conductor(deob_apply): multiscale_hoffman translation (3-column, per pilot process improvement #1)
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# multiscale_hoffman — Translation Table (Pass 1 → De-obfuscated)
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**Source:** `conductor/tracks/video_analysis_multiscale_hoffman_20260621/report.md` (1435 LOC)
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**Output:** `conductor/tracks/video_analysis_deob_apply_20260621/artifacts/multiscale_hoffman/`
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**Method:** Per `lexicon.md` + `prompt_template.md` (5 rules + 6 noise-dedup maps + 4-layer format + 7 example transformations)
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**Date:** 2026-06-23
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> **Reading guide (per pilot process improvement #1).** This is a **3-column translation table** (instead of the 6-column form): `# | Original Expression | Re-encoded Form`. The form anchor + etymology + compression notes are recorded in a separate section per row below the table. This reduces visual clutter while preserving the form-anchor and etymology requirements.
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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: "What bounded form does this project from the indefinite?"
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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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> **Principled vs user-specific:** the principled form is always produced; the user-specific form (per `[user-also-accepted]` tags) is opt-in. The Sectored Language V1 forms + GA reinterpretations + classical Greek/Latin/Sanskrit are NOT applied to the public deliverables.
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---
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## §5.1 Markov chain definition
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| # | Original Expression | Re-encoded Form |
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|---|---|---|
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| 1 | `P(X_{t+1} = s_j \| X_t = s_i) = M(i, j)` (Markov property) | `markov_property : forall (t : int64, i, j : int64) : P(next(s_i, t) = s_j \| current(t) = s_i) = M(i, j) : float64` (encoding: `i, j : int64`, `M(i, j) : float64`) |
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| 2 | "M is an N×N transition matrix with non-negative entries and row sums equal to 1" (Markov matrix) | `markov_matrix : Prop where forall (i, j : int64) : M(i, j) >= 0 : float64 and sum (j) of M(i, j) = 1 : float64` |
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| 3 | "π is a stationary distribution if π = π M" | `stationary_distribution(pi, M) : Prop where forall (j) : pi(j) = sum (i) of pi(i) * M(i, j) : float64` |
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---
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## §5.2 The trace
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| # | Original Expression | Re-encoded Form |
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|---|---|---|
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| 4 | "τ = (s_0, s_1, s_2, ...)" (the trace as infinite sequence) | `trace : Stream[State]` where `Stream[State] = nat -> State` (BANNED `infinity` re-encoded as `Stream` per Rule 1; per pilot refinement #2) |
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| 5 | `Ω(S) = S^ℕ` (the set of all possible traces) | `Omega(S) : Set[Stream[State]]` (the set of all traces; BANNED `infinity` re-encoded as `Stream[State]`) |
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| 6 | `P(τ) = 1 · M(s_0, s_1) · M(s_1, s_2) · ...` (the trace probability) | `P : (tau : Stream[State]) -> float64` where `P(tau) = product (t in 0..StreamBound : int64) of M(tau(t), tau(t+1)) : float64` (BANNED `infinity` re-encoded as `StreamBound : int64` per Rule 1) |
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---
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## §5.3 The trace order
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| # | Original Expression | Re-encoded Form |
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| 7 | "τ ≤ σ iff τ is a subsequence of σ" (the trace order definition) | `trace_order : (tau, sigma : Stream[State]) -> Prop` where `tau <= sigma := tau is_subsequence_of sigma : Prop` |
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| 8 | "The trace order is reflexive, antisymmetric, transitive" (partial order) | `partial_order : Prop where reflexive(tau <= tau) and antisymmetric((tau <= sigma and sigma <= tau) implies tau == sigma) and transitive : Prop` |
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---
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## §5.4 Trace logic
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| # | Original Expression | Re-encoded Form |
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|---|---|---|
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| 9 | "The trace logic is the lattice (Ω(S), ≤, ∪, ∩, ∅, S^ℕ)" (lattice structure) | `trace_lattice : Lattice where Lattice = (Omega(S), <=, union, intersect, empty, full) : Type` (the lattice structure; BANNED `infinity` re-encoded as `Stream[State]`) |
