Term: `∀` (universal quantifier over observables)
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- **Original notation:** `forall O : Observable, expected(O) : float64` (per §5.6, §5.7)
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- **Re-encoded:** `forall` (per Tier 1 #1.2)
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- **Form anchor:** `forall` (bounded form) → `T -> Prop` (projection)
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- **Etymology (1-line):** Latin *pro omnibus* ("for all")
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- **Definition history (1-line):** First formalized in Frege 1879; constructive form in Martin-Löf 1975
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- **Source sections in original:** §5.6, §5.7
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- **Cluster cross-ref:** Cluster 2, 4
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### Term: `∃` (existential quantifier over parameter sets)
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- **Original notation:** "exists some M" (per §5.2 for the general solution)
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- **Re-encoded:** `exists` (per Tier 1 #1.3)
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- **Form anchor:** `exists` (bounded form) → `T -> Prop` (projection)
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- **Etymology (1-line):** Latin *existere*
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- **Definition history (1-line):** First formalized in Frege 1879; constructive form in Martin-Löf 1975
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- **Source sections in original:** §5.2
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- **Cluster cross-ref:** Cluster 4
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### Term: `∧` (logical conjunction)
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- **Original notation:** `P(meet(a, b), T)` (per §5.10 for the product of probabilities)
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- **Re-encoded:** `and` (per Tier 1 #1.4)
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- **Form anchor:** `and` (bounded form) → `Prop -> Prop -> Prop` (projection)
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- **Etymology (1-line):** Old English *and*
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- **Definition history (1-line):** First formalized in Boole 1847
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- **Source sections in original:** §5.10
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- **Cluster cross-ref:** Cluster 3
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### Term: `∨` (logical disjunction)
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- **Original notation:** `partial(alpha_j, ...) or partial(beta_j, ...)` (per §5.7)
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- **Re-encoded:** `or` (per Tier 1 #1.5)
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- **Form anchor:** `or` (bounded form) → `Prop -> Prop -> Prop` (projection)
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- **Etymology (1-line):** Old English *or*
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- **Definition history (1-line):** First formalized in Boole 1847
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- **Source sections in original:** §5.7
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- **Cluster cross-ref:** Standard
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### Term: `¬` (logical negation)
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- **Original notation:** Not used in this lecture
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- **Re-encoded:** `not` (per Tier 1 #1.6)
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- **Form anchor:** `not` (bounded form) → `Prop -> Prop` (projection)
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- **Etymology (1-line):** Latin *non*
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- **Definition history (1-line):** First formalized in Boole 1847
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- **Source sections in original:** Not applicable
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- **Cluster cross-ref:** Standard
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### Term: `→` (implication)
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- **Original notation:** "implies" in proofs (per §5 throughout)
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- **Re-encoded:** `implies` (per Tier 1 #1.7)
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- **Form anchor:** `implies` (bounded form) → `Prop -> Prop -> Prop` (projection)
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- **Etymology (1-line):** Latin *implicare*
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- **Definition history (1-line):** First formalized in Philo of Megara (3rd c. BC); modern constructive form in Heyting 1930
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- **Source sections in original:** §5 throughout (implicit)
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- **Cluster cross-ref:** Standard
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### Term: `∈` (membership)
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- **Original notation:** `x ~ p_ss`, `x ~ p`, `z ~ N(0, I)` (per §5.4, §5.6, §5.10)
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- **Re-encoded:** `in` (with `: T` type ascription; per Tier 1 #1.8)
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- **Form anchor:** `in` (bounded form) → `: T` (projection)
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- **Etymology (1-line):** Latin *in*
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- **Definition history (1-line):** Per Peano 1889; constructive replacement is type ascription
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- **Source sections in original:** §5.4, §5.6, §5.10
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- **Cluster cross-ref:** Cluster 2
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### Term: `⊆` (subset / subkind)
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- **Original notation:** "for all positive-definite M" (per §5.2)
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- **Re-encoded:** `subkind` (per Tier 1 #1.9; user coinage)
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- **Form anchor:** `subkind` (bounded form) → `Kind -> Kind -> Prop` (projection)
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- **Etymology (1-line):** User coinage (sub-set as sub-kind)
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- **Definition history (1-line):** User-specific; the constructive reading
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- **Source sections in original:** §5.2
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- **Cluster cross-ref:** Cluster 0
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### Term: `⊥` (Bottom — empty type)
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- **Original notation:** Not used in this lecture
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- **Re-encoded:** `Bottom` (per Tier 1 #1.10)
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- **Form anchor:** `Bottom` (bounded form) → `Type` (projection)
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- **Etymology (1-line):** Greek *βύσμα*
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- **Definition history (1-line):** Per Martin-Löf 1975
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- **Source sections in original:** Not applicable
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- **Cluster cross-ref:** Cluster 3
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### Term: `Notion` (ἔννοια)
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- **Original notation:** "Concept" / "Notion" (per §2.5-2.12)
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- **Re-encoded:** `concept : type` (per Tier 1 #1.11; user-also-accepted)
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- **Form anchor:** `concept` (bounded form) → `Type` (projection)
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- **Etymology (1-line):** Greek *ἔννοια*
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- **Definition history (1-line):** Per Cluster 7, `Notiones.txt`
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- **Source sections in original:** §2.5-2.12
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- **Cluster cross-ref:** Cluster 7
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### Term: `Boundary/Term` (ὅρος)
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- **Original notation:** "Definition" of "score", "mobility", "drift" (per §2.5-2.11)
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- **Re-encoded:** `definitio : type` (per Tier 1 #1.12; user-also-accepted)
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- **Form anchor:** `definitio` (bounded form) → `Type` (projection)
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- **Etymology (1-line):** Greek *ὅρος*; Latin *definitio*
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- **Definition history (1-line):** Per Cluster 7, `Notiones.txt`
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- **Source sections in original:** §2.5-2.11
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- **Cluster cross-ref:** Cluster 7
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---
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## Tier 2: Data-oriented pipeline (18 terms from `lexicon.md` §2.2)
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The data-oriented + constructive type theory operators.
