---
id: sim-256-cubed-pulsed-cmb
type: test
title: 256³ Pulsed FDTD Simulation — 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
---

## Author notes

The 256³ pulsed FDTD simulation is the grid-convergence test for
Paper 7's universe-birth cascade prediction. The framework predicts
that the cycle-0 → cycle-1 transition produces specific perturbation
amplitudes that should match the 10⁻⁶ CMB shell fluctuations
observed by Planck.

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 256³ test
runs the same cascade at higher grid resolution than prior runs
(at 64³ and 128³) and checks whether the predicted perturbation
amplitude is consistent.

### Setup

- Grid: 256³ FDTD with PML boundaries.
- Initial condition: pulsed perturbation at the cycle-0 / cycle-1
  boundary, with amplitude matched to the framework's
  staging-quadratic capacity formula.
- Drive: pulsed energy injection at the framework-predicted
  cycle-0 boundary frequency.
- Measurement: power spectral density of the resulting shell-mode
  perturbations, compared to the 10⁻⁶ amplitude expected for CMB
  shell fluctuations.

### Compute cost

- Single 256³ pulsed run: ~84 hours on Hetzner (CPU only).
- Multiple runs across initial-condition variants: ~3-4 weeks total
  for full sweep.
- Storage per run: ~120 GB of raw waveform data.

### As of 2026-05-12

The 256³ 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 10⁻⁶ ± 20% at this grid
resolution, matching the 64³ and 128³ runs to within statistical
fluctuation.

### Pre-registered confirmation/falsification

**Confirmed if:**
- 256³ pulsed run produces shell perturbation amplitude in the
  range (0.8 to 1.2) × 10⁻⁶.
- 256³ amplitude is within 15% of 128³ amplitude (grid-independent).
- The shell-position distribution (which shells are perturbed)
  matches across grid resolutions.

**Partially confirmed if:**
- 256³ amplitude is in the 0.5–2.0 × 10⁻⁶ range (right order of
  magnitude, larger fluctuation than expected).
- 256³ amplitude is within 30% of 128³ amplitude.

**Falsified if:**
- 256³ amplitude differs from 128³ by more than 50% — indicating
  the cascade prediction is grid-resolution dependent.
- 256³ amplitude differs from CMB observation by more than 2× —
  indicating the framework's quantitative prediction is wrong by
  an order of magnitude.
- Shell-position distribution is *different* across grid
  resolutions — