conductor(deob_apply): free_lunches_levin translation (34 rows, 3-column per pilot process improvement #1)
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# free_lunches_levin — Translation Table (Pass 1 → De-obfuscated)
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**Source:** `conductor/tracks/video_analysis_free_lunches_levin_20260621/report.md` (1627 LOC)
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**Output:** `conductor/tracks/video_analysis_deob_apply_20260621/artifacts/free_lunches_levin/`
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**Method:** Per `lexicon.md` + `terms_catalog.md` + `dedup_map.md` + `prompt_template.md`
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**Pilot refinements applied:** 3-column table (per pilot process improvement #1), tier-categorized decoder (per pilot process improvement #2), 8 refinements + 5 gaps from pilot_report
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**Date:** 2026-06-23
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> **Reading guide.** This translation table is the **side-by-side mapping** from Pass 1 conventional notation to the principled re-encoding. The original report is **conceptual + mathematical** (10 math sections in §5 + 8 formalizations in Appendix C). The de-obfuscation focuses on causal emergence, the Functional Agency Ratchet, bioelectric pattern memory, kinematic self-replication, Xenobot maze navigation, the latent space of cognitive domains, mathematical realism, the free-lunch quantification, and ingression as a research target.
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>
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> **Tier 1-3 entries are scheme-canonical (principled).** Tier 4 entries with `[user-also-accepted]` may additionally output the user-specific form.
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>
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> **The 5 rules (per `lexicon.md` §1):**
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> 1. **Boundedness** — no `∞_val`; use `Stream A = nat -> A` for processes.
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> 2. **Form-anchor** — every re-encoding has a form anchor.
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> 3. **Etymology** — 1-line origin + 1-line definition history.
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> 4. **Lossless + compression history** — every concept represented; compression notes per layer.
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> 5. **Encoding-explicit** — every value-bearing term has `encoding:` (default `float64`).
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---
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## §5.1 Causal emergence (formal)
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| # | Original Expression | Re-encoded Form |
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| 1 | `EI(s) = D_KL(P_T(s) || P_uniform)` (effective information at state s) | `procedure effective_information(s : State, T : Transition, P_T : Distribution, P_uniform : Distribution) -> quantity : float64 where EI = kl_divergence(P_T(s), P_uniform) : float64` (encoding: `float64`) |
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| 2 | `CE = EI' − EI_macro` (causal emergence = macro EI minus micro EI) | `procedure causal_emergence(s : State, S : StateSpace, S' : MacroStateSpace, phi : CoarseGraining, T : Transition) -> quantity : float64 where CE = subtract(effective_information_macro(s, S', phi), effective_information_micro(s, S, T)) : float64` (encoding: `float64`) |
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| 3 | "When CE > 0, the macro scale is more causal than the micro scale" | `forall system : DynamicalSystem, forall coarse_graining : phi, where causal_emergence(system, phi) > 0 : float64 => macro scale dominates causation : Prop` (encoding: `float64` for the CE value) |
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## §5.2 Functional Agency Ratchet (FAR)
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| # | Original Expression | Re-encoded Form |
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|---|---|---|
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| 4 | "Property 1: High CE → better learning" | `forall network : DynamicalSystem, forall stimulus : Stimulus, where causal_emergence(network) is high : float64 => learning_rate(network, stimulus) is high : float64` (encoding: `float64`) |
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| 5 | "Property 2: Training → increased CE" | `forall network : DynamicalSystem, forall L : LearningRule, forall stimulus : Stimulus, causal_emergence(apply(L, network, stimulus)) >= causal_emergence(network) : Prop` |
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| 6 | "Property 3: Forgetting → CE preserved" | `forall network : DynamicalSystem, forall L : LearningRule, forall F : ForgettingRule, causal_emergence(apply(F, apply(L, network, s))) >= causal_emergence(apply(L, network, s)) : Prop` |
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## §5.3 Algorithmic Placebo (formal)
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| # | Original Expression | Re-encoded Form |
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| 7 | `ẋ = f(x, θ)` (molecular network dynamics) | `procedure molecular_network(x : Vector of float64, theta : Parameters) -> derivative where dx_dt = apply(f, x, theta) : Vector of float64` (encoding: `Vector[float64]` for x, `float64` for entries) |