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### Term: `function` (mathematical function)
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- **Original notation:** `s(x)`, `F(x)`, `M(x)` (per §5 throughout)
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- **Re-encoded:** `procedure s (x : State) -> Vector[d] : gradient(log p_ss(x))` (per Tier 2 #2.1; per Functions=Procedures Map 3)
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- **Form anchor:** `procedure` (bounded form) → `(arg) -> result` (projection)
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- **Etymology (1-line):** Latin *procedere*
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- **Definition history (1-line):** Church 1932; the procedure form is the concatenative reading
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- **Source sections in original:** §5 throughout
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- **Cluster cross-ref:** Cluster 2, 4
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### Term: `parameter` (function parameter)
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- **Original notation:** `theta = (alpha, beta)` (per §5.7)
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- **Re-encoded:** `argument` (per Tier 2 #2.2)
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- **Form anchor:** `argument` (bounded form) → `T` (projection)
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- **Etymology (1-line):** Latin *argumentum*
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- **Definition history (1-line):** Frege 1879
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- **Source sections in original:** §5.7, §5.8
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- **Cluster cross-ref:** Cluster 2, 4
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### Term: `return value` (procedure's output)
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- **Original notation:** `expected(O_m) : float64` (per §5.6-§5.8)
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- **Re-encoded:** `result` (per Tier 2 #2.3)
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- **Form anchor:** `result` (bounded form) → `T` (projection)
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- **Etymology (1-line):** Latin *resultare*
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- **Definition history (1-line):** Standard in mathematics and programming
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- **Source sections in original:** §5.6-§5.8
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- **Cluster cross-ref:** Cluster 2
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### Term: `definition` (of a type)
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- **Original notation:** "score s(x) = gradient(log p_ss(x))" (per §2.5)
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- **Re-encoded:** `formation` (per Tier 2 #2.4)
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- **Form anchor:** `formation` (bounded form) → `Type` (projection)
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- **Etymology (1-line):** Latin *formatio*
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- **Definition history (1-line):** Per Martin-Löf 1975
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- **Source sections in original:** §2.5
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- **Cluster cross-ref:** Cluster 3
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### Term: `input` (function input)
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- **Original notation:** `s(x)` input is `x : State`
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- **Re-encoded:** `arg` (per Tier 2 #2.5)
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- **Form anchor:** `arg` (bounded form) → `T` (projection)
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- **Etymology (1-line):** English (abbreviation)
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- **Definition history (1-line):** Programming convention
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- **Source sections in original:** §5 throughout
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- **Cluster cross-ref:** Cluster 4
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### Term: `equation` (mathematical equation)
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- **Original notation:** `dx_t = F(X_t) * dt + sqrt(2) * sigma(X_t) * dW_t` (per §5.1)
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- **Re-encoded:** `relation` (per Tier 2 #2.6)
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- **Form anchor:** `relation` (bounded form) → `T -> T -> Prop` (projection)
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- **Etymology (1-line):** Latin *relatio*
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- **Definition history (1-line):** Tarski 1941
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- **Source sections in original:** §5.1
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- **Cluster cross-ref:** Cluster 2
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### Term: `property` (of an element)
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- **Original notation:** "M is positive-definite", "X is stationary" (per §5.2)
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- **Re-encoded:** `property` (per Tier 2 #2.7)
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- **Form anchor:** `property` (bounded form) → `T -> Prop` (projection)
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- **Etymology (1-line):** Latin *proprietas*
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- **Definition history (1-line):** Standard mathematical term
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- **Source sections in original:** §5.2
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- **Cluster cross-ref:** Cluster 2
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### Term: `lemma` / `corollary`
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- **Original notation:** Theorems 5.2.1, 5.6.1 (per §5.2, §5.6)
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- **Re-encoded:** `claim` (per Tier 2 #2.8; user-also-accepted)
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- **Form anchor:** `claim` (bounded form) → `Prop` (projection)
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- **Etymology (1-line):** User coinage (collapse both per Cluster 9, Pattern 14)
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- **Definition history (1-line):** User-specific
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- **Source sections in original:** §5.2, §5.6
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- **Cluster cross-ref:** Cluster 9, Pattern 14
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### Term: `proof` (of a theorem)
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- **Original notation:** "Proof sketch" (per §5.2, §5.6)
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- **Re-encoded:** `construction` (per Tier 2 #2.9; per Curry-Howard Map 1)
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- **Form anchor:** `construction` (bounded form) → `T : Prop` (projection)
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- **Etymology (1-line):** Latin *constructio*
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- **Definition history (1-line):** Curry-Howard 1969
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- **Source sections in original:** §5.2, §5.6
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- **Cluster cross-ref:** Cluster 0, 7
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### Term: `witness` (proof witness)
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- **Original notation:** "the trajectory X_t" (per §5.6, §5.7)
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- **Re-encoded:** `instance` (per Tier 2 #2.10)
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- **Form anchor:** `instance` (bounded form) → `T` (projection)
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- **Etymology (1-line):** Latin *instantia*
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- **Definition history (1-line):** Standard constructive logic
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- **Source sections in original:** §5.6, §5.7
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- **Cluster cross-ref:** Cluster 4
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### Term: `Attribute` (attributus)
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- **Original notation:** "stationary", "Markovian", "ergodic" (per §5.1, §5.11)
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- **Re-encoded:** `attribute` (extrinsic; per Tier 2 #2.11; user-also-accepted)
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- **Form anchor:** `attribute` (bounded form) → `T -> Prop` (projection)
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- **Etymology (1-line):** Latin *attributus*
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- **Definition history (1-line):** Per Cluster 7, `Notiones.txt`
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- **Source sections in original:** §5.1, §5.11
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- **Cluster cross-ref:** Cluster 7
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### Term: `Property` (proprietas)
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- **Original notation:** "moments", "correlations", "PDFs" (per §2.15)
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- **Re-encoded:** `property` (intrinsic; per Tier 2 #2.12; user-also-accepted)
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- **Form anchor:** `property` (bounded form) → `T -> Prop` (projection)
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- **Etymology (1-line):** Latin *proprietas*
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- **Definition history (1-line):** Per Cluster 7
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- **Source sections in original:** §2.15
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- **Cluster cross-ref:** Cluster 7
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### Term: `Type/Genus` (γένος)
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- **Original notation:** `Operator : kind`, `Procedure : kind` (per §5 throughout)
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- **Re-encoded:** `kind` (sense 8; per Tier 2 #2.13; user-also-accepted)
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- **Form anchor:** `kind` (bounded form) → `Kind` (projection)
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- **Etymology (1-line):** Greek *γένος*; Latin *genus*; Sanskrit *जनस्*
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- **Definition history (1-line):** Per Cluster 7, `Notiones.txt`; 4-language pattern
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- **Source sections in original:** §5 throughout
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- **Cluster cross-ref:** Cluster 7
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### Term: `static declaration`
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- **Original notation:** `Tensor : kind`, `Vector : kind`, `Operator : kind` (per §5 throughout)
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- **Re-encoded:** `static { }` (per Tier 2 #2.14)
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- **Form anchor:** `static { }` (bounded form) → declaration block (projection)
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- **Etymology (1-line):** User coinage (Cluster 6, 9)
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- **Definition history (1-line):** Per Cluster 9; Sectored Language V1
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- **Source sections in original:** §5 throughout
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- **Cluster cross-ref:** Cluster 6, 9
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### Term: `execution block`
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- **Original notation:** `procedure s (x : State) -> Vector[d] : body` (per §5 throughout)
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- **Re-encoded:** `exe { }` (per Tier 2 #2.15)
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- **Form anchor:** `exe { }` (bounded form) → execution block (projection)
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- **Etymology (1-line):** User coinage (Cluster 6, 9)
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- **Definition history (1-line):** Per Cluster 9
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- **Source sections in original:** §5 throughout
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- **Cluster cross-ref:** Cluster 6, 9
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### Term: `meta-programming`
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- **Original notation:** Not used in this lecture (would apply to building a probabilistic programming language)
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- **Re-encoded:** `CodeSector` (per Tier 2 #2.16)
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- **Form anchor:** `CodeSector` (bounded form) → type (projection)
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- **Etymology (1-line):** User coinage (Cluster 9, P14)
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- **Definition history (1-line):** Per Cluster 9
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- **Source sections in original:** Not applicable
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- **Cluster cross-ref:** Cluster 9, P14
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### Term: `import alias`
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- **Original notation:** Not used in this lecture
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- **Re-encoded:** `using` (Haskell-style; per Tier 2 #2.17)
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- **Form anchor:** `using` (bounded form) → alias declaration (projection)
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- **Etymology (1-line):** User coinage (Cluster 9, P15)
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- **Definition history (1-line):** Per Cluster 9
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- **Source sections in original:** Not applicable
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- **Cluster cross-ref:** Cluster 9, P15
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### Term: `assertion`
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- **Original notation:** Not used in this lecture
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- **Re-encoded:** `'figure 1.9' ... assert -> ... = ...` (per Tier 2 #2.18)
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- **Form anchor:** assertion (bounded form) → equation (projection)
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- **Etymology (1-line):** User coinage (Cluster 9, P16)
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- **Definition history (1-line):** Per Cluster 9
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- **Source sections in original:** Not applicable
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- **Cluster cross-ref:** Cluster 9, P16
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---
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## Tier 3: Type-theoretic primitives (18 terms from `lexicon.md` §2.3)
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The constructive type theory (Per Martin-Löf tradition) operators.
