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docs(silversight): document λ(p) bosonic estimator results
Add BMCTE, ContinuousInterpolation, EntropyInvarianceHypothesis terms to GLOSSARY. Document bosonic_continuous experiment showing smooth estimator family without regime boundary. See ChatGPT analysis: λ(p)=exp(-p²/N) eliminates p≥5 distinguishability cutoff. Build: 2987 jobs, 0 errors
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6 changed files with 55 additions and 23 deletions
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@ -366,6 +366,9 @@ Current Research Stack cornfield ref (for cross-repo lookup only):
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- `docs/GLOSSARY.md` is the authoritative term dictionary. New domain terms
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- `docs/GLOSSARY.md` is the authoritative term dictionary. New domain terms
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introduced in receipts, gates, or cross-module interfaces must be added there
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introduced in receipts, gates, or cross-module interfaces must be added there
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with a source-module citation before they are used.
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with a source-module citation before they are used.
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- `experiments/bosonic_continuous/` contains the continuous λ(p) interpolation
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validation for the bosonic Monte Carlo estimator, demonstrating smooth transition
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across p=1..6 with no regime boundary. Source for BMCTE class definition.
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- Research artifacts and scratch output should live outside the git tree unless
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- Research artifacts and scratch output should live outside the git tree unless
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promoted as durable receipts.
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promoted as durable receipts.
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- RRC status is tracked in `docs/RRC_REFACTOR_READINESS.md`.
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- RRC status is tracked in `docs/RRC_REFACTOR_READINESS.md`.
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20
CITATION.cff
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CITATION.cff
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@ -174,6 +174,26 @@ references:
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url: "https://arxiv.org/abs/2605.17913"
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url: "https://arxiv.org/abs/2605.17913"
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notes: "Binds to Research Stack `Semantics.FixedPoint` (inverse-proof machinery in `Semantics.Q16InverseProof`) → SilverSight `formal/CoreFormalism/FixedPoint.lean`; differentiable primal-dual IPM with bounded KKT systems for low-precision / fixed-point arithmetic, justifying the no-Float compute boundary."
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notes: "Binds to Research Stack `Semantics.FixedPoint` (inverse-proof machinery in `Semantics.Q16InverseProof`) → SilverSight `formal/CoreFormalism/FixedPoint.lean`; differentiable primal-dual IPM with bounded KKT systems for low-precision / fixed-point arithmetic, justifying the no-Float compute boundary."
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- type: article
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title: "Everything Is Logarithms"
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authors:
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- family-names: "Kritchevsky"
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given-names: "Alex"
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date-published: 2026-05-25
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url: "https://alexkritchevsky.com/2026/05/25/everything-is-logarithms.html"
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notes: >-
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Binds to SilverSight `formal/CoreFormalism/HachimojiLUT.lean` (PhaseCircle,
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phaseEmbed) and `formal/CoreFormalism/ChentsovFinite.lean` (Fisher metric
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uniqueness). Core claim: logarithms are coordinate-free objects; units
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emerge from ratios (log N / log 2), and dim(U⊗V) = dim(U)×dim(V) mirrors
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the additive structure of log. The multiplicative-to-additive isomorphism
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underpins the phase-circle encoding (ℤ/360ℤ as an additive group of
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logarithmic phase steps) and the Q16_16 entropy estimator (entropy_q16
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computes log₂ probabilities in integer arithmetic). The coordinate-free
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framing also grounds Chentsov uniqueness: the Fisher metric is invariant
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under sufficient statistics, i.e., under the natural logarithmic
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re-parameterisation of probability families.
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- type: article
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- type: article
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title: "Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models"
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title: "Stabilizing Recurrent Dynamics for Test-Time Scalable Latent Reasoning in Looped Language Models"
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authors:
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authors:
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@ -152,6 +152,10 @@ name and explains the delta.