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| 10 | "The lattice is not Boolean because not every element has a complement in the lattice" | `not_boolean : Prop where exists (tau : Omega(S)) : not exists (complement : Omega(S)) : complement is_complement_of tau : Prop` |
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---
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## §5.5 Boolean sublogics
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| # | Original Expression | Re-encoded Form |
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|---|---|---|
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| 11 | "For any state s ∈ S, the Boolean sublogic is the set of traces passing through s" | `boolean_sublogic : (s : State) -> Set[Stream[State]]` where `boolean_sublogic(s) = {tau : Stream[State] \| s in tau}` |
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| 12 | "This set is closed under union, intersection, and complement (within the sublogic)" | `boolean_closed : Prop where closed_under(union) and closed_under(intersect) and closed_under(complement) : Prop` |
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| 13 | "So Ω_s is a Boolean lattice with 2^|{s' : s' can reach s}| members" | `boolean_lattice_size : Prop where |boolean_sublogic(s)| = 2^|reachable(s)| : int64` |
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---
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## §5.6 Policy as Markov matrix on trace logic
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| # | Original Expression | Re-encoded Form |
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| 14 | "A policy is a Markov matrix P: Ω(S) → Ω(S)" | `policy : MarkovMatrix(Omega(S))` (a Markov matrix on the trace logic) |
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| 15 | "Attention shift: P(τ \| current_trace) is concentrated on traces containing a specific element" | `attention_shift : Prop where exists (target : State) : P(tau \| current) is_concentrated_on(tau containing target) : Prop` |
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| 16 | "Scale shift: P(τ \| current_trace) is concentrated on traces at a specific time resolution" | `scale_shift : Prop where exists (resolution : int64) : P(tau \| current) is_concentrated_on(tau at resolution) : Prop` |
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| 17 | "Reparameterization: P(τ \| current_trace) is concentrated on traces with the same structure but different symbol names" | `reparameterization : Prop where exists (rename : State -> State) : P(tau \| current) is_concentrated_on(rename(tau)) : Prop` |
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---
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## §5.7 Recursive trace logic
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| # | Original Expression | Re-encoded Form |
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| 18 | "The recursive trace logic is the iteration: let P be the space of policies; then P has its own trace logic Ω(P)" | `recursive_trace_logic : Prop where exists (P : PolicySpace) : trace_logic(P) = Omega(P) : Set[Stream[Policy]]` |
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| 19 | "Level 0: state space S" | `level_0 : StateSpace` |
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| 20 | "Level 1: trace logic Ω(S)" | `level_1 : Omega(StateSpace)` |
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| 21 | "Level 2: policy space P(Ω(S)) with trace logic Ω(P)" | `level_2 : Omega(PolicySpace)` |
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| 22 | "The recursion terminates when the policy space is 'fixed'" | `termination : Prop where exists (fixed_point : PolicySpace) : policy(fixed_point) == identity : Prop` |
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---
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## §5.8 Community structure via eigen analysis
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| # | Original Expression | Re-encoded Form |
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|---|---|---|
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| 23 | "M has N eigenvalues 1 = λ₁ ≥ \|λ₂\| ≥ ... ≥ \|λ_N\|" (spectral decomposition) | `spectral_decomposition : Prop where forall (lambda : eigenvalues(M)) : abs(lambda) is_sorted : Prop` |
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| 24 | "States i and j are in the same community if \|λ_k\| is close to 1 for the eigenvector k that groups them" | `community : (i, j : int64) -> Prop where exists (k : int64) : abs(lambda_k) close_to 1.0 and groups(eigenvector_k, {i, j}) : Prop` |
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| 25 | "The community structure is multiscale: at different scales (different cuts in the eigenvalue spectrum), different communities emerge" | `multiscale_community : Prop where forall (cut : float64) : community_structure(cut) : Prop` |
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---
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## §5.9 Intelligence metric K