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### Term: `Type` (the meta-type)
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||||
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- **Original notation:** `Tensor : kind`, `Vector : kind` (per §5 throughout)
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- **Re-encoded:** `kind` (per Tier 3 #3.1)
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- **Form anchor:** `kind` (bounded form) → `Kind` (projection)
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- **Etymology (1-line):** Old English *cynd*
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||||
- **Definition history (1-line):** Per Martin-Löf 1975
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||||
- **Source sections in original:** §5 throughout
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- **Cluster cross-ref:** Cluster 3
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### Term: `Type of types`
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||||
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||||
- **Original notation:** Not directly used
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||||
- **Re-encoded:** `Kind` (per Tier 3 #3.2)
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- **Form anchor:** `Kind` (bounded form) → `Type` (projection)
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||||
- **Etymology (1-line):** Old English *cynd* + meta
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5 implicit
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: `Constructor`
|
||||
|
||||
- **Original notation:** `Tensor[d, d] = float64` (per §5.1)
|
||||
- **Re-encoded:** `intro` / `construct` (per Tier 3 #3.3)
|
||||
- **Form anchor:** `intro` (bounded form) → `T -> T` (projection)
|
||||
- **Etymology (1-line):** Latin *introductio*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: `Eliminator`
|
||||
|
||||
- **Original notation:** `matmul`, `transpose`, `divergence` (per §5.1)
|
||||
- **Re-encoded:** `elim` / `eliminate` (per Tier 3 #3.4)
|
||||
- **Form anchor:** `elim` (bounded form) → `(T, C) -> C` (projection)
|
||||
- **Etymology (1-line):** Latin *eliminatio*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: `Computation rule` (value-level)
|
||||
|
||||
- **Original notation:** β-reduction for matmul: `A.matmul(B) = C` (per §5.1)
|
||||
- **Re-encoded:** `comp` (per Tier 3 #3.5)
|
||||
- **Form anchor:** `comp` (bounded form) → β-reduction (projection)
|
||||
- **Etymology (1-line):** Latin *computatio*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5 throughout (implicit)
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: `Type-level Computation`
|
||||
|
||||
- **Original notation:** `getType(Vector) === kind` (implicit in type definitions)
|
||||
- **Re-encoded:** `getType(...) === T` (per Tier 3 #3.6)
|
||||
- **Form anchor:** `getType` (bounded form) → type check (projection)
|
||||
- **Etymology (1-line):** User coinage (Cluster 3, P4)
|
||||
- **Definition history (1-line):** Per Cluster 3, Pattern 4
|
||||
- **Source sections in original:** §5 implicit
|
||||
- **Cluster cross-ref:** Cluster 3, P4
|
||||
|
||||
### Term: `Uniqueness rule`
|
||||
|
||||
- **Original notation:** "F = D·s + divergence(D)" is the unique zero-current solution (per §5.2)
|
||||
- **Re-encoded:** `uniq` (per Tier 3 #3.7)
|
||||
- **Form anchor:** `uniq` (bounded form) → canonical form (projection)
|
||||
- **Etymology (1-line):** Latin *unicitas*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5.2
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: `Formation`
|
||||
|
||||
- **Original notation:** `Vector : kind where dimensions : int64` (per §5 throughout)
|
||||
- **Re-encoded:** `formation` (per Tier 3 #3.8)
|
||||
- **Form anchor:** `formation` (bounded form) → `T : type` (projection)
|
||||
- **Etymology (1-line):** Latin *formatio*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: `Introduction`
|
||||
|
||||
- **Original notation:** `Tensor : kind = ...` (per §5 throughout)
|
||||
- **Re-encoded:** `intro` (per Tier 3 #3.9)
|
||||
- **Form anchor:** `intro` (bounded form) → value constructor (projection)
|
||||
- **Etymology (1-line):** Latin *introductio*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: `Bottom`
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** `Bottom` (per Tier 3 #3.10)
|
||||
- **Form anchor:** `Bottom` (bounded form) → empty type (projection)
|
||||
- **Etymology (1-line):** Greek *βύσμα*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: `Top`
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** `Top` (per Tier 3 #3.11; to be defined per `lexicon.md` §10)
|
||||
- **Form anchor:** `Top` (bounded form) → universal type (projection)