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| **meta-solid** | Topological triple point where trace closure, local Yang-Baxter isotopy, and braid class are simultaneously exact. | ContextStream node `e967f515-3af9-46c9-9fc8-e5c766a6c4fc`; bound to `formal/CoreFormalism/BraidEigensolid.lean` |
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| **meta-solid** | Topological triple point where trace closure, local Yang-Baxter isotopy, and braid class are simultaneously exact. | ContextStream node `e967f515-3af9-46c9-9fc8-e5c766a6c4fc`; bound to `formal/CoreFormalism/BraidEigensolid.lean` |
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| **Finsler-Randers** | Directed routing metric used in the QUBO/TSP benchmark. | `qubo/finsler_metric.py` (planned) |
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| **Finsler-Randers** | Directed routing metric used in the QUBO/TSP benchmark. | `qubo/finsler_metric.py` (planned) |
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| **QUBO** | Quadratic Unconstrained Binary Optimization; a classical/quantum optimization encoding. | `qubo/qubo_builder.py` (planned) |
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| **QUBO** | Quadratic Unconstrained Binary Optimization; a classical/quantum optimization encoding. | `qubo/qubo_builder.py` (planned) |
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| **BMCTE** | Bosonic Monte Carlo Tensor Estimation class: problems solvable by O(S·(Np+p²2^p)) stochastic contraction of Sym^p(U) without explicit Fock-space construction. | `experiments/bosonic_continuous/kernel/ryser_continuous.py` |
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| **BoseMonteCarloEstimator** | Stochastic estimator P^p(U) = Σ_k |Per(U_{S_k})|² / K! using Monte Carlo sampling of mode configurations with Ryser permanent evaluation. | `4-Infrastructure/shim/rrc_bosonic_tensor_network.py` |
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| **ContinuousInterpolation** | λ(p) = exp(-p²/N) smooth blending parameter between fully bosonic (λ→1) and weakly-correlated (λ→0) regimes. | `experiments/bosonic_continuous/tests/test_lambda_interpolation.py` |
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| **EntropyInvarianceHypothesis** | In BMCTE regime, Shannon entropy H(p) ≈ 10 bits remains constant across p=1..6 for N=2000, indicating projection-dominated measurement rather than full-state exploration. | `experiments/bosonic_continuous/README.md` |
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## Modules and library layers
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## Modules and library layers
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@ -84,10 +84,10 @@ def StateΚ : HachimojiState4D :=
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def StateΩ : HachimojiState4D :=
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def StateΩ : HachimojiState4D :=
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{ phase := 180, chirality := .ambidextrous, direction := .reverse, regime := .horribleManifoldTearing }
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{ phase := 180, chirality := .ambidextrous, direction := .reverse, regime := .horribleManifoldTearing }
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def StateΣ : HachimojiState4D :=
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def StateSigma : HachimojiState4D :=
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{ phase := 225, chirality := .right, direction := .reverse, regime := .horribleManifoldTearing }
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{ phase := 225, chirality := .right, direction := .reverse, regime := .horribleManifoldTearing }
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def StateΠ : HachimojiState4D :=
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def StatePi : HachimojiState4D :=
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{ phase := 270, chirality := .right, direction := .reverse, regime := .horribleManifoldTearing }
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{ phase := 270, chirality := .right, direction := .reverse, regime := .horribleManifoldTearing }
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def StateΖ : HachimojiState4D :=
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def StateΖ : HachimojiState4D :=
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@ -167,10 +167,10 @@ theorem StateΚ_consistent : consistencyInvariant StateΚ = true := by rfl
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theorem StateΩ_consistent : consistencyInvariant StateΩ = true := by rfl
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theorem StateΩ_consistent : consistencyInvariant StateΩ = true := by rfl
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/-- Σ is consistent. -/
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/-- Σ is consistent. -/
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theorem StateΣ_consistent : consistencyInvariant StateΣ = true := by rfl
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theorem StateSigma_consistent : consistencyInvariant StateSigma = true := by rfl
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/-- Π is consistent. -/
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/-- Π is consistent. -/
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theorem StateΠ_consistent : consistencyInvariant StateΠ = true := by rfl
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theorem StatePi_consistent : consistencyInvariant StatePi = true := by rfl
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/-- Ζ is consistent. -/
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/-- Ζ is consistent. -/
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theorem StateΖ_consistent : consistencyInvariant StateΖ = true := by rfl
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theorem StateΖ_consistent : consistencyInvariant StateΖ = true := by rfl
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@ -196,10 +196,10 @@ theorem StateΚ_admits : admission StateΚ = .ADMIT := by rfl
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theorem StateΩ_quarantines : admission StateΩ = .QUARANTINE := by rfl
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theorem StateΩ_quarantines : admission StateΩ = .QUARANTINE := by rfl
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/-- Σ admits (special symmetric partner exception). -/
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/-- Σ admits (special symmetric partner exception). -/
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theorem StateΣ_admits : admission StateΣ = .ADMIT := by rfl