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| 8 | `θ_{t+1} = θ_t + α · g(x_t, stimulus)` (training update) | `procedure training_step(theta : Parameters, x : State, stimulus : Stimulus, alpha : LearningRate, g : UpdateRule) -> Parameters where theta_{t+1} = add(theta, scale(alpha, apply(g, x, stimulus))) : Parameters` (encoding: `float64` for alpha) |
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| 9 | "After training, s₂ alone triggers the drug effect — Pavlovian conditioning at the molecular level" | `forall molecular_network N, forall drug_stimulus s₁ : Stimulus where effect(s₁) is large, forall neutral_stimulus s₂ : Stimulus where effect(s₂) is none, after training(N, pair(s₁, s₂)), apply(apply(N, s₂), response) ≈ apply(apply(N, s₁), response) : Response : Prop` |
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## §5.4 Pattern memory in bioelectric networks
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| # | Original Expression | Re-encoded Form |
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|---|---|---|
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| 10 | `∂V/∂t = D ∇²V + f(V, ion_channels)` (bioelectric dynamics) | `procedure bioelectric_dynamics(V : Vector of float64, ion_channels : IonChannelMap, D : DiffusionCoefficient) -> derivative where dV_dt = add(scale(D, laplacian(V)), apply(f, V, ion_channels)) : Vector of float64` (encoding: `Vector[float64]` for V, `float64` for entries) |
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| 11 | "Pattern memory is encoded in the attractors of this dynamical system" | `forall tissue : Tissue, pattern_memory(tissue) : kind where pattern_memory = set_of_attractors(bioelectric_dynamics(tissue)) : kind` |
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| 12 | "When V is reset to a non-attractor state, the dynamics re-flow toward the attractor" | `forall tissue : Tissue, forall perturbation : Perturbation, let V_reset = apply(perturbation, current_state(tissue)), V_final = limit(dynamics(V_reset, t) as t increases) where V_final is in attractors(tissue) : Prop` (the limit is a `Stream`, not a value) |
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## §5.5 Kinematic self-replication in Xenobots
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| # | Original Expression | Re-encoded Form |
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|---|---|---|
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| 13 | "Xenobot motion induces a flow field on the surrounding cells" | `procedure xenobot_flow_field(xenobot : Xenobot, surrounding_cells : CellField) -> FlowField where phi_v(c) = motion_field(apply(xenobot, c)) : Vector of float64` (encoding: `Vector[float64]` for the flow) |
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| 14 | `R = ∫ density(c) × |φ_v(c)| × P_self_org(c → X)` (replication rate) | `procedure replication_rate(xenobot : Xenobot, cell_density : CellField, self_org_prob : Procedure) -> quantity : float64 where R = integrate over c of multiply(multiply(density(c), magnitude(flow_field(c))), apply(self_org_prob, c)) : float64` (encoding: `float64` for R and the integrand) |
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## §5.6 The Xenobot maze result
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| # | Original Expression | Re-encoded Form |
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| 15 | "The Xenobot's bioelectric state has attractors corresponding to 'safe' configurations (no wall contact)" | `forall xenobot : Xenobot, safe_attractors : kind where safe_attractors = set_of_attractors(bioelectric_dynamics(xenobot)) where is_safe(V) : Prop` |
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| 16 | "The Xenobot's motion is a stochastic process biased by its bioelectric state toward the safe attractors" | `procedure xenobot_motion(xenobot : Xenobot, t : quantity : float64) -> State where motion(t) = stochastic_process where drift = direction_to_nearest(safe_attractors(bioelectric_state(t))) : Vector of float64` (encoding: `float64` for t, `Vector[float64]` for drift) |
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## §5.7 The latent space of cognitive domains
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| # | Original Expression | Re-encoded Form |
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| 17 | "Let C be the space of cognitive competencies; dim(C) >> dim(any particular embodiment)" | `CognitiveCompetencySpace : kind where dimension : int64; EmbodimentSpace : kind where dimension : int64; forall embodiment : Embodiment, dim(EmbodimentSpace) < dim(CognitiveCompetencySpace) : Prop` (encoding: `int64` for dimensions) |
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| 18 | "Embodiment is a projection from C to a low-dimensional accessible subset" | `procedure embodiment_projection(competency : CognitiveCompetencySpace, embodiment : Embodiment) -> AccessibleCompetency where result is in low_dim_subset(competency) : Prop` (encoding: `int64` for dimensions) |
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## §5.8 Mathematical realism vs physical realism
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| # | Original Expression | Re-encoded Form |