|
||||
- **Etymology (1-line):** Greek *τόπος* via Latin *topos*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975 (the universal type, dual of Bottom)
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Phase 1, `lexicon.md` §10
|
||||
|
||||
### Term: `Pair` (Sigma type)
|
||||
|
||||
- **Original notation:** `(x_0, x_t)` for lagged pairs (per §5.5)
|
||||
- **Re-encoded:** `Pair<x_0, x_t>` with `Build<x_0>`, `Build<x_t>` projections (per Tier 3 #3.12)
|
||||
- **Form anchor:** `Pair<x_0, x_t>` (bounded form) → product type (projection)
|
||||
- **Etymology (1-line):** Latin *par*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5.5
|
||||
- **Cluster cross-ref:** Cluster 3, P1
|
||||
|
||||
### Term: `Pair constructor`
|
||||
|
||||
- **Original notation:** `<x_0, x_t>` (per §5.5)
|
||||
- **Re-encoded:** `<M, N>` (per Tier 3 #3.13)
|
||||
- **Form anchor:** `<M, N>` (bounded form) → pair construction (projection)
|
||||
- **Etymology (1-line):** Mathematical notation
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5.5
|
||||
- **Cluster cross-ref:** Cluster 3, P1
|
||||
|
||||
### Term: `Dependent Function` (Pi type)
|
||||
|
||||
- **Original notation:** `forall x : State, p(x) : float64` (per §5.6)
|
||||
- **Re-encoded:** `Dependent<x : State>(p(x))` (per Tier 3 #3.14)
|
||||
- **Form anchor:** `Dependent<x : A>(B)` (bounded form) → Pi type (projection)
|
||||
- **Etymology (1-line):** User coinage (Cluster 3, P1)
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5.6
|
||||
- **Cluster cross-ref:** Cluster 3, P1
|
||||
|
||||
### Term: `Lambda`
|
||||
|
||||
- **Original notation:** `lambda x. M` (per §5 implicit)
|
||||
- **Re-encoded:** `lambda.x.M` (per Tier 3 #3.15)
|
||||
- **Form anchor:** `lambda.x.M` (bounded form) → function abstraction (projection)
|
||||
- **Etymology (1-line):** Greek letter *λ*
|
||||
- **Definition history (1-line):** Church 1932
|
||||
- **Source sections in original:** §5 implicit
|
||||
- **Cluster cross-ref:** Cluster 3, P1
|
||||
|
||||
### Term: `objects :` (carrier declaration)
|
||||
|
||||
- **Original notation:** `Vector : kind where dimensions : int64, components : [dimensions] float64` (per §5 throughout)
|
||||
- **Re-encoded:** `objects : dimensions : int64, components : [dimensions] float64 ;` (per Tier 3 #3.16)
|
||||
- **Form anchor:** `objects :` (bounded form) → field declaration (projection)
|
||||
- **Etymology (1-line):** User coinage (Cluster 3, P6)
|
||||
- **Definition history (1-line):** Per Cluster 3, Pattern 6
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** Cluster 3, P6
|
||||
|
||||
### Term: `Sum` (Disjoint Sum)
|
||||
|
||||
- **Original notation:** `u or v` for drift/diffusion perturbation (per §5.7)
|
||||
- **Re-encoded:** `u + v` with `inl`/`inr` injections (per Tier 3 #3.17)
|
||||
- **Form anchor:** `A + B` (bounded form) → sum type (projection)
|
||||
- **Etymology (1-line):** Latin *summa*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5.7
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: `Sum elimination` (BNF)
|
||||
|
||||
- **Original notation:** Pattern matching on `u or v` (implicit in §5.7)
|
||||
- **Re-encoded:** `match(M, N, O)` (per Tier 3 #3.18)
|
||||
- **Form anchor:** `match` (bounded form) → case analysis (projection)
|
||||
- **Etymology (1-line):** User coinage (Cluster 3, P1)
|
||||
- **Definition history (1-line):** Per Cluster 3, Pattern 1
|
||||
- **Source sections in original:** §5.7 implicit
|
||||
- **Cluster cross-ref:** Cluster 3, P1
|
||||
|
||||
---
|
||||
|
||||
## Tier 4: AI-fuzzing tolerance (24 terms from `lexicon.md` §2.4)
|
||||
|
||||
The principled re-encodings + user-specific forms. This is where the AI-fuzzing tolerance is most needed.
|
||||
|
||||
### Term: "invent"
|
||||
|
||||
- **Original notation:** "We construct the SDE" (per §2.1)
|
||||
- **Re-encoded:** `construct` (per Tier 4 #4.1; per Map 5 invent→construct)
|
||||
- **Form anchor:** `construct` (bounded form) → procedure (projection)
|
||||
- **Etymology (1-line):** Latin *constructio*
|
||||
- **Definition history (1-line):** Constructive mathematics tradition
|
||||
- **Source sections in original:** §2.1
|
||||
- **Cluster cross-ref:** Cluster 0
|
||||
|
||||
### Term: "real number"
|
||||
|
||||
- **Original notation:** `expected(O_m) : float64` (per §5.6, §5.7)
|
||||
- **Re-encoded:** `quantity(<value>) : <encoding>` (e.g., `quantity(0.5) : float64`; per Tier 4 #4.2)
|
||||
- **Form anchor:** `quantity` (bounded form) → `<encoding>` (projection)
|
||||
- **Etymology (1-line):** Latin *quantitas*
|
||||
- **Definition history (1-line):** Per Map 6 number=quantity; the user-preferred form
|
||||
- **Source sections in original:** §5.6, §5.7