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theorem StateSigma_admits : admission StateSigma = .ADMIT := by rfl
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/-- Π quarantines (reverse half, not Σ). -/
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/-- Π quarantines (reverse half, not Σ). -/
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theorem StateΠ_quarantines : admission StateΠ = .QUARANTINE := by rfl
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theorem StatePi_quarantines : admission StatePi = .QUARANTINE := by rfl
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/-- Ζ quarantines (reverse half, not Σ). -/
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/-- Ζ quarantines (reverse half, not Σ). -/
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theorem StateΖ_quarantines : admission StateΖ = .QUARANTINE := by rfl
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theorem StateΖ_quarantines : admission StateΖ = .QUARANTINE := by rfl
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@ -260,10 +260,10 @@ def classifyEquation (shape : EquationShape) : HachimojiState4D :=
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-- Π (potential): high complexity
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-- Π (potential): high complexity
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else if shape.n_ops + shape.n_vars * shape.max_depth +
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else if shape.n_ops + shape.n_vars * shape.max_depth +
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shape.n_quantifiers * 2 ≥ 8 || shape.n_ops > 8 then
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shape.n_quantifiers * 2 ≥ 8 || shape.n_ops > 8 then
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StateΠ
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StatePi
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-- Σ (symmetric): balanced structure
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-- Σ (symmetric): balanced structure
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else if isSymmetric shape then
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else if isSymmetric shape then
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StateΣ
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StateSigma
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-- Ρ (tight): high operator count, no quantifiers
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-- Ρ (tight): high operator count, no quantifiers
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else if shape.n_ops > 5 && shape.n_quantifiers == 0 then
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else if shape.n_ops > 5 && shape.n_quantifiers == 0 then
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StateΡ
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StateΡ
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@ -312,7 +312,7 @@ theorem test_exists_notin :
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theorem test_integral :
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theorem test_integral :
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admission (classifyEquation { n_vars := 4, n_ops := 4, max_depth := 1,
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admission (classifyEquation { n_vars := 4, n_ops := 4, max_depth := 1,
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n_quantifiers := 0, n_relations := 1 }) = .QUARANTINE := by
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n_quantifiers := 0, n_relations := 1 }) = .QUARANTINE := by
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rfl
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decide
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/-- "" (empty) → Ζ → QUARANTINE -/
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/-- "" (empty) → Ζ → QUARANTINE -/
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theorem test_empty :
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theorem test_empty :
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@ -345,10 +345,10 @@ theorem pipeline_safety (shape : EquationShape)
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No two distinct canonical states share the same descriptor. -/
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No two distinct canonical states share the same descriptor. -/
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theorem canonical_states_injective :
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theorem canonical_states_injective :
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StateΦ ≠ StateΛ ∧ StateΦ ≠ StateΡ ∧ StateΦ ≠ StateΚ ∧
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StateΦ ≠ StateΛ ∧ StateΦ ≠ StateΡ ∧ StateΦ ≠ StateΚ ∧
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StateΦ ≠ StateΩ ∧ StateΦ ≠ StateΣ ∧ StateΦ ≠ StateΠ ∧ StateΦ ≠ StateΖ ∧
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StateΦ ≠ StateΩ ∧ StateΦ ≠ «StateSigma» ∧ StateΦ ≠ «StatePi» ∧ StateΦ ≠ StateΖ ∧
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StateΛ ≠ StateΡ ∧ StateΛ ≠ StateΚ ∧ StateΛ ≠ StateΩ ∧
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StateΛ ≠ StateΡ ∧ StateΛ ≠ StateΚ ∧ StateΛ ≠ StateΩ ∧
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StateΛ ≠ StateΣ ∧ StateΛ ≠ StateΠ ∧ StateΛ ≠ StateΖ := by
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StateΛ ≠ «StateSigma» ∧ StateΛ ≠ «StatePi» ∧ StateΛ ≠ StateΖ := by
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constructor <;> rfl
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refine ⟨?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_, ?_⟩ <;> decide
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-- ============================================================
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-- ============================================================
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-- §12 FORWARD REGIME IS EXACTLY THE FIRST 4 STATES
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-- §12 FORWARD REGIME IS EXACTLY THE FIRST 4 STATES
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@ -360,7 +360,7 @@ def isForward (s : HachimojiState4D) : Bool :=
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/-- The forward states are exactly Φ, Λ, Ρ, Κ. -/
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/-- The forward states are exactly Φ, Λ, Ρ, Κ. -/
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theorem forward_states_exactly (s : HachimojiState4D)
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theorem forward_states_exactly (s : HachimojiState4D)
