From 9312dd7f49f5d25d20b97d9ede75b7b65f5f0286 Mon Sep 17 00:00:00 2001 From: Brandon Schneider Date: Wed, 13 May 2026 20:39:39 -0500 Subject: [PATCH] chore: add Menger/Koch model extraction JSON from ChatGPT session Extracted 12 mathematical components from 414-message session. Comparison against existing codebase: 3 STRONG, 2 GOOD, 5 PARTIAL, 1 MINIMAL, 1 NONE coverage (Reuleaux triangle missing entirely). --- ...nger_koch_model_extraction_2026-05-13.json | 214 ++++++++++++++++++ 1 file changed, 214 insertions(+) create mode 100644 shared-data/data/stack_solidification/menger_koch_model_extraction_2026-05-13.json diff --git a/shared-data/data/stack_solidification/menger_koch_model_extraction_2026-05-13.json b/shared-data/data/stack_solidification/menger_koch_model_extraction_2026-05-13.json new file mode 100644 index 00000000..31b039ff --- /dev/null +++ b/shared-data/data/stack_solidification/menger_koch_model_extraction_2026-05-13.json @@ -0,0 +1,214 @@ +{ + "source": { + "title": "Menger Koch Fractal", + "session_timestamp": "2026-05-14T00:32:40.150Z", + "url": "https://chatgpt.com/c/6a026cb8-15e4-83ea-9328-6dbcbf7d6f34", + "total_messages": 414, + "message_hash": "579971ed08d8c38f6fad685acc06d215f932d8f7ac7d139b800ab349516892f8" + }, + "derived_components": { + "menger_koch_divergence": { + "description": "Menger/Koch hybrid fractal divergence model", + "equations": [ + "F_{n+1} = K_\u03b2(\u2202M_\u03b1(F_n)) \u222a core(M_\u03b1(F_n))", + "D_Koch = ln 4 / ln 3", + "D_Menger = ln 20 / ln 3", + "D_MK(n) = boundary_complexity_n / (interior_mass_n + \u03b5)", + "D_MK(n) \u223c (4/3)^n / ((20/27)^n + \u03b5) \u223c (9/5)^n" + ], + "domain": "cosmology/DESI", + "status": "concept", + "coverage": "GOOD", + "existing_files": [ + "0-Core-Formalism/lean/Semantics/Semantics/TopologyFractalEncoding.lean \u2014 fractal encoding topology, witness benchmarks", + "6-Documentation/docs/distilled/DESI_Menger_Probe_Result.md \u2014 q_void \u2192 Menger sponge mapping", + "6-Documentation/docs/distilled/ObserverScale_RegimeGate_VoidScar.md \u2014 F_MK = Bind(MengerVoid, KochScar, \u0394_\u03c6\u03b3\u03bb)", + "4-Infrastructure/shim/holographic_carving_probe.py \u2014 Menger-style carving via threshold-band exclusion" + ], + "gap": "No Lean theorems for D_Koch, D_Menger divergence formula. All conceptual docs." + }, + "scale_observer_operator": { + "description": "Scale-aware observer-location operator (You Are Here)", + "equations": [ + "Z(O,x,r) = physics visible to observer O at position x and scale r", + "Z(O,x,r1) \u2260 Z(O,x,r2) \u2014 physics at different scales" + ], + "domain": "foundations", + "status": "concept", + "coverage": "PARTIAL", + "existing_files": [ + "6-Documentation/docs/distilled/ObserverScale_RegimeGate_VoidScar.md \u2014 observer-scale regime gates", + "6-Documentation/docs/s3c_projected_geodesic_resolution_refinement_2026-05-10.md \u2014 folded observer frame as Menger seed" + ], + "gap": "Z(O,x,r) operator not formalized in Lean. No scale-aware observer type exists." + }, + "hyper_eigenvalue": { + "description": "Merged geometry \u2192 single hyper-eigenvalue for regime identification", + "equations": [ + "\u03a8(r) = [\u03a9_M, R_K, D_q, \u039b, \u03b2_0,\u03b2_1,\u03b2_2, P, C, \u03b7, \u03b5]", + "H_{O,r} \u03a8(r) = \u03bb_*(O,r) \u03a8(r)" + ], + "domain": "spectral", + "status": "concept", + "coverage": "STRONG", + "existing_files": [ + "0-Core-Formalism/lean/Semantics/Semantics/FAMM.lean \u2014 eigenmass computation, fammWriteEigenmass", + "0-Core-Formalism/lean/Semantics/Semantics/ThresholdVector.lean \u2014 eigenmode regime switching, Theta_lambda", + "4-Infrastructure/shim/boundary_activation_field_probe.py \u2014 HyperEigenTransition receipts", + "6-Documentation/docs/research/PCIE_IDLE_CYCLE_SUBSTRATE_SPEC.md \u2014 HyperEigenSpectrum kernel, 11-component BindOperator", + "6-Documentation/docs/distilled/BoundaryEigenFire.md \u2014 boundary as weighted eigenmode superposition" + ], + "gap": "H_{O,r} \u03a8 = \u03bb_* \u03a8 is defined but not a proven Lean eigendecomposition. No actual linear operator." + }, + "boundary_superposition": { + "description": "Boundary as encoded superposition surface (wall of fire)", + "equations": [ + "B(x) = \u03a3_i \u03b1_i(x) \u03c6_i(x)", + "\u03c6_i \u2208 {\u03c1, \u2207\u03c1, T, \u03c3, \u03ba, \u03b2, \u03b7, \u03b5}" + ], + "domain": "geometry/field", + "status": "concept", + "coverage": "STRONG", + "existing_files": [ + "0-Core-Formalism/lean/Semantics/Semantics/HCMMR/Kernels/BoundaryEigenFire.lean \u2014 Lean kernel: ||B_\u2202(x)|| > \u0398_activation", + "4-Infrastructure/shim/boundary_activation_field_probe.py \u2014 B(x,r) probe with COMMIT/HOLD/REJECT classification", + "6-Documentation/docs/distilled/BoundaryEigenFire.md \u2014 full wall-of-fire spec" + ], + "gap": "\u03a3_i \u03b1_i \u03c6_i superposition formula not explicitly proven in Lean. Kernel is threshold-gate, not field." + }, + "desi_cosmic_web": { + "description": "DESI-scale cosmic web modeled as Menger/Koch/multifractal stack", + "equations": [ + "C_DESI = Bind(\u03a9_M, R_K, D_q, \u039b(r), \u03b2_k(r), P_c, H(z), \u03b5)" + ], + "domain": "cosmology", + "status": "concept", + "coverage": "GOOD", + "existing_files": [ + "6-Documentation/docs/distilled/DESI_Menger_Probe_Result.md \u2014 DESI probe with Menger geometry", + "4-Infrastructure/shim/bodegaflow_horn_fiber_refinements.md \u2014 16D horn-fiber with weighted distances, sector accessibility", + "6-Documentation/docs/distilled/16D_Manifold_Adjustment.md \u2014 trim/expand residual cost rules" + ], + "gap": "No Lean DESI module. No calibrated \u039bCDM comparison. No observational data binding." + }, + "nanoscroll_16d": { + "description": "Archimedean nanoscroll as geometric proxy for 16D state manifold", + "equations": [ + "r(\u03b8) = r0 + (h/2\u03c0)\u03b8, 0 \u2264 \u03b8 \u2264 2\u03c0N", + "S_16(\u03b8,z) = [x,y,z, q1..q13] in Q0.16", + "Cell16 = 16 channels \u00d7 16 bits = 256 bits = 32 bytes" + ], + "domain": "materials/computation", + "status": "concept", + "coverage": "PARTIAL", + "existing_files": [ + "6-Documentation/docs/speculative-materials/RecoveredSessionMaterialConcepts.md \u2014 MXene nanoscroll as 2D\u21921D transport surface", + "6-Documentation/docs/speculative-materials/AdaptiveMaterialMathApplicationMap.md \u2014 MXene\u2192PIST crosswalk", + "6-Documentation/docs/distilled/Pythagorean_Theorem_and_Beyond.md \u2014 scroll geometry as chiral ladder rails", + "6-Documentation/docs/s3c_projected_geodesic_resolution_refinement_2026-05-10.md \u2014 folded 16D interior" + ], + "gap": "No actual nanoscroll simulation code. No Q0.16 Cell16 implementation. All speculative docs." + }, + "braidshard_eigenwall": { + "description": "Vulkan-sharded Q0.16 eigenwall with braid packet routing", + "equations": [ + "S_16^{t+1} = Clamp[LocalUpdate(S_16^t) + BraidRoute(\u0393_t) + BoundaryFire(B_\u2202) - ResidualPenalty(R_t)]", + "W_{t+1} = CoverCheck(S_16^{t+1}, H_t)", + "Branch only if R_{t+1} \u2260 0" + ], + "domain": "computation/GPU", + "status": "architectural", + "coverage": "PARTIAL", + "existing_files": [ + "5-Applications/parquet_compressor/src/shifters/pist.rs \u2014 Rust PIST shifter (has shard-like structure)", + "6-Documentation/docs/research/PCIE_IDLE_CYCLE_SUBSTRATE_SPEC.md \u2014 Vulkan compute sharding, sparse binding, timeline semaphores", + "0-Core-Formalism/lean/Semantics/Semantics/BraidSerial.lean \u2014 BraidFrame, parallel encoded strands", + "0-Core-Formalism/lean/Semantics/Semantics/BraidedFieldPaths.lean \u2014 braid field path routing", + "6-Documentation/docs/distilled/Pythagorean_Theorem_and_Beyond.md \u2014 BraidStorm FAMM architecture" + ], + "gap": "No unified Vulkan shard + braid route integration. Components exist in isolation." + }, + "reuleaux_3circle": { + "description": "Compass-and-straightedge 3 equal circles in Reuleaux triangle", + "equations": [ + "r_small = (3\u221a3 - \u221a(3+4\u221a3)) / (6\u221a3 + 2\u221a(3+4\u221a3)) * R", + "R = circumradius of equilateral triangle" + ], + "domain": "geometry", + "status": "concept", + "coverage": "NONE", + "existing_files": [], + "gap": "Reuleaux triangle geometry not present anywhere