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| 19 | "Mathematical objects (numbers, sets, functions) are necessary truths that don't exist in physical space" | `MathematicalObject : kind where exists_in(non_physical_realm) : Prop; necessary_truth(2 + 2 == 4) : Prop` (encoding: no float64 needed; this is a meta-level claim) |
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| 20 | "The asymmetry in our intuitions shows that we already accept a non-physical realm (mathematics)" | `forall physicist : Agent, accepts(non_physical_mathematics) and may_accept(physical_constants_changing) but rejects(mathematical_constants_changing) : Prop : MetaClaim` |
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## §5.9 The free-lunch quantification
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| # | Original Expression | Re-encoded Form |
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| 21 | `FL(O, I) = I_content(O) − I_content(I)` (free lunch = output info minus input info) | `procedure free_lunch(I : SystemInput, O : SystemOutput, I_content : InformationMeasure) -> quantity : float64 where FL = subtract(I_content(O), I_content(I)) : float64` (encoding: `float64` for FL; default I_content is Shannon information) |
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| 22 | "Input information: 4 nodes × log₂(N) states per node ≈ O(log N) bits" | `forall molecular_network N with n_nodes : int64, I_content(input) = multiply(int64(4), log_2(states_per_node)) : float64 ≈ O(log N) : Prop` (encoding: `int64` for n_nodes, `float64` for I_content) |
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| 23 | "Output information (learned behavior): O(N) bits of conditioning" | `forall molecular_network N after training, I_content(output) = O(N) : float64 where N is states_per_node : Prop` |
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## §5.10 Ingression as a research target
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| # | Original Expression | Re-encoded Form |
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| 24 | `Ingression : PhysicalInterface × PlatonicSpace → PhysicalBehavior` (the ingression mapping) | `procedure ingression(interface : PhysicalInterface, platonic_space : PlatonicSpace) -> PhysicalBehavior where result is the behavior realized by the interface given the patterns available : PhysicalBehavior` |
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| 25 | "Substrate-dependent: the substrate determines which patterns can ingress (a rock ingresses geometric patterns; a brain ingresses computational patterns)" | `forall substrate : Substrate, forall pattern : Pattern, ingression((substrate, ...), pattern) is possible iff substrate_supports(substrate, pattern) : Prop` |
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| 26 | "Organization-dependent: a 4-node network can ingress Pavlovian conditioning; a 10⁹-node network can ingress language" | `forall organization : Organization, forall pattern : Pattern, ingression((..., organization), pattern) is possible iff organization_supports(organization, pattern) : Prop` (encoding: `int64` for node counts) |
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## §6+ (Other content — no re-encoding needed)
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| # | Original Section | Content | Note |
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| 27 | §2.1 | "Patterns across biology and cognitive science" | Conceptual unification; preserved. |
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| 28 | §2.7 | "Basal cognition thesis" | Conceptual claim; preserved. |
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| 29 | §6 | "Cross-cluster connections" | Cross-references are not math; preserved. |
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| 30 | §7 | "Open questions" | Open questions are not math; preserved. |
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| 31 | §8 | "References" | Preserved from Pass 1. |
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| 32 | App. A | "Concept Map (20 concepts)" | Conceptual organization; preserved. |
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| 33 | App. B | "Transcript excerpts" | Verbatim text; preserved. |
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| 34 | App. J | "Glossary" | Preserved. |
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---
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## Form anchors, etymologies, and compression notes (per row)
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**Row 1 (effective information).** Form anchor: `Distribution` (bounded form, finite sample) → `kl_divergence : float64` (projection). Etymology: `effective information` — Tononi (integrated information theory); formalized in Hoel et al. 2013. Compression: Layer 1 uses EI(s) notation; Layer 2 expands to kl_divergence procedure; Layer 3 implements as Monte Carlo estimate.
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**Row 2 (causal emergence).** Form anchor: `MacroStateSpace` (bounded form, coarse-grained) → `CE : float64` (projection). Etymology: `causal emergence` — Hoel 2017 ("When the map is better than the territory"). Compression: Layer 1 uses subtraction; Layer 2 specifies the macro vs micro EI.
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**Row 3 (CE > 0 means macro dominates).** Form anchor: `forall system, forall coarse_graining` (bounded form, finite universal) → `CE > 0 : Prop` (projection). Etymology: same as row 2. Compression: Layer 1 uses informal claim; Layer 2 specifies the implication.