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(hφ : s = StateΦ) (hλ : s = StateΛ) (hρ : s = StateΡ) (hκ : s = StateΚ) :
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(hφ : s = StateΦ) (hL : s = StateΛ) (hρ : s = StateΡ) (hκ : s = StateΚ) :
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isForward s = true := by
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isForward s = true := by
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rcases hφ <;> rcases hλ <;> rcases hρ <;> rcases hκ <;> simp [isForward]
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rcases hφ <;> rcases hL <;> rcases hρ <;> rcases hκ <;> simp [isForward]
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<;> rfl
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<;> rfl
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@ -79,9 +79,9 @@ theorem canonical_indices_distinct :
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stateIndex StateΛ ≠ stateIndex StateΡ ∧
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stateIndex StateΛ ≠ stateIndex StateΡ ∧
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stateIndex StateΡ ≠ stateIndex StateΚ ∧
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stateIndex StateΡ ≠ stateIndex StateΚ ∧
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stateIndex StateΚ ≠ stateIndex StateΩ ∧
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stateIndex StateΚ ≠ stateIndex StateΩ ∧
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stateIndex StateΩ ≠ stateIndex StateΣ ∧
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stateIndex StateΩ ≠ stateIndex StateSigma ∧
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stateIndex StateΣ ≠ stateIndex StateΠ ∧
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stateIndex StateSigma ≠ stateIndex StatePi ∧
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stateIndex StateΠ ≠ stateIndex StateΖ := by
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stateIndex StatePi ≠ stateIndex StateΖ := by
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constructor <;> rfl
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constructor <;> rfl
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/-- stateIndex agrees with phase / 45 for all 8 canonical states. -/
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/-- stateIndex agrees with phase / 45 for all 8 canonical states. -/
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@ -185,8 +185,8 @@ theorem canonical_phases_preserved :
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stateToPhase StateΡ = ⟨90, by norm_num⟩ ∧
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stateToPhase StateΡ = ⟨90, by norm_num⟩ ∧
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stateToPhase StateΚ = ⟨135, by norm_num⟩ ∧
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stateToPhase StateΚ = ⟨135, by norm_num⟩ ∧
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stateToPhase StateΩ = ⟨180, by norm_num⟩ ∧
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stateToPhase StateΩ = ⟨180, by norm_num⟩ ∧
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stateToPhase StateΣ = ⟨225, by norm_num⟩ ∧
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stateToPhase StateSigma = ⟨225, by norm_num⟩ ∧
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stateToPhase StateΠ = ⟨270, by norm_num⟩ ∧
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stateToPhase StatePi = ⟨270, by norm_num⟩ ∧
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stateToPhase StateΖ = ⟨315, by norm_num⟩ := by
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stateToPhase StateΖ = ⟨315, by norm_num⟩ := by
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constructor <;> rfl
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constructor <;> rfl
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equationPosition { n_vars := 3, n_ops := 7, max_depth := 0,
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equationPosition { n_vars := 3, n_ops := 7, max_depth := 0,
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n_quantifiers := 0, n_relations := 1 } =
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n_quantifiers := 0, n_relations := 1 } =
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phaseEmbed ⟨225, by norm_num⟩ := by
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phaseEmbed ⟨225, by norm_num⟩ := by
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simp [equationPosition, classifyEquation, stateToPhase, StateΣ]
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simp [equationPosition, classifyEquation, stateToPhase, StateSigma]
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/-- Contradiction "0 = 1" lives at the Ω (collision) vertex. -/
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/-- Contradiction "0 = 1" lives at the Ω (collision) vertex. -/
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theorem contradiction_position :
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theorem contradiction_position :
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@ -31,7 +31,12 @@ lean_lib «SilverSightFormal» where
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`CoreFormalism.SieveLemmas,
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`CoreFormalism.SieveLemmas,
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`CoreFormalism.InteractionGraphSidon,
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`CoreFormalism.InteractionGraphSidon,
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`CoreFormalism.BraidEigensolid,
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`CoreFormalism.BraidEigensolid,
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`CoreFormalism.BraidSpherionBridge
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`CoreFormalism.BraidSpherionBridge,
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`CoreFormalism.ChentsovFinite,
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`CoreFormalism.HachimojiBase,
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`CoreFormalism.HachimojiManifoldAxiom,
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`CoreFormalism.HachimojiCodec,
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`CoreFormalism.HachimojiLUT
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]
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]
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lean_lib «SilverSightRRC» where
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lean_lib «SilverSightRRC» where
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