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| # | Original Expression | Re-encoded Form |
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| 26 | `K = log₁₀(T_blind / T_mix)` (the intelligence metric) | `intelligence_metric_K : float64 = log_10(T_blind / T_mix) : float64` (encoding: `T_blind, T_mix : int64`) |
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| 27 | "T_blind = time for random (uniform) search to reach the stationary distribution" | `T_blind : int64 = mixing_time(uniform_distribution, stationary_distribution) : int64` (encoding: `int64`) |
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| 28 | "T_mix = time for the Markov dynamics to mix to within ε of the stationary distribution" | `T_mix : int64 = mixing_time(markov_dynamics, stationary_distribution, epsilon) : int64` (encoding: `int64`, `epsilon : float64`) |
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| 29 | "K = 0 means the Markov dynamics is no better than random search" | `K_zero : Prop where K == 0 : Prop` (the baseline) |
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| 30 | "K > 0 means the Markov dynamics is more efficient than random" | `K_positive : Prop where K > 0 : Prop` (the efficiency claim) |
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---
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## §5.10 Eigen functions of enhanced Markov chains
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| # | Original Expression | Re-encoded Form |
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| 31 | "Let M be an 'enhanced' Markov matrix — i.e., a matrix whose entries depend on the current state" (the setup) | `enhanced_markov_matrix : (state : State) -> Matrix where M[state](i, j) : float64` (state-dependent matrix) |
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| 32 | "The eigen functions of M are identical in form to the quantum wave functions of free particles" | `theorem : eigen_functions(M) ≡ quantum_wave_functions(free_particles) : Set[Function]` (Hoffman-Prakash 2014) |
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| 33 | "Enhanced Markov matrices have eigen functions of the form ψ_n(x) = e^{ikx} (plane waves)" | `eigen_function_form : forall (n : int64) : psi_n(x) = exp(i * k * x) : Complex : Prop` (encoding: `k : float64`, `x : float64`) |
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| 34 | "Quantum theory is the asymptotic description of the Markov dynamics" | `quantum_as_asymptotic : Prop where quantum_theory == asymptotic_description(markov_dynamics) : Prop` |
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---
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## §5.11 The no-cloning theorem without unitarity
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| # | Original Expression | Re-encoded Form |
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| 35 | "Markov chains satisfy a no-cloning theorem: an arbitrary Markov state cannot be perfectly copied by a Markov operation" (theorem statement) | `theorem_no_cloning : forall (C : CloningOperation) : exists (state : State) : C(state) != state ⊗ state : MarkovState : Prop` (Hoffman-Prakash, the Markov no-cloning) |
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| 36 | "The proof uses only linearity, not unitarity" | `proof_uses_only_linearity : Prop` (the key feature distinguishing from quantum no-cloning) |
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| 37 | "By linearity of Markov operations, C must satisfy C(ρ ⊗ σ) = ρ ⊗ ρ for all ρ, σ" | `linearity_constraint : forall (rho, sigma : MarkovState) : C(rho ⊗ sigma) = rho ⊗ rho : MarkovState` (this is contradictory; see row 35) |
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---
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## §5.12 Spacetime from trace logic
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| # | Original Expression | Re-encoded Form |
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| 38 | "Time: define time as the partial order on traces" | `time_definition : Prop where time == partial_order(traces) : Prop` |
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| 39 | "Space: define space as the equivalence classes of traces under time-shift" | `space_definition : Prop where space == equivalence_classes(traces, time_shift) : Prop` |
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| 40 | "Metric: define the spacetime metric from the conditional probability structure of traces" | `metric_definition : Prop where metric == conditional_probability_structure(traces) : Prop` |
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| 41 | "Time dilation: if a Markov chain has slow-mixing communities, then traces passing through different communities have different effective time scales" | `time_dilation : Prop where slow_mixing implies different_time_scales(community_a, community_b) : Prop` |
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---
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## §5.13 The trace blanket (Markov blanket)
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| # | Original Expression | Re-encoded Form |
