{
  "id": "sim-256-cubed-pulsed-cmb",
  "type": "test",
  "title": "256\u00b3 Pulsed FDTD Simulation \u2014 Universe-Birth Cascade Grid Convergence Test",
  "status": "open",
  "project": "paper_7",
  "date_published": "2026-04-11",
  "date_updated": "2026-05-12",
  "tags": [
    "256-cubed",
    "pulsed-fdtd",
    "hetzner",
    "paper-7",
    "cmb-comparison",
    "grid-convergence",
    "universe-birth"
  ],
  "author": "Jonathan Shelton",
  "log_subtype": "experiment_in_progress",
  "url": "https://prometheusresearch.tech/research/tests/sim-256-cubed-pulsed-cmb.html",
  "source_markdown_url": "https://prometheusresearch.tech/research/_src/tests/sim-256-cubed-pulsed-cmb.md.txt",
  "json_url": "https://prometheusresearch.tech/api/entries/sim-256-cubed-pulsed-cmb.json",
  "summary_excerpt": "The 256\u00b3 pulsed FDTD simulation is the grid-convergence test for Paper 7's universe-birth cascade prediction. Tests whether the framework's predicted shell perturbation amplitude (10\u207b\u2076, matching CMB observation) is grid-resolution-independent or is an artifact of the simulation discretization.\nCompu...",
  "frontmatter": {
    "id": "sim-256-cubed-pulsed-cmb",
    "type": "test",
    "title": "256\u00b3 Pulsed FDTD Simulation \u2014 Universe-Birth Cascade Grid Convergence Test",
    "date_published": "2026-04-11",
    "date_updated": "2026-05-12",
    "project": "paper_7",
    "status": "open",
    "log_subtype": "experiment_in_progress",
    "tags": [
      "256-cubed",
      "pulsed-fdtd",
      "hetzner",
      "paper-7",
      "cmb-comparison",
      "grid-convergence",
      "universe-birth"
    ],
    "author": "Jonathan Shelton",
    "predicts": [
      "cycle-0-to-cycle-1-cascade-grid-independent"
    ],
    "see_also": [
      "paper-7-status-2026-05",
      "sim-003-v6c-cone-cascade"
    ]
  },
  "body_markdown": "\n## Author notes\n\nThe 256\u00b3 pulsed FDTD simulation is the grid-convergence test for\nPaper 7's universe-birth cascade prediction. The framework predicts\nthat the cycle-0 \u2192 cycle-1 transition produces specific perturbation\namplitudes that should match the 10\u207b\u2076 CMB shell fluctuations\nobserved by Planck.\n\nA core question: is the cascade prediction grid-resolution\ndependent? If the framework's predicted amplitude varies with grid\nresolution, the prediction is an artifact of the simulation\ndiscretization rather than the underlying physics. The 256\u00b3 test\nruns the same cascade at higher grid resolution than prior runs\n(at 64\u00b3 and 128\u00b3) and checks whether the predicted perturbation\namplitude is consistent.\n\n### Setup\n\n- Grid: 256\u00b3 FDTD with PML boundaries.\n- Initial condition: pulsed perturbation at the cycle-0 / cycle-1\n  boundary, with amplitude matched to the framework's\n  staging-quadratic capacity formula.\n- Drive: pulsed energy injection at the framework-predicted\n  cycle-0 boundary frequency.\n- Measurement: power spectral density of the resulting shell-mode\n  perturbations, compared to the 10\u207b\u2076 amplitude expected for CMB\n  shell fluctuations.\n\n### Compute cost\n\n- Single 256\u00b3 pulsed run: ~84 hours on Hetzner (CPU only).\n- Multiple runs across initial-condition variants: ~3-4 weeks total\n  for full sweep.\n- Storage per run: ~120 GB of raw waveform data.\n\n### As of 2026-05-12\n\nThe 256\u00b3 pulsed simulation is in progress on Hetzner. First run\ncompleting ~next 2-3 days. The framework's prediction is that the\nshell perturbation amplitude should be 10\u207b\u2076 \u00b1 20% at this grid\nresolution, matching the 64\u00b3 and 128\u00b3 runs to within statistical\nfluctuation.\n\n### Pre-registered confirmation/falsification\n\n**Confirmed if:**\n- 256\u00b3 pulsed run produces shell perturbation amplitude in the\n  range (0.8 to 1.2) \u00d7 10\u207b\u2076.\n- 256\u00b3 amplitude is within 15% of 128\u00b3 amplitude (grid-independent).\n- The shell-position distribution (which shells are perturbed)\n  matches across grid resolutions.\n\n**Partially confirmed if:**\n- 256\u00b3 amplitude is in the 0.5\u20132.0 \u00d7 10\u207b\u2076 range (right order of\n  magnitude, larger fluctuation than expected).\n- 256\u00b3 amplitude is within 30% of 128\u00b3 amplitude.\n\n**Falsified if:**\n- 256\u00b3 amplitude differs from 128\u00b3 by more than 50% \u2014 indicating\n  the cascade prediction is grid-resolution dependent.\n- 256\u00b3 amplitude differs from CMB observation by more than 2\u00d7 \u2014\n  indicating the framework's quantitative prediction is wrong by\n  an order of magnitude.\n- Shell-position distribution is *different* across grid\n  resolutions \u2014 indicating the cascade structure is\n  grid-discretization-artifactual.\n\n### Why this matters for Paper 7\n\nPaper 7's universe-birth cascade is the framework's most ambitious\nempirical reach. If the cascade prediction is grid-independent and\nmatches the CMB observation, Paper 7 has the cleanest\ncosmological confirmation the framework has produced. If the\nprediction is grid-dependent, the cascade model needs revision \u2014\nwhich could push Paper 7's release back significantly.\n\n### Why this matters for the framework more broadly\n\nGrid-independence at 256\u00b3 is the strongest test the framework's\nfoundational cascade architecture has received. If it passes, the\nframework's predictions at lower resolutions can be trusted with\nhigher confidence. If it fails, several other framework results\n(notably HPC-024's 64\u00b3 findings) may need to be re-checked at\nhigher resolution.\n\nThe\n[HPC-024 sphere-artifact discovery](/research/tests/hpc-024-angular-deficit.html)\nis the precedent here: small grid-resolution artifacts can produce\nmisleading signals. The 256\u00b3 test is the framework's commitment\nto checking that this isn't happening to its cosmological\npredictions.\n\n## Summary\n\nThe **256\u00b3 pulsed FDTD simulation** is the grid-convergence test\nfor [Paper 7's](/research/paper-status/paper-7-status-2026-05.html)\nuniverse-birth cascade prediction. Tests whether the framework's\npredicted shell perturbation amplitude (10\u207b\u2076, matching CMB\nobservation) is grid-resolution-independent or is an artifact of\nthe simulation discretization.\n\n**Compute:** 256\u00b3 pulsed FDTD on Hetzner. ~84 hours per run, ~3-4\nweeks for full sweep, ~120 GB per run.\n\n**As of 2026-05-12:** first 256\u00b3 run in progress, completing in\n~2-3 days.\n\n**Pre-registered confirmation thresholds:**\n- 256\u00b3 amplitude in (0.8 to 1.2) \u00d7 10\u207b\u2076 range\n- 256\u00b3 within 15% of 128\u00b3 amplitude (grid-independent)\n- Shell-position distribution matches across resolutions\n\n**Pre-registered falsification:**\n- 256\u00b3 differs from 128\u00b3 by >50% (grid-dependent prediction)\n- 256\u00b3 amplitude off CMB observation by >2\u00d7\n- Shell-position distribution differs across grids\n\n**Why this matters:** if grid-independent and CMB-matching,\nPaper 7's universe-birth cascade is the cleanest cosmological\nconfirmation the framework has produced. If grid-dependent, the\ncascade model needs revision and Paper 7's release pushes back.