================================================================================ TEST DESCRIPTION: 5D Wave Propagation Engine ================================================================================ Date: 2026-03-23 Author: Jonathan Shelton Status: PRE-REGISTERED — predictions locked before code is written Project: 4D Research → 5D Extension Methodology: Output-agnostic. Predictions below are what we expect. The engine reports what it finds. Disagreement is data. ================================================================================ I. PURPOSE ================================================================================ Test whether the 4D field, when given a 5th spatial dimension to expand into, produces the structure predicted by the {2,3} cycling framework. The 4D engine identified the 24-cell as the organizing geometry of 4D space, with two intensity channels (dual orientations, twin peaks in the z-profile). The 5D engine asks: what does the 4D geometry PRODUCE when it becomes the source? KEY PRINCIPLE: The 4D geometry becomes the pulse. We do not hand-place a 5D geometry. We use the 4D output as the initial condition and let the 5D structure EMERGE. II. THEORETICAL BASIS ================================================================================ From the {2,3} cycling framework (5d_exploration_notes.txt, 2026-03-23): First cycle: {2,3} on SIGNAL → geometry (1D→2D→3D) Second cycle: {2,3} on GEOMETRY → meta-geometry (4D→5D→6D) 4D = new 1D (the geometric pulse, the substrate) 5D = new 2D (the geometric ground state, the efficient foundation) The 4D field's dual-channel structure (twin intensity peaks from the 24-cell's self-dual orientations) provides the RHYTHM: - The two walls of the "stomach" cavity pulse - The oscillation between dual orientations IS the heartbeat - The space between the peaks is where structure can form This is analogous to how the original f|t pulse created space for 2D geometry to form. The 4D geometric pulse creates space for 5D geometry. III. SOURCE: 4D OUTPUT AS 5D INPUT ================================================================================ Method: 1. Load the 4D engine cross-section at c=1.700 (the resonance point where the field reorganizes: 25 peaks, 3x autocorrelation, 2.5x P/N) 2. Use this 3D intensity field as the SOURCE DISTRIBUTION for the 5D wave equation 3. The 4D field is placed at the v=0 midplane of the 5D grid (where v is the 5th spatial coordinate) 4. The 5D wave equation propagates this field into the v-direction The 5D grid: x, y, z, w, v - x, y, z, w: inherited from 4D structure - v: the new 5th spatial dimension EQUATION: ∂²ψ/∂t² = c² (∂²ψ/∂x² + ∂²ψ/∂y² + ∂²ψ/∂z² + ∂²ψ/∂w² + ∂²ψ/∂v²) Same FDTD approach as the 4D engine, extended to 5 spatial dimensions. GRID SIZE CONSTRAINT: N=32: 32⁵ = 33,554,432 cells. ~256 MB per field array. Feasible. N=48: 48⁵ = 254,803,968 cells. ~2 GB per field array. Tight but possible. N=64: 64⁵ = 1,073,741,824 cells. ~8 GB. Likely too large for VPS. START WITH N=32. If results are promising, attempt N=48. IV. FRAMERATE SWEEP ================================================================================ The 5D framerate is unknown. We sweep. Since 5D = new 2D in the cycling framework, and the original 2D had dimensional constant a=1.500, the 5D sweep should explore a range that includes the possibility of the 5D framerate being HIGHER than 4D's. Sweep range: c_5d = 1.5 to 2.5 (in steps of 0.05) Focus range: c_5d = 1.7 to 2.2 (finer steps of 0.025) Rationale: if the ratio progression is monotonically increasing (1.0 → 1.5 → 1.618 → 1.7 → ?), the 5D ratio likely sits above 1.7. The sweep extends to 2.5 to avoid truncating the search space. V. PRE-REGISTERED PREDICTIONS ================================================================================ These predictions are LOCKED before any code is written or data is seen. PREDICTION 1: THREE INTENSITY CHANNELS The v-axis intensity profile (analogous to the z-profile in 4D) should show THREE peaks, not two. 4D showed 2 peaks (positive/anti-positive dual orientations). 