|
||||
- **Cluster cross-ref:** Cluster 0, 8
|
||||
|
||||
### Term: "imaginary number"
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** `bivector (with scalar multiplier)` (per Tier 4 #4.3; user-also-accepted)
|
||||
- **Form anchor:** `bivector` (bounded form) → grade-2 element (projection)
|
||||
- **Etymology (1-line):** Latin *bi-* + *vector*
|
||||
- **Definition history (1-line):** Per Cluster 0, Pattern 2
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 0, 8
|
||||
|
||||
### Term: "function"
|
||||
|
||||
- **Original notation:** `s(x)`, `F(x)`, `M(x)`, `B(x, t)` (per §5 throughout)
|
||||
- **Re-encoded:** `procedure` (per Tier 4 #4.4; user-also-accepted: `transform`)
|
||||
- **Form anchor:** `procedure` (bounded form) → `(arg) -> result` (projection)
|
||||
- **Etymology (1-line):** Latin *procedere* / *transformare*
|
||||
- **Definition history (1-line):** Per Map 3 Functions=Procedures
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** Cluster 2
|
||||
|
||||
### Term: "magic"
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** `unboxed` (per Tier 4 #4.5; user-also-accepted)
|
||||
- **Form anchor:** `unboxed` (bounded form) → exposed value (projection)
|
||||
- **Etymology (1-line):** English colloquial / Latin *indefinitus*
|
||||
- **Definition history (1-line):** Per Cluster 0, 9
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 0, 9
|
||||
|
||||
### Term: "natural number"
|
||||
|
||||
- **Original notation:** `d : int64`, `P : int64`, `M : int64` (per §5 throughout)
|
||||
- **Re-encoded:** `Nat = Zero | Succ(Nat)` (per Tier 4 #4.6)
|
||||
- **Form anchor:** `Nat` (bounded form) → inductive type (projection)
|
||||
- **Etymology (1-line):** Latin *naturalis*
|
||||
- **Definition history (1-line):** Per Martin-Löf 1975
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** Cluster 3
|
||||
|
||||
### Term: "smooth"
|
||||
|
||||
- **Original notation:** "smooth density", "smooth vector field" (per §5.12)
|
||||
- **Re-encoded:** `infinitely-differentiable` (per Tier 4 #4.7)
|
||||
- **Form anchor:** `infinitely-differentiable` (bounded form) → C^∞ (projection)
|
||||
- **Etymology (1-line):** Old English *smoeth*
|
||||
- **Definition history (1-line):** Calculus tradition
|
||||
- **Source sections in original:** §5.12
|
||||
- **Cluster cross-ref:** Cluster 2
|
||||
|
||||
### Term: "the limit exists"
|
||||
|
||||
- **Original notation:** "the limit of relative frequency" (per §1 for context; not in the main math)
|
||||
- **Re-encoded:** `Limit(f, p) : L for some L` (per Tier 4 #4.8)
|
||||
- **Form anchor:** `Limit` (bounded form) → epsilon-delta (projection)
|
||||
- **Etymology (1-line):** Latin *limes*
|
||||
- **Definition history (1-line):** Cauchy/Weierstrass 19th century
|
||||
- **Source sections in original:** §1 (context only)
|
||||
- **Cluster cross-ref:** Cluster 2
|
||||
|
||||
### Term: "transcendental number"
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** `template expression for producing a value at a given resolution` (per Tier 4 #4.9)
|
||||
- **Form anchor:** template expression (bounded form) → value at resolution (projection)
|
||||
- **Etymology (1-line):** Latin *transcendere*
|
||||
- **Definition history (1-line):** Per Cluster 1, Pattern 7
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 1, 0
|
||||
|
||||
### Term: "dot product"
|
||||
|
||||
- **Original notation:** `F.dot(gradient)` (per §5.6)
|
||||
- **Re-encoded:** `length-projection product` (per Tier 4 #4.10; user-also-accepted: `'scalar product'`)
|
||||
- **Form anchor:** `scalar product` (bounded form) → dot product (projection)
|
||||
- **Etymology (1-line):** English *dot* / Latin *scalar*
|
||||
- **Definition history (1-line):** Per Cluster 9; Sectored Language V1
|
||||
- **Source sections in original:** §5.6
|
||||
- **Cluster cross-ref:** Cluster 1, 9
|
||||
|
||||
### Term: "cross product"
|
||||
|
||||
- **Original notation:** `A.contract(B)` (per §5.6)
|
||||
- **Re-encoded:** `wedge product` (3D; per Tier 4 #4.11; user-also-accepted: `'cross product'`)
|
||||
- **Form anchor:** `wedge` (bounded form) → exterior product (projection)
|
||||
- **Etymology (1-line):** English *cross* / Old English *weecg*
|
||||
- **Definition history (1-line):** Per Cluster 1, 8, 9
|
||||
- **Source sections in original:** §5.6
|
||||
- **Cluster cross-ref:** Cluster 1, 8, 9
|
||||
|
||||
### Term: "anti-wedge"
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** `regressive product` / `contraction` / `interior product` (per Tier 4 #4.12)
|
||||
- **Form anchor:** `regressive product` (bounded form) → anti-wedge (projection)
|
||||
- **Etymology (1-line):** Latin *regressus* / *contractio* / *interior*
|
||||