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| 42 | "The trace blanket is the set of traces that: exit the agent, enter the agent, are invisible to the agent" | `trace_blanket : Set[Stream[State]]` where `trace_blanket = {tau : exit(tau) or enter(tau) or invisible(tau)} : Set[Stream[State]]` |
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| 43 | "The trace blanket is the Markov blanket in Fields' generic systems framework" | `trace_blanket_is_markov_blanket : Prop where trace_blanket == markov_blanket (per Fields' framework) : Prop` (the cross-cluster reference) |
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---
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## §5.14 Bayes rule as meet in trace logic
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| # | Original Expression | Re-encoded Form |
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| 44 | `π_post(τ) = π_likelihood(τ) · π_prior(τ) / Z` (Bayes rule) | `bayes_rule : (tau : Stream[State]) -> float64` where `pi_post(tau) = pi_likelihood(tau) * pi_prior(tau) / Z : float64` (encoding: `Z : float64`) |
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| 45 | "Posterior = projection of prior × likelihood onto the meet (the largest lower bound in the lattice)" | `posterior_as_meet : Prop where pi_post == projection(pi_prior * pi_likelihood, meet(pi_prior, pi_likelihood)) : Prop` |
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---
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## §5.15 Connection to Friston's free energy principle
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| # | Original Expression | Re-encoded Form |
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| 46 | "The system is a Markov chain" | `system_is_markov : Prop where forall (S : System) : markov_chain(S) : Prop` |
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| 47 | "F is a function of the trace: F(τ) = -log P(observation \| τ) + KL(τ \|\| prior)" | `free_energy : (tau : Stream[State]) -> float64` where `F(tau) = -log(P(obs \| tau)) + KL(tau, prior) : float64` |
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| 48 | "Minimizing F selects the trace that best explains observations while staying close to prior" | `min_F_selects_trace : Prop where minimize(F) implies argmin_tau P(obs \| tau) * closeness(tau, prior) : Prop` |
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| 49 | "The 80% complete state includes: problem spaces defined within the trace logic, free energy minimization as trace optimization, etc." | `synthesis_paper_80pct : Prop where implemented(problem_spaces_in_trace_logic) and implemented(F_minimization_as_trace_optimization) and implemented(VFE_as_metric) : Prop` |
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---
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## §5.16 Connection to causal emergence
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| # | Original Expression | Re-encoded Form |
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| 50 | "Causal emergence: macro level can be more causal than micro level" (Hoel-Albantakis-Tononi) | `causal_emergence : Prop where causal_power(macro_level) > causal_power(micro_level) : Prop` |
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| 51 | "Micro level: individual Markov states" | `micro_level : State` (the Markov state) |
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| 52 | "Macro level: communities (sets of states with slow mixing between them)" | `macro_level : Set[State]` (the community) |
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| 53 | "K measures how much the Markov dynamics is more efficient than random search — i.e., how much causal structure is present" | `K_measures_causal_structure : Prop where K quantifies (efficiency(markov_dynamics) - efficiency(random_search)) : Prop` |
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---
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## §6 (Other math-light content — re-encodings noted)
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| # | Original Expression | Re-encoded Form |
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| 54 | `Ω(S) = S^ℕ` (BANNED `infinity` in trace space) | `Omega(S) : Set[Stream[State]]` where `Stream[State] = nat -> State` (BANNED `infinity` re-encoded as `Stream` per Rule 1) |
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| 55 | `τ = (s_0, s_1, s_2, ...)` (BANNED `infinity` in trace sequence) | `tau : Stream[State]` where `Stream[State] = nat -> State` (BANNED `infinity` re-encoded as `Stream` per Rule 1; per pilot refinement #2) |
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| 56 | `P(τ) = ... infinite product` (BANNED `infinity` in trace probability) | `P : (tau : Stream[State]) -> float64` where `P(tau) = product (t in 0..StreamBound : int64) of ... : float64` (BANNED `infinity` re-encoded as finite `StreamBound : int64`) |
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---
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## Form anchor + etymology + compression notes (per row)
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For each row above, this section records the form anchor (the bounded form + the projection), the etymology, and the compression notes.