5D should show 3 peaks (positive, anti-positive, neutral). MEASUREMENT: Total intensity per v-slice, plotted across the v-axis. SUCCESS: 3 distinct peaks in the profile. FAILURE: 2 peaks (4D pattern persists) or >3 peaks or no peaks. PREDICTION 2: GROUND-STATE CHARACTER The 5D structure should show signatures of EFFICIENCY, not complexity. 5D = new 2D = the ground state. Expect: - High symmetry order (the pattern should be regular, not chaotic) - Fewer distinct peak types than 4D (simplification, not complexification) - The {2,3} filter should hold: any emergent peak count or symmetry should factor into 2s and 3s only MEASUREMENT: Peak count, symmetry order parameter, autocorrelation. SUCCESS: Autocorrelation >= 4D levels (0.207), peak count factorable by {2,3} only. FAILURE: Autocorrelation drops below 4D levels (disorganization). PREDICTION 3: WIDENING The intensity spread should be WIDER than 4D, not narrower. The monotonic increase thesis predicts continued expansion. MEASUREMENT: Intensity-weighted radius at midplane vs 4D equivalent. SUCCESS: 5D spread > 4D spread (normalized to grid size). FAILURE: 5D spread < 4D spread (contraction/regression). PREDICTION 4: THE NEUTRAL CHANNEL The third peak (neutral) should have DIFFERENT character from the positive and anti-positive peaks: - It may be lower intensity (emergent, not primary) - It may be broader (less concentrated, more diffuse) - It should sit BETWEEN the positive and anti-positive peaks on the v-axis (mediating position) MEASUREMENT: Relative intensity and width of the three peaks. SUCCESS: Third peak is distinct in character from the other two. FAILURE: All three peaks are identical (which would still be interesting but wouldn't confirm the neutral hypothesis). PREDICTION 5: RESONANCE AT A SPECIFIC c_5d There should be a 5D framerate value where the field REORGANIZES, analogous to c=1.700 in 4D. At this value: - Peak count should change (drop or restructure) - Autocorrelation should spike - Energy should redistribute MEASUREMENT: Sweep metrics across c_5d range. SUCCESS: A sharp resonance point exists. FAILURE: Smooth, featureless sweep (no preferred framerate). VI. WHAT WE ARE NOT PREDICTING ================================================================================ - The exact 5D framerate (we don't know it — that's what the sweep finds) - The exact geometry that emerges (we're letting it emerge, not placing it) - Whether the results will support or contradict the framework (the engine reports what it finds) The test is designed to be USEFUL whether predictions succeed or fail. Failure is data. Unexpected results are the most valuable kind. VII. AUDIT PROTOCOL ================================================================================ Same as 4D engine (AUDIT_PROTOCOL.txt): 1. Internal self-audit after results 2. Contrarian audit (challenge every finding) 3. External audit: Grok + Gemini 4. Score threshold: >= 7/10 from both external auditors 5. Only promoted to audited/ folder if all audits pass VIII. COMPUTATIONAL PLAN ================================================================================ Phase 1: N=32, coarse sweep (c_5d = 1.5 to 2.5, step 0.1) Purpose: Find the landscape. Where are the interesting regions? Estimated time: ~10-15 min per c value × 11 values = 2-3 hours Phase 2: N=32, fine sweep (focus region from Phase 1, step 0.025) Purpose: Locate resonance points. Estimated time: depends on focus region width Phase 3: N=48, targeted runs at identified resonance points Purpose: Higher resolution confirmation. Estimated time: ~1-2 hours per c value (larger grid) All results saved to: 4d_research/results/unaudited/5d_engine/ ================================================================================ PREDICTIONS LOCKED. CODE FOLLOWS. ================================================================================