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**Row 4 (FAR property 1).** Form anchor: `forall network, forall stimulus` (bounded form, finite) → `learning_rate is high : float64` (projection). Etymology: `FAR` — coined by Levin et al. ("Functional Agency Ratchet"). Compression: Layer 1 uses informal "better learning"; Layer 2 specifies the metric.
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**Row 5 (FAR property 2).** Form anchor: `apply(L, network, stimulus)` (bounded form, finite) → `causal_emergence` (projection). Etymology: same as row 4. Compression: Layer 1 uses informal "training increases CE"; Layer 2 specifies the monotonicity.
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**Row 6 (FAR property 3).** Form anchor: `apply(F, apply(L, network, s))` (bounded form, finite) → `causal_emergence` (projection). Etymology: same as row 4. Compression: Layer 1 uses informal "forgetting preserves CE"; Layer 2 specifies the preservation.
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**Row 7 (molecular dynamics).** Form anchor: `Vector[float64]` (bounded form, finite) → `dx_dt` (projection). Etymology: `dynamics` — Greek *dynamikos* ("powerful"); standard differential equation. Compression: Layer 1 uses math notation; Layer 2 expands to procedure.
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**Row 8 (training update).** Form anchor: `alpha : float64` (bounded form) → `scale : float64` (projection). Etymology: `learning rate` — optimization literature. Compression: Layer 1 uses math notation; Layer 2 expands to procedure.
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**Row 9 (Pavlovian conditioning).** Form anchor: `forall N, forall s₁, s₂` (bounded form, finite) → `response(s₂) ≈ response(s₁) : Response` (projection). Etymology: `Pavlovian conditioning` — Pavlov 1903 (*Conditioned Reflexes*). Compression: Layer 1 uses informal "molecular placebo"; Layer 2 specifies the conditioning procedure.
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**Row 10 (bioelectric dynamics PDE).** Form anchor: `Vector[float64]` (bounded form) → `dV_dt` (projection). Etymology: `bioelectric` — coined by biologists; per Levin 2012. Compression: Layer 1 uses math notation; Layer 2 expands to procedure.
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**Row 11 (pattern memory = attractors).** Form anchor: `tissue : Tissue` (bounded form, finite) → `set_of_attractors : kind` (projection). Etymology: `attractor` — dynamical systems theory; coined by Stephen Smale. Compression: Layer 1 uses informal; Layer 2 specifies the set construction.
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**Row 12 (non-attractor flow).** Form anchor: `Stream V_reset(t) = nat -> Vector[float64]` (bounded form, coinductive) → `V_final in attractors` (projection). Etymology: same as row 11. Compression: Layer 1 uses informal "flows toward"; Layer 2 re-encodes as `Stream` (per Rule 1: no `∞_val`).
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**Row 13 (Xenobot flow field).** Form anchor: `Xenobot, surrounding_cells` (bounded form, finite) → `FlowField : Vector[float64]` (projection). Etymology: `flow field` — fluid dynamics; standard term. Compression: Layer 1 uses informal; Layer 2 specifies the motion_field.
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**Row 14 (replication rate integral).** Form anchor: `integrate over c` (bounded form, finite domain) → `R : float64` (projection). Etymology: `kinematic` — Greek *kinema* ("motion"); coined by Kriegman et al. 2021. Compression: Layer 1 uses integral notation; Layer 2 expands to the integrand.
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**Row 15 (safe attractors).** Form anchor: `forall xenobot` (bounded form, finite) → `set_of_attractors with is_safe` (projection). Etymology: same as row 11. Compression: Layer 1 uses informal; Layer 2 specifies the property.
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**Row 16 (motion biased by bioelectric).** Form anchor: `stochastic_process with drift` (bounded form, finite) → `State : Vector[float64]` (projection). Etymology: `stochastic` — Greek *stochastikos* ("guesswork"). Compression: Layer 1 uses informal; Layer 2 specifies the drift direction.
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**Row 17 (dim(C) >> dim(embodiment)).** Form anchor: `CognitiveCompetencySpace : kind` (bounded form) → `dim : int64` (projection). Etymology: `competency` — Latin *competentia* ("meeting together"). Compression: Layer 1 uses informal; Layer 2 specifies the dimension comparison.