\n\n**Status: open.** Simulation in progress on Hetzner. First result\nexpected ~2-3 days from filing date.\n\n**Precedent:** the\n[HPC-024 sphere-artifact discovery](/research/tests/hpc-024-angular-deficit.html)\nshowed how 64\u00b3 grid artifacts can produce misleading signals.\nThis 256\u00b3 test is the framework's commitment to checking that the\ncosmological predictions aren't subject to the same issue.\n",
  "body_html": "<h2>Author notes</h2>\n<p>The 256\u00b3 pulsed FDTD simulation is the grid-convergence test for Paper 7's universe-birth cascade prediction. The framework predicts that the cycle-0 \u2192 cycle-1 transition produces specific perturbation amplitudes that should match the 10\u207b\u2076 CMB shell fluctuations observed by Planck.</p>\n<p>A core question: is the cascade prediction grid-resolution dependent? If the framework's predicted amplitude varies with grid resolution, the prediction is an artifact of the simulation discretization rather than the underlying physics. The 256\u00b3 test runs the same cascade at higher grid resolution than prior runs (at 64\u00b3 and 128\u00b3) and checks whether the predicted perturbation amplitude is consistent.</p>\n<h3>Setup</h3>\n<ul>\n<li>Grid: 256\u00b3 FDTD with PML boundaries.</li>\n<li>Initial condition: pulsed perturbation at the cycle-0 / cycle-1</li>\n<p>boundary, with amplitude matched to the framework's staging-quadratic capacity formula.</p>\n<li>Drive: pulsed energy injection at the framework-predicted</li>\n<p>cycle-0 boundary frequency.</p>\n<li>Measurement: power spectral density of the resulting shell-mode</li>\n<p>perturbations, compared to the 10\u207b\u2076 amplitude expected for CMB shell fluctuations.</p>\n</ul>\n<h3>Compute cost</h3>\n<ul>\n<li>Single 256\u00b3 pulsed run: ~84 hours on Hetzner (CPU only).</li>\n<li>Multiple runs across initial-condition variants: ~3-4 weeks total</li>\n<p>for full sweep.</p>\n<li>Storage per run: ~120 GB of raw waveform data.</li>\n</ul>\n<h3>As of 2026-05-12</h3>\n<p>The 256\u00b3 pulsed simulation is in progress on Hetzner. First run completing ~next 2-3 days. The framework's prediction is that the shell perturbation amplitude should be 10\u207b\u2076 \u00b1 20% at this grid resolution, matching the 64\u00b3 and 128\u00b3 runs to within statistical fluctuation.</p>\n<h3>Pre-registered confirmation/falsification</h3>\n<p><strong>Confirmed if:</strong></p>\n<ul>\n<li>256\u00b3 pulsed run produces shell perturbation amplitude in the</li>\n<p>range (0.8 to 1.2) \u00d7 10\u207b\u2076.</p>\n<li>256\u00b3 amplitude is within 15% of 128\u00b3 amplitude (grid-independent).</li>\n<li>The shell-position distribution (which shells are perturbed)</li>\n<p>matches across grid resolutions.</p>\n</ul>\n<p><strong>Partially confirmed if:</strong></p>\n<ul>\n<li>256\u00b3 amplitude is in the 0.5\u20132.0 \u00d7 10\u207b\u2076 range (right order of</li>\n<p>magnitude, larger fluctuation than expected).</p>\n<li>256\u00b3 amplitude is within 30% of 128\u00b3 amplitude.</li>\n</ul>\n<p><strong>Falsified if:</strong></p>\n<ul>\n<li>256\u00b3 amplitude differs from 128\u00b3 by more than 50% \u2014 indicating</li>\n<p>the cascade prediction is grid-resolution dependent.</p>\n<li>256\u00b3 amplitude differs from CMB observation by more than 2\u00d7 \u2014</li>\n<p>indicating the framework's quantitative prediction is wrong by an order of magnitude.