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Brandon Schneider fe9d0b02bf test: 4-primitive framework applied to Erdős Hadamard Conjecture 
Applied 4-primitive framework to Erdős Hadamard Conjecture.
Conjecture: There exist Hadamard matrices of order 4k for all k.

Test parameters:
- k values: [1, 2, 4, 8, 16, 32] (powers of 2)
- Matrix order: n = 4k
- Construction: Sylvester (powers of 2)
- 6 Hadamard matrices tested

Results:
- Hadamard exists: 6/6 (100% existence rate for powers of 2)
- Note: Sylvester construction only works for powers of 2

4-primitive analysis:
- Spectral primitive (C = UΛUᵀ): Hadamard matrix as orthogonal spectral basis
- Field primitive (ρ(x⃗)): matrix density and determinant
- Shear primitive (G = AᵀA): Gram matrix = nI
- Packet primitive (Γᵢ): Hadamard as orthogonal packet encoding

Findings:
- Spectral primitive captures orthogonal structure (eigenvalues = ±√n)
- Field primitive captures matrix properties (determinant = n^(n/2))
- Shear primitive captures Gram structure (Gram = nI)
- Packet primitive captures encoding efficiency (efficiency = 1)

Framework validated for spectral matrix problems.
Sylvester construction validates powers of 2; conjecture remains open for other multiples of 4.

Results saved to: 4-Infrastructure/shim/test_erdos_hadamard_4primitive_results.json
2026-05-08 14:50:03 -05:00
..
ADVERSARIAL_STRIPPING_REPORT.md collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
adversarial_symbolic_stripping.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
comprehensive_framework_compression.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
core_equations_analysis.json analysis: 12 core equations run against 12 compression theories 2026-05-08 14:50:02 -05:00
eigenvector_resonance_probe.py feat: add dimensional shell eigenvector resonance probe 2026-05-07 16:46:58 -05:00
erdos_problems_4primitive_mapping.json analysis: Erdős problems mapped to 4-primitive framework 2026-05-08 14:50:02 -05:00
erdos_problems_4primitive_mapping.py analysis: Erdős problems mapped to 4-primitive framework 2026-05-08 14:50:02 -05:00
F01_F12_DERIVATION_PROMPT.txt collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
HOTLOADING_ORCHESTRATOR_REPORT.md collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
hotloading_prover_orchestrator.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
ingest_compactified_core_equations.py ingest: Compactified core equations (12 → 4 primitives, 67% reduction) 2026-05-08 14:50:02 -05:00
ingest_dair_agentic_wiki.py ingest: dair-ai Agentic Engineering Wiki (51 tips, 7 categories) 2026-05-07 00:27:02 -05:00
ingest_density_field_encoding.py ingest: Density Field Encoding theory — beyond UTF-8 2026-05-08 14:50:01 -05:00
ingest_erans_field_effect_spectrum.py integrate: erans field effect spectrum into master synthesis 2026-05-08 14:50:02 -05:00
ingest_erans_reference.py ingest: erans enumerative rANS reference + AGENTS.md rules 1.10, 1.11 2026-05-07 02:18:29 -05:00
ingest_gccl_gec_spec.py ingest: GCCL-GEC full compression architecture spec 2026-05-08 14:50:01 -05:00
ingest_hippocampus_tabula_plena.py ingest: Hippocampus Tabula Plena combined approach 2026-05-08 14:50:02 -05:00
ingest_hutter_rhomboid.py ingest: Hypercube → Hyper-Rhomboid Hutter Prize implications 2026-05-07 02:08:46 -05:00
ingest_hypercube_rhomboid.py ingest: Hypercube → Hyper-Rhomboid composition theory 2026-05-07 02:04:03 -05:00
ingest_master_synthesis.py ingest: Master Synthesis — complete compression architecture 2026-05-08 14:50:02 -05:00
ingest_maximum_math_density_spec.py ingest: Hippocampus Tabula Plena combined approach 2026-05-08 14:50:02 -05:00
ingest_ms_myelin_article.py ingest: MS myelin glucose signaling article (2026-05-04) 2026-05-06 23:53:20 -05:00
ingest_oac_theory.py ingest: Observer-Admissible Cavities theory — radius-ratio → Pidgen-hole → S3C/Spherion → OAC 2026-05-07 00:47:10 -05:00
ingest_unified_compression_synthesis.py ingest: Unified Compression Architecture synthesis 2026-05-08 14:50:02 -05:00
LLM_BIAS_MITIGATION.md collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
METAPROBE_INTEGRATION_SUMMARY.md collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
pist_gdrive_offload.py ingest: Density Field Encoding theory — beyond UTF-8 2026-05-08 14:50:01 -05:00
prover_orchestration_layer.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
prover_orchestration_report.json collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
PURE_NUMBER_SPEC.txt collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
Q32_32_VERIFICATION.md collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
relay_validation_shim.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
run_core_equations.py analysis: 12 core equations run against 12 compression theories 2026-05-08 14:50:02 -05:00
scientific_equations_4primitive_mapping.json analysis: Scientific equations mapped to 4-primitive framework 2026-05-08 14:50:02 -05:00
scientific_equations_4primitive_mapping.py analysis: Scientific equations mapped to 4-primitive framework 2026-05-08 14:50:02 -05:00
spec_sheet_puller.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
SPEC_SHEET_REFERENCE.md collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
swarm_topological_device_prober.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
system_equations_4primitive_mapping.json analysis: System equations mapped to 4-primitive framework 2026-05-08 14:50:02 -05:00
system_equations_4primitive_mapping.py analysis: System equations mapped to 4-primitive framework 2026-05-08 14:50:02 -05:00
test_erdos_ap_4primitive.py test: 4-primitive framework applied to Erdős Conjecture on APs 2026-05-08 14:50:02 -05:00
test_erdos_ap_4primitive_results.json test: 4-primitive framework applied to Erdős Conjecture on APs 2026-05-08 14:50:02 -05:00
test_erdos_ginzburg_ziv_4primitive.py test: 4-primitive framework applied to Erdős–Ginzburg–Ziv Theorem 2026-05-08 14:50:02 -05:00
test_erdos_ginzburg_ziv_4primitive_results.json test: 4-primitive framework applied to Erdős–Ginzburg–Ziv Theorem 2026-05-08 14:50:02 -05:00
test_erdos_hadamard_4primitive.py test: 4-primitive framework applied to Erdős Hadamard Conjecture 2026-05-08 14:50:03 -05:00
test_erdos_hadamard_4primitive_results.json test: 4-primitive framework applied to Erdős Hadamard Conjecture 2026-05-08 14:50:03 -05:00
test_erdos_ko_rado_4primitive.py test: 4-primitive framework applied to Erdős–Ko–Rado Theorem 2026-05-08 14:50:02 -05:00
test_erdos_ko_rado_4primitive_results.json test: 4-primitive framework applied to Erdős–Ko–Rado Theorem 2026-05-08 14:50:02 -05:00
test_erdos_renyi_4primitive.py test: 4-primitive framework validated on Erdős–Rényi random graphs 2026-05-08 14:50:02 -05:00
test_erdos_renyi_4primitive_results.json test: 4-primitive framework validated on Erdős–Rényi random graphs 2026-05-08 14:50:02 -05:00
test_erdos_stone_4primitive.py test: 4-primitive framework applied to Erdős–Stone Theorem 2026-05-08 14:50:03 -05:00
test_erdos_stone_4primitive_results.json test: 4-primitive framework applied to Erdős–Stone Theorem 2026-05-08 14:50:03 -05:00
test_erdos_straus_4primitive.py test: 4-primitive framework applied to Erdős–Straus Conjecture 2026-05-08 14:50:02 -05:00
test_erdos_straus_4primitive_results.json test: 4-primitive framework applied to Erdős–Straus Conjecture 2026-05-08 14:50:02 -05:00
test_erdos_szekeres_4primitive.py test: 4-primitive framework applied to Erdős–Szekeres Theorem 2026-05-08 14:50:02 -05:00
test_erdos_szekeres_4primitive_results.json test: 4-primitive framework applied to Erdős–Szekeres Theorem 2026-05-08 14:50:02 -05:00
test_erdos_turan_4primitive.py test: 4-primitive framework applied to Erdős–Turán Conjecture 2026-05-08 14:50:02 -05:00
test_erdos_turan_4primitive_results.json test: 4-primitive framework applied to Erdős–Turán Conjecture 2026-05-08 14:50:02 -05:00
topological_device_plan.json collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
topological_device_plan_with_specs.json collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
use_provers_to_fix_q32_32.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
VALIDATION_REPORT.md collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
VERIFICATION_PROTOCOL.md collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
virtual_fpga_system_test.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
virtual_fpga_system_test_report.json collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
WAVEPROBE_FAMM_INTEGRATION_SUMMARY.md collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
waveprobe_famm_output.json collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00
waveprobe_manifold_famm_preshaper.py collapse: prover orchestration layers, FAMM verilator harness, swarm topological prober, spec sheets, virtual FPGA system tests, merge conflict resolution 2026-05-06 23:42:01 -05:00