- **Definition history (1-line):** Per Cluster 1, Pattern 6
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 1, P6
|
||||
|
||||
### Term: "negative"
|
||||
|
||||
- **Original notation:** `-epsilon * v` for negative perturbation (per §5.6)
|
||||
- **Re-encoded:** `F² operator` (the explicit-flip; per Tier 4 #4.13)
|
||||
- **Form anchor:** `F²` (bounded form) → twice-applied flip (projection)
|
||||
- **Etymology (1-line):** Latin *negare*
|
||||
- **Definition history (1-line):** Per Cluster 1, Pattern 7
|
||||
- **Source sections in original:** §5.6
|
||||
- **Cluster cross-ref:** Cluster 1, P7
|
||||
|
||||
### Term: "infinity"
|
||||
|
||||
- **Original notation:** `integral from 0 to infinity` (per §5.6)
|
||||
- **Re-encoded:** **BANNED** as a value per Rule 1; re-encoded as `T_max : float64` (the bounded integral bound)
|
||||
- **Form anchor:** N/A (BANNED)
|
||||
- **Etymology (1-line):** Latin *infinitas*
|
||||
- **Definition history (1-line):** Per Cluster 0; the BANNED infinity is per Rule 1 + per user's 2026-06-23 directive
|
||||
- **Source sections in original:** §5.6, §5.7
|
||||
- **Cluster cross-ref:** Cluster 0
|
||||
|
||||
### Term: "point"
|
||||
|
||||
- **Original notation:** `x : State = Vector[d]` (per §5 throughout)
|
||||
- **Re-encoded:** `Punctum` (Latin) / `σημεῖον` (Greek) (per Tier 4 #4.15; user-also-accepted)
|
||||
- **Form anchor:** `Punctum` (bounded form) → 0-dim element (projection)
|
||||
- **Etymology (1-line):** Greek *σημεῖον*; Latin *punctum*
|
||||
- **Definition history (1-line):** Per Cluster 7, 8
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** Cluster 7, 8
|
||||
|
||||
### Term: "straight line"
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** `Εὐθεῖα` (Greek) / `linea recta` (Latin) (per Tier 4 #4.16; user-also-accepted)
|
||||
- **Form anchor:** `Εὐθεῖα` (bounded form) → 1-dim element (projection)
|
||||
- **Etymology (1-line):** Greek *εὐθεῖα*
|
||||
- **Definition history (1-line):** Per Cluster 7
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 7
|
||||
|
||||
### Term: "kernel" (cross-domain)
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** `discrete subsystem that holds a continuous process up` (per Tier 4 #4.17)
|
||||
- **Form anchor:** `discrete subsystem` (bounded form) → support (projection)
|
||||
- **Etymology (1-line):** Old English *cyrnel*
|
||||
- **Definition history (1-line):** Per Cluster 0, Cluster B, P8
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 0, P8
|
||||
|
||||
### Term: "Bourbaki"
|
||||
|
||||
- **Original notation:** Per Cluster 0 — the source of reification problem
|
||||
- **Re-encoded:** **FOIL** (cultural opponent; per Tier 4 #4.18)
|
||||
- **Form anchor:** N/A (FOIL)
|
||||
- **Etymology (1-line):** Nicolas Bourbaki (pseudonym)
|
||||
- **Definition history (1-line):** Per Cluster 0, 9
|
||||
- **Source sections in original:** §2 implicit (per Cluster 0, Pattern 6)
|
||||
- **Cluster cross-ref:** Cluster 0, 9
|
||||
|
||||
### Term: "real" (in reals)
|
||||
|
||||
- **Original notation:** `expected(O_m) : float64` (per §5.6)
|
||||
- **Re-encoded:** `kind : Real` resolves to `quantity : float64` (per Tier 4 #4.19)
|
||||
- **Form anchor:** `kind : Real` (bounded form) → `quantity : float64` (projection)
|
||||
- **Etymology (1-line):** Latin *realis*
|
||||
- **Definition history (1-line):** Per Cluster 0, Cluster A, P2; user 2026-06-23
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** Cluster 0, A, P2
|
||||
|
||||
### Term: "Pi"
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** `kind : Pi` resolves to `quantity : float64` (per Tier 4 #4.20)
|
||||
- **Form anchor:** `kind : Pi` (bounded form) → `quantity : float64` (projection)
|
||||
- **Etymology (1-line):** Greek *πῖ*
|
||||
- **Definition history (1-line):** Per Cluster 0, DM2 §25; user 2026-06-23
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 0, DM2 §25
|
||||
|
||||
### Term: "quantity" (a value)
|
||||
|
||||
- **Original notation:** `expected(O_m) : float64` (per §5.6)
|
||||
- **Re-encoded:** `quantity(<value>) : <encoding>` (per Tier 4 #4.21)
|
||||
- **Form anchor:** `quantity` (bounded form) → `<encoding>` (projection)
|
||||
- **Etymology (1-line):** Latin *quantitas*
|
||||
- **Definition history (1-line):** Per user 2026-06-23
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** User 2026-06-23
|
||||
|
||||
### Term: "scalar" (a value)
|
||||
|
||||
- **Original notation:** `dt : float64`, `epsilon : float64`, `sigma : float64` (per §5 throughout)
|
||||
- **Re-encoded:** `scalar : <encoding>` (per Tier 4 #4.22)
|
||||
- **Form anchor:** `scalar` (bounded form) → `<encoding>` (projection)
|
||||
- **Etymology (1-line):** Latin *scalaris*
|
||||
- **Definition history (1-line):** Per user 2026-06-23
|
||||
- **Source sections in original:** §5 throughout
|
||||
- **Cluster cross-ref:** User 2026-06-23
|
||||
|
||||
### Term: "Lengyel's Standard GA"
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** **FOIL** (per Tier 4 #4.23)
|
||||
- **Form anchor:** N/A (FOIL)
|
||||
- **Etymology (1-line):** (named reference)
|
||||
- **Definition history (1-line):** Per Cluster 0
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 0
|
||||
|
||||
### Term: "Standard GA" (Hestenes, Dorst)
|
||||
|
||||
- **Original notation:** Not used in this lecture
|
||||
- **Re-encoded:** **FOIL** (per Tier 4 #4.24)
|
||||
- **Form anchor:** N/A (FOIL)
|
||||
- **Etymology (1-line):** (named reference)
|
||||
- **Definition history (1-line):** Per Cluster 0
|
||||
- **Source sections in original:** Not applicable
|
||||
- **Cluster cross-ref:** Cluster 0
|
||||
|
||||
---
|
||||
|
||||
## Decoded: encoding-explicit re-encodings (per Rule 5)
|
||||
|
||||
The following terms have explicit `encoding:` attributes per Rule 5:
|
||||
|
||||
| Term | Encoding | Conventional → Re-encoded |
|
||||
|---|---|---|
|
||||
| `Vector[d] : float64` | `float64` | "real-valued vector" → `Vector[d] : float64` |
|
||||
| `Tensor[d, d] : float64` | `float64` | "matrix" → `Tensor[d, d] : float64` |
|
||||
| `L_DSM(theta) : float64` | `float64` | "loss" → `Loss : float64` |
|
||||
| `expected(O_m) : float64` | `float64` | "expected value" → `expected : Observable -> float64` |
|
||||
| `dt, dW_t : float64` | `float64` | "infinitesimal increment" → `dt : float64`, `dW_t : float64` |
|
||||
| `epsilon : float64` | `float64` | "perturbation parameter" → `epsilon : float64` |
|
||||
| `sigma : float64` (noise scale) | `float64` | "noise scale" → `NoiseScale : float64` |
|
||||
| `sigma : float64` (in `Sigma(x; beta)` for diffusion) | `float64` | "diffusion coefficient" → `DiffusionCoeff : float64` |
|
||||
| `lambda : float64` (Tikhonov) | `float64` | "regularization" → `TikhonovCoeff : float64` |
|
||||
| `omega : float64` (angular frequency) | `float64` | "angular frequency" → `AngularFreq : float64` |
|
||||
| `T_max : float64` (trajectory length) | `float64` | "trajectory length" → `TrajectoryLength : float64` |
|
||||
| `d : int64` (state dimension) | `int64` | "dimension" → `Dim : int64` |
|
||||
| `P : int64` (parameter count) | `int64` | "parameter count" → `ParamCount : int64` |
|
||||
| `M : int64` (observable count) | `int64` | "observable count" → `ObsCount : int64` |
|
||||
| `N_samples, N_params, N_obs, N_lag : int64` | `int64` | "counts" → `Count : int64` |
|
||||
| `d_threshold : int64 = 10^4` | `int64` | "dimension threshold" → `DimThreshold : int64` |
|
||||
| `PlaSim SST raw_dimension : int64 = 2000` | `int64` | "dimension" → `Dim : int64` |
|
||||
| `KS Fourier_modes : int64 = 512` | `int64` | "Fourier modes" → `FourierModes : int64` |
|
||||
| `KS observed_modes : int64 = 32` | `int64` | "observed modes" → `ObservedModes : int64` |
|
||||
|
||||
---
|
||||
|
||||
## Decoded: FOILs and BANNED (per `lexicon.md` §2.4 Tier 4)
|
||||
|
||||
- **`Bourbaki`** is a FOIL (per Cluster 0, Pattern 6). Not directly referenced in this lecture.
|
||||
- **`"infinity"` (in §5.6 GFDT integral)** is BANNED as a value per Rule 1. Re-encoded as `T_max : float64` (the bounded integral bound).
|
||||
- **`Standard GA`** is a FOIL. Not referenced.
|
||||
- **`Lengyel's Standard GA`** is a FOIL. Not referenced.
|
||||
|
||||
---
|
||||
|
||||
## Verification (per `lexicon.md` §12)
|
||||
|
||||
- [x] **Lossless** — 72 terms decoded (12 Tier 1 + 18 Tier 2 + 18 Tier 3 + 24 Tier 4)
|
||||
- [x] **Bounded** — no `∞_val`. The "infinity" in §5.6 GFDT integral is BANNED per Rule 1 and re-encoded as `T_max : float64`.
|
||||
- [x] **Encoding-explicit** — every value-bearing term has `encoding:` (default `float64`; `int64` for exact integers).
|
||||
- [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] **Tier-categorized** — per pilot process improvement #2 (organized by Tier 1-4, not by math section).
|
||||
|
||||
---
|
||||
|
||||
## See also
|
||||
|
||||
- `lexicon.md` (the codified operational spec) — see §2.4 Tier 4 entries 4.1-4.24
|
||||
- `dedup_map.md` (the 6 noise-dedup maps)
|
||||
- `score_dynamics_giorgini_translation.md` (the side-by-side table) — 57 rows
|
||||
- `score_dynamics_giorgini_deobfuscated.md` (the re-encoded report) — 12 math sections
|
||||
|
||||
---
|
||||
|
||||
*End of `score_dynamics_giorgini_decoder.md`. Total: 72 terms decoded across 4 tiers. The shape of the re-encoding, not the verbatim content of any specific sample. Per pilot process improvement #2: tier-categorized (not by math section).*
|
||||
Reference in New Issue
Block a user