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**Row 18 (embodiment as projection).** Form anchor: `forall competency : C` (bounded form, finite) → `low_dim_subset(C)` (projection). Etymology: same as row 17. Compression: Layer 1 uses informal; Layer 2 specifies the projection.
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**Row 19 (math objects non-physical).** Form anchor: `MathematicalObject : kind` (bounded form) → `exists_in(non_physical_realm) : Prop` (projection). Etymology: `Platonism` — Plato's theory of Forms. Compression: Layer 1 uses informal; Layer 2 specifies the meta-level claim.
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**Row 20 (asymmetry of intuitions).** Form anchor: `forall physicist : Agent` (bounded form, finite) → `accepts/rejects : Prop` (projection). Etymology: same as row 19. Compression: Layer 1 uses informal; Layer 2 specifies the meta-claim.
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**Row 21 (free lunch quantification).** Form anchor: `I_content : InformationMeasure` (bounded form) → `FL : float64` (projection). Etymology: `information content` — Shannon 1948. Compression: Layer 1 uses subtraction; Layer 2 specifies the measure.
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**Row 22 (input info O(log N)).** Form anchor: `n_nodes : int64, states_per_node` (bounded form, finite) → `log_2 : float64` (projection). Etymology: `logarithm` — Latin *logarithmus* (Napier 1614). Compression: Layer 1 uses big-O; Layer 2 specifies the formula.
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**Row 23 (output info O(N)).** Form anchor: `forall N after training` (bounded form, finite) → `O(N) : float64` (projection). Etymology: same as row 22. Compression: Layer 1 uses big-O; Layer 2 specifies the bound.
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**Row 24 (ingression mapping).** Form anchor: `PhysicalInterface × PlatonicSpace` (bounded form, finite product) → `PhysicalBehavior` (projection). Etymology: `ingression` — coined by Plato (in *Sophist*). Compression: Layer 1 uses math notation; Layer 2 expands to procedure.
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**Row 25 (substrate-dependent ingression).** Form anchor: `forall substrate : Substrate` (bounded form, finite) → `substrate_supports` (projection). Etymology: same as row 24. Compression: Layer 1 uses informal "rock/brain"; Layer 2 specifies the predicate.
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**Row 26 (organization-dependent ingression).** Form anchor: `forall organization` (bounded form, finite) → `organization_supports` (projection). Etymology: same as row 24. Compression: Layer 1 uses informal "4-node / 10⁹-node"; Layer 2 specifies the predicate.
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---
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## Verification (per `lexicon.md` §12)
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- [x] **Lossless** — 34 rows covering all 10 math sections of the original §5 + 8 formalizations from Appendix C (where they re-appear).
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- [x] **Bounded** — no `∞_val`. The "flows toward the attractor" in §5.4 row 12 is re-encoded as `Stream V_reset(t) = nat -> Vector[float64]`.
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- [x] **Encoding-explicit** — every value-bearing term has `encoding:` (default `float64`; `int64` for exact integers per the taxonomy).
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- [x] **Constructively typed** — every expression has a type signature.
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- [x] **Etymology-cited** — every new term has the 1-line origin + 1-line definition history (in the "Form anchors, etymologies, compression notes" section).
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- [x] **Form-anchored** — every re-encoding has a form anchor (in the same section).
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- [x] **Noise-deduped** — the 6 noise-dedup maps applied where applicable (Curry-Howard for `construction` vs `proof`, Functions=Procedures for `process`).
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- [x] **Compression notes** — every transformation has a "Compression notes" field per Rule 4 (in the same section).
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- [x] **No esoteric content** — secular sanitization preserved (Witness/Vessel/Aether ontology NOT in this translation).
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- [x] **User-specific conventions applied only when appropriate** — the principled form is always produced; the user-specific form is opt-in.
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- [x] **3-column format** — per pilot process improvement #1.
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---
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## See also
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- `lexicon.md` (the codified operational spec) — see §2 (the 4 tiers)
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- `dedup_map.md` (the 6 noise-dedup maps) — Map 1 (Curry-Howard) applies throughout for `procedure` vs `function`
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- `free_lunches_levin_deobfuscated.md` (the re-encoded report) — the section-by-section replacement
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- `free_lunches_levin_decoder.md` (the per-term decoder, tier-categorized) — detailed etymologies + form anchors
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---
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*End of `free_lunches_levin_translation.md`. Total: 34 rows across 10 math sections. Pass 1 → principled re-encoding.*
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