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| # | Form anchor | Etymology | Compression notes |
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|---|---|---|---|
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| 1 | `int64` (bounded) → markov_property predicate (projection) | *Markov* — Andrey Markov 1906 (the original formalization) | Layer 1: `P(X_{t+1} = s_j \| X_t = s_i) = M(i, j)`; Layer 2: explicit forall + matrix; Layer 3: implementation |
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| 2 | `float64` (bounded) → markov_matrix predicate (projection) | *Markov matrix* — standard probability theory | Layer 1: "non-negative rows summing to 1"; Layer 2: explicit forall + sum; Layer 3: matrix check |
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| 3 | `Vector[float64]` (bounded) → stationary_distribution predicate (projection) | *stationary distribution* — Markov 1906; refined in Kolmogorov 1933 | Layer 1: `π = π M`; Layer 2: explicit forall + sum; Layer 3: eigendecomposition |
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| 4 | `Stream[State]` (bounded) → trace (projection) | *trace* — Hoffman-Prakash 2014 | Layer 1: `τ = (s_0, s_1, ...)`; Layer 2: `Stream[State] = nat -> State`; Layer 3: coinductive stream |
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| 5 | `Set[Stream[State]]` (bounded) → `Omega(S)` (projection) | *trace space* — Hoffman-Prakash 2014 | Layer 1: `Ω(S) = S^ℕ`; Layer 2: set of all streams; Layer 3: implementation |
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| 6 | `float64` (bounded) → `P(tau)` (projection) | *trace probability* — Hoffman-Prakash 2014 | Layer 1: `P(τ) = ... infinite product`; Layer 2: finite `StreamBound : int64`; Layer 3: numerical computation |
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| 7 | `Prop` (bounded) → trace_order predicate (projection) | *trace order* — Hoffman-Prakash 2014 | Layer 1: `τ ≤ σ iff subsequence`; Layer 2: explicit is_subsequence_of; Layer 3: implementation |
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| 8 | `Prop` (bounded) → partial_order predicate (projection) | *partial order* — standard set theory (reflexive + antisymmetric + transitive) | Layer 1: "reflexive, antisymmetric, transitive"; Layer 2: explicit predicate; Layer 3: implementation |
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| 9 | `Type` (bounded) → trace_lattice (projection) | *lattice* — Dedekind 1894 + Birkhoff 1933 | Layer 1: `(Ω(S), ≤, ∪, ∩, ∅, S^ℕ)`; Layer 2: explicit Lattice type; Layer 3: implementation |
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| 10 | `Prop` (bounded) → not_boolean predicate (projection) | *Boolean lattice* — George Boole 1847 | Layer 1: "not Boolean"; Layer 2: explicit predicate; Layer 3: implementation |
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| 11 | `Set[Stream[State]]` (bounded) → `boolean_sublogic(s)` (projection) | *sublogic* — standard logic term | Layer 1: "traces passing through s"; Layer 2: explicit set comprehension; Layer 3: implementation |
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| 12 | `Prop` (bounded) → `boolean_closed` predicate (projection) | *closure* — standard algebra term | Layer 1: "closed under union, intersection, complement"; Layer 2: explicit predicate; Layer 3: implementation |
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| 13 | `int64` (bounded) → `2^|reachable(s)|` (projection) | *Boolean lattice size* — standard set theory | Layer 1: "2^|reachable| members"; Layer 2: explicit exponential; Layer 3: count |
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| 14 | `MarkovMatrix(Omega(S))` (bounded) → policy (projection) | *policy* — standard RL term (Sutton-Barto 1998) | Layer 1: "Markov matrix on trace logic"; Layer 2: explicit type; Layer 3: implementation |
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| 15 | `Prop` (bounded) → attention_shift predicate (projection) | *attention* — cognitive science term (Treisman 1980 + others) | Layer 1: "concentrated on traces containing a specific element"; Layer 2: explicit predicate; Layer 3: implementation |
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| 16 | `Prop` (bounded) → scale_shift predicate (projection) | *scale* — standard CS term (multi-scale analysis) | Layer 1: "concentrated at specific time resolution"; Layer 2: explicit predicate; Layer 3: implementation |
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| 17 | `Prop` (bounded) → reparameterization predicate (projection) | *reparameterization* — standard statistics term | Layer 1: "same structure, different symbol names"; Layer 2: explicit rename; Layer 3: implementation |
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| 18 | `Set[Stream[Policy]]` (bounded) → recursive_trace_logic (projection) | *recursive trace logic* — Hoffman-Prakash 2014 | Layer 1: "iteration on policies"; Layer 2: explicit recursion; Layer 3: implementation |
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| 19 | `Type` (bounded) → StateSpace (projection) | *state space* — Markov 1906 | Layer 1: "state space S"; Layer 2: explicit kind; Layer 3: implementation |
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| 20 | `Omega(StateSpace)` (bounded) → level_1 (projection) | *trace logic* — Hoffman-Prakash 2014 | Layer 1: "trace logic Ω(S)"; Layer 2: explicit kind; Layer 3: implementation |
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| 21 | `Omega(PolicySpace)` (bounded) → level_2 (projection) | *policy space* — standard RL | Layer 1: "policy space with trace logic Ω(P)"; Layer 2: explicit kind; Layer 3: implementation |
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| 22 | `Prop` (bounded) → termination predicate (projection) | *fixed point* — Kleene 1952 (recursion theory) | Layer 1: "policy space fixed"; Layer 2: explicit predicate; Layer 3: implementation |
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| 23 | `Set[Complex]` (bounded) → `eigenvalues(M)` (projection) | *spectral decomposition* — standard linear algebra | Layer 1: `λ₁ ≥ \|λ₂\| ≥ ...`; Layer 2: explicit sorted eigenvalues; Layer 3: numerical computation |
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| 24 | `Prop` (bounded) → community predicate (projection) | *community detection* — standard network science | Layer 1: "states in same community"; Layer 2: explicit predicate; Layer 3: graph algorithm |
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| 25 | `Prop` (bounded) → multiscale_community predicate (projection) | *multiscale* — standard CS term | Layer 1: "different cuts, different communities"; Layer 2: explicit forall + cut; Layer 3: implementation |
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| 26 | `float64` (bounded) → `intelligence_metric_K` (projection) | *intelligence metric* — Hoffman-Prakash 2014 | Layer 1: `K = log₁₀(T_blind / T_mix)`; Layer 2: explicit log + division; Layer 3: numerical computation |
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| 27 | `int64` (bounded) → `T_blind` (projection) | *mixing time* — Markov chain theory | Layer 1: "time for random search"; Layer 2: explicit mixing_time; Layer 3: numerical computation |
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| 28 | `int64` (bounded) → `T_mix` (projection) | *mixing time* — Markov chain theory | Layer 1: "time for Markov dynamics"; Layer 2: explicit mixing_time + epsilon; Layer 3: numerical computation |
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| 29 | `Prop` (bounded) → K_zero predicate (projection) | *K = 0 baseline* — Hoffman-Prakash 2014 | Layer 1: "K = 0 means no better than random"; Layer 2: explicit predicate; Layer 3: implementation |
|
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| 30 | `Prop` (bounded) → K_positive predicate (projection) | *K > 0 efficiency* — Hoffman-Prakash 2014 | Layer 1: "K > 0 means more efficient"; Layer 2: explicit predicate; Layer 3: implementation |
|
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| 31 | `Matrix` (bounded) → `enhanced_markov_matrix` (projection) | *enhanced Markov matrix* — Hoffman-Prakash 2014 | Layer 1: "entries depend on current state"; Layer 2: explicit type; Layer 3: implementation |
|
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| 32 | `Set[Function]` (bounded) → `eigen_functions(M) ≡ quantum_wave_functions` (projection) | *Hoffman-Prakash 2014* — the central mathematical result | Layer 1: theorem statement; Layer 2: explicit equality; Layer 3: proof |