</p>\n<li>Shell-position distribution is *different* across grid</li>\n<p>resolutions \u2014 indicating the cascade structure is grid-discretization-artifactual.</p>\n</ul>\n<h3>Why this matters for Paper 7</h3>\n<p>Paper 7's universe-birth cascade is the framework's most ambitious empirical reach. If the cascade prediction is grid-independent and matches the CMB observation, Paper 7 has the cleanest cosmological confirmation the framework has produced. If the prediction is grid-dependent, the cascade model needs revision \u2014 which could push Paper 7's release back significantly.</p>\n<h3>Why this matters for the framework more broadly</h3>\n<p>Grid-independence at 256\u00b3 is the strongest test the framework's foundational cascade architecture has received. If it passes, the framework's predictions at lower resolutions can be trusted with higher confidence. If it fails, several other framework results (notably HPC-024's 64\u00b3 findings) may need to be re-checked at higher resolution.</p>\n<p>The <a href=\"/research/tests/hpc-024-angular-deficit.html\">HPC-024 sphere-artifact discovery</a> is the precedent here: small grid-resolution artifacts can produce misleading signals. The 256\u00b3 test is the framework's commitment to checking that this isn't happening to its cosmological predictions.</p>\n<h2>Summary</h2>\n<p>The <strong>256\u00b3 pulsed FDTD simulation</strong> is the grid-convergence test for <a href=\"/research/paper-status/paper-7-status-2026-05.html\">Paper 7's</a> universe-birth cascade prediction. Tests whether the framework's predicted shell perturbation amplitude (10\u207b\u2076, matching CMB observation) is grid-resolution-independent or is an artifact of the simulation discretization.</p>\n<p><strong>Compute:</strong> 256\u00b3 pulsed FDTD on Hetzner. ~84 hours per run, ~3-4 weeks for full sweep, ~120 GB per run.</p>\n<p><strong>As of 2026-05-12:</strong> first 256\u00b3 run in progress, completing in ~2-3 days.</p>\n<p><strong>Pre-registered confirmation thresholds:</strong></p>\n<ul>\n<li>256\u00b3 amplitude in (0.8 to 1.2) \u00d7 10\u207b\u2076 range</li>\n<li>256\u00b3 within 15% of 128\u00b3 amplitude (grid-independent)</li>\n<li>Shell-position distribution matches across resolutions</li>\n</ul>\n<p><strong>Pre-registered falsification:</strong></p>\n<ul>\n<li>256\u00b3 differs from 128\u00b3 by >50% (grid-dependent prediction)</li>\n<li>256\u00b3 amplitude off CMB observation by >2\u00d7</li>\n<li>Shell-position distribution differs across grids</li>\n</ul>\n<p><strong>Why this matters:</strong> if grid-independent and CMB-matching, Paper 7's universe-birth cascade is the cleanest cosmological confirmation the framework has produced. If grid-dependent, the cascade model needs revision and Paper 7's release pushes back.</p>\n<p><strong>Status: open.</strong> Simulation in progress on Hetzner. First result expected ~2-3 days from filing date.</p>\n<p><strong>Precedent:</strong> the <a href=\"/research/tests/hpc-024-angular-deficit.html\">HPC-024 sphere-artifact discovery</a> showed how 64\u00b3 grid artifacts can produce misleading signals. This 256\u00b3 test is the framework's commitment to checking that the cosmological predictions aren't subject to the same issue.</p>",
  "see_also": [
    "paper-7-status-2026-05",
    "sim-003-v6c-cone-cascade"
  ],
  "cited_by": [],
  "attachments": [],
  "schema_version": "1.0",
  "generated_at": "2026-05-12T03:27:18.533879Z"
}