in the Research Stack. Zero files, zero docs." + }, + "gabriel_horn_cosmic": { + "description": "Gabriel's Horn spatial model \u2014 finite volume, infinite surface via torsion", + "equations": [ + "V = \u03c0 \u222b_1^\u221e (1/x)\u00b2 dx = \u03c0 (finite)", + "A = 2\u03c0 \u222b_1^\u221e (1/x)\u221a(1+1/x\u2074) dx = \u221e (infinite)", + "Apparent expansion = torsion widening the infinite surface, not volume increase" + ], + "domain": "cosmology", + "status": "concept", + "coverage": "PARTIAL", + "existing_files": [ + "4-Infrastructure/shim/bodegaflow_horn_fiber_refinements.md \u2014 16D horn-fiber, torsion-widening surface, cosmic acceleration without homogeneous expansion", + "6-Documentation/docs/distilled/16D_Manifold_Adjustment.md \u2014 trim/expand rules for manifold", + "0-Core-Formalism/lean/Semantics/Semantics/TorsionalPIST.lean \u2014 quaternion RG flow in shell space, torsion transport" + ], + "gap": "Gabriel's Horn finite-volume/infinite-surface theorem not formalized in Lean. Torsion-is-widening claim not proven." + }, + "pi_phi_tau_constants": { + "description": "Constant architecture: \u03c0=closure/orbit, \u03c6=randomness/spiral, \u03c4=coupling", + "equations": [ + "\u03c0 = closure / orbit / shell constant", + "\u03c6 = randomness / growth / spiral constant", + "\u03c4 = time / torsion / coupling constant" + ], + "domain": "foundations", + "status": "concept", + "coverage": "MINIMAL", + "existing_files": [ + "6-Documentation/docs/distilled/Pythagorean_Theorem_and_Beyond.md \u2014 references \u03c0 as orbit/closure, \u03c6 as ratio constant", + "0-Core-Formalism/lean/Semantics/Semantics/HydrogenicPhiTorsionBraid.lean \u2014 phi-torsion braid kernel" + ], + "gap": "No formal constant architecture. \u03c0/\u03c6/\u03c4 role definitions not in Lean. All docs-level." + }, + "shadow_fiber_horn": { + "description": "All reality as projection-shadow of 16D object (BodegaFlow)", + "equations": [ + "Big Bang = first superposition, NaN relative to current-state model", + "Orange \u2260 black hole \u2260 galaxy, but all submit to same underlying laws", + "Space not expanding as volume \u2014 torsion widening infinite surface" + ], + "domain": "foundations/ontology", + "status": "thesis", + "coverage": "STRONG", + "existing_files": [ + "4-Infrastructure/shim/bodegaflow_horn_fiber_refinements.md \u2014 16D horn-fiber object, sector accessibility, projection model", + "6-Documentation/docs/distilled/16D_Manifold_Adjustment.md \u2014 trim/expand manifold rules", + "6-Documentation/docs/s3c_projected_geodesic_resolution_refinement_2026-05-10.md \u2014 folded 16D interior, receipted return surface", + "6-Documentation/docs/x86_64_rainbow_raccoon_optimizations.md \u2014 16D\u21924D projection/4D\u219216D reconstruction via SVD" + ], + "gap": "No Lean module for the 16D\u21923D projection operator. SVD approach exists only in optimization docs." + }, + "prime_line_witness_cover": { + "description": "Witness-first, residual-only expansion (from prime-line coverage)", + "equations": [ + "Cover \u2192 certify \u2192 branch only where cover fails", + "1024-bit coverage bitmasks, popcount, no floating point", + "Maintain witness cover. Expand only on awkward residuals." + ], + "domain": "computation/algorithm", + "status": "architectural", + "coverage": "PARTIAL", + "existing_files": [ + "0-Core-Formalism/lean/Semantics/Semantics/CompressionMechanicsBridge.lean \u2014 substrate admissibility, defect witness must be admissible", + "4-Infrastructure/shim/rrc_equation_classifier_table.csv \u2014 Q_Factor with witness coverage proxy", + "4-Infrastructure/shim/torsion_indexed_network_witness_topology_probe.py \u2014 ladder rule with residual expansion", + "0-Core-Formalism/lean/Semantics/Semantics/InvariantReceipt/Instances/DeltaPhiGammaKLambda.lean \u2014 R_DPG residual: expansion factor", + "6-Documentation/wiki/Concept-Archive.md \u2014 full-sweep Lean witnesses for COUCH values" + ], + "gap": "No bitmask witness cover implementation. No popcount-based coverage check. Prime-line pattern not integrated." + } + } +} \ No newline at end of file