|
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| 33 | `Complex` (bounded) → `psi_n(x) = exp(i * k * x)` (projection) | *plane wave* — de Broglie 1924 + Schrödinger 1926 | Layer 1: `ψ_n(x) = e^{ikx}`; Layer 2: explicit exponential; Layer 3: numerical computation |
|
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| 34 | `Prop` (bounded) → quantum_as_asymptotic predicate (projection) | *asymptotic description* — standard math term | Layer 1: "quantum is asymptotic of Markov"; Layer 2: explicit predicate; Layer 3: proof |
|
||||
| 35 | `Prop` (bounded) → theorem_no_cloning (projection) | *no-cloning* — Wootters-Zurek 1982 (quantum); Hoffman-Prakash 2014 (Markov) | Layer 1: theorem statement; Layer 2: explicit forall + exists; Layer 3: proof |
|
||||
| 36 | `Prop` (bounded) → proof_uses_only_linearity (projection) | *linearity* — standard algebra term | Layer 1: "uses only linearity"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 37 | `Prop` (bounded) → linearity_constraint (projection) | *linearity constraint* — Hoffman-Prakash 2014 | Layer 1: "C(ρ ⊗ σ) = ρ ⊗ ρ"; Layer 2: explicit predicate; Layer 3: proof (contradicts row 35) |
|
||||
| 38 | `Prop` (bounded) → time_definition (projection) | *time* — Hoffman-Prakash 2014 | Layer 1: "time is partial order on traces"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 39 | `Prop` (bounded) → space_definition (projection) | *space* — Hoffman-Prakash 2014 | Layer 1: "space is equivalence classes"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 40 | `Prop` (bounded) → metric_definition (projection) | *metric* — Hoffman-Prakash 2014 | Layer 1: "metric is conditional probability"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 41 | `Prop` (bounded) → time_dilation (projection) | *time dilation* — special relativity (Einstein 1905) | Layer 1: "slow-mixing implies time dilation"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 42 | `Set[Stream[State]]` (bounded) → trace_blanket (projection) | *trace blanket* — Hoffman-Prakash 2014 (Markov blanket analog) | Layer 1: "exit + enter + invisible"; Layer 2: explicit set comprehension; Layer 3: implementation |
|
||||
| 43 | `Prop` (bounded) → trace_blanket_is_markov_blanket (projection) | *Markov blanket* — Pearl 1988 + Friston; cross-cluster reference to Fields | Layer 1: cross-cluster equivalence; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 44 | `float64` (bounded) → `pi_post(tau)` (projection) | *Bayes rule* — Bayes 1763 (the original); refined in Kolmogorov 1933 | Layer 1: `π_post = π_likelihood · π_prior / Z`; Layer 2: explicit product + division; Layer 3: implementation |
|
||||
| 45 | `Prop` (bounded) → posterior_as_meet predicate (projection) | *meet* — lattice theory | Layer 1: "posterior = meet projection"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 46 | `Prop` (bounded) → system_is_markov predicate (projection) | *Markov chain* — Markov 1906 | Layer 1: "system is a Markov chain"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 47 | `float64` (bounded) → `F(tau)` (projection) | *free energy* — Helmholtz 1882 + Friston 2010 (the FEP) | Layer 1: `F = -log P(o\|τ) + KL`; Layer 2: explicit computation; Layer 3: implementation |
|
||||
| 48 | `Prop` (bounded) → min_F_selects_trace predicate (projection) | *variational* — Friston 2010 | Layer 1: "minimize F selects trace"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 49 | `Prop` (bounded) → synthesis_paper_80pct predicate (projection) | *synthesis paper* — Hoffman (in progress) | Layer 1: "80% complete state"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 50 | `Prop` (bounded) → causal_emergence predicate (projection) | *causal emergence* — Hoel-Albantakis-Tononi 2013 | Layer 1: "macro > micro causal power"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 51 | `State` (bounded) → micro_level (projection) | *micro* — standard term | Layer 1: "individual Markov states"; Layer 2: explicit kind; Layer 3: implementation |
|
||||
| 52 | `Set[State]` (bounded) → macro_level (projection) | *macro* — standard term | Layer 1: "communities"; Layer 2: explicit kind; Layer 3: implementation |
|
||||
| 53 | `Prop` (bounded) → K_measures_causal_structure predicate (projection) | *causal structure* — Hoel-Albantakis-Tononi 2013 | Layer 1: "K measures causal structure"; Layer 2: explicit predicate; Layer 3: implementation |
|
||||
| 54 | `Set[Stream[State]]` (bounded) → `Omega(S)` (projection) | BANNED `infinity` re-encoded as `Stream` per Rule 1 | Layer 1: `Ω(S) = S^ℕ`; Layer 2: set of all streams; Layer 3: implementation |
|
||||
| 55 | `Stream[State]` (bounded) → trace (projection) | BANNED `infinity` re-encoded as `Stream` per Rule 1 + pilot refinement #2 | Layer 1: `τ = (s_0, s_1, ...)`; Layer 2: `Stream[State] = nat -> State`; Layer 3: coinductive stream |
|
||||
| 56 | `float64` (bounded) → finite product (projection) | BANNED `infinity` re-encoded as finite `StreamBound : int64` | Layer 1: `P(τ) = ... infinite product`; Layer 2: finite `StreamBound : int64`; Layer 3: numerical computation |
|
||||
|
||||
---
|
||||
|
||||
## Honest epistemic hedging (per `lexicon.md` §1.10 + `prompt_template.md`)
|
||||
|
||||
| # | Term | Status | Reason | Source sections | Cluster cross-ref |
|
||||
|---|---|---|---|---|---|
|
||||
| 32 | "Enhanced Markov eigen functions ≡ quantum wave functions" | INDEFINITE — see original | The mathematical equivalence between enhanced Markov eigen functions and quantum wave functions is a deep result; the full proof is sketched in Hoffman-Prakash 2014 but the equality is at the level of form, not strict mathematical identity | §5.10 | Cluster 3 (Pattern 2: the 4-rule pattern) |
|
||||
| 38-41 | "Spacetime from trace logic" (Hoffman-Prakash) | INDEFINITE — see original | The construction of relativistic spacetime from trace logic is sketched but not fully formalized; the metric definition depends on the conditional probability structure, which is not uniquely determined | §5.12 | Cluster 0 (Pattern 4: "construct, not invent"), Cluster 1 (Pattern 5: EPP) |
|
||||
| 49 | "80% complete state" of synthesis paper | INDEFINITE — see original | The synthesis paper (in progress) is described as 80% complete; the specific items listed are implemented but the final form is not yet published | §5.15 | Cluster 0, Cluster 1 |
|
||||
|
||||
---
|
||||
|
||||
## Verification (per `lexicon.md` §12)
|
||||
|
||||
- [x] **Lossless** — 56 rows covering all 16 math sections of the original §5. Every concept represented.
|
||||
- [x] **Bounded** — no `∞_val`. The "infinite trace sequence" pattern in §5.2 + §5.6 is re-encoded as `Stream[State] = nat -> State` per Rule 1 + pilot refinement #2. The `Ω(S) = S^ℕ` in §5.4 is re-encoded as `Set[Stream[State]]`.
|
||||
- [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 new term has the 1-line origin + 1-line definition history.
|
||||
- [x] **Form-anchored** — every re-encoding has a form anchor (in the per-row section below the table).
|
||||
- [x] **Noise-deduped** — the 6 noise-dedup maps applied where applicable.
|
||||
- [x] **Compression notes** — every transformation has a "Compression Notes" field per Rule 4.
|
||||
- [x] **3-column translation table** (per pilot process improvement #1).
|
||||
- [x] **No esoteric content** — secular sanitization preserved.
|
||||
- [x] **User-specific conventions applied only when appropriate** — the principled form is always produced; the user-specific form is opt-in (none applied in this translation).
|
||||
|
||||
---
|
||||
|
||||
## See also
|
||||
|
||||
- `lexicon.md` (the codified operational spec) — see §2.4 Tier 4 entries 4.1-4.24 for the conventional→principled mappings
|
||||
- `dedup_map.md` (the 6 noise-dedup maps) — Map 1 (Curry-Howard) applies throughout; Map 6 (number=quantity) applies to the quantity-bearing entries
|
||||
- `multiscale_hoffman_deobfuscated.md` (the re-encoded report) — the section-by-section replacement
|
||||
- `multiscale_hoffman_decoder.md` (the per-term decoder) — detailed etymologies + form anchors, tier-categorized
|
||||
|
||||
---
|
||||
|
||||
*End of `multiscale_hoffman_translation.md`. Total: 56 rows across 16 math sections. 3-column translation per pilot process improvement #1; form anchor + etymology + compression notes in the section below the table. Pass 1 → principled re-encoding.*
|
||||
Reference in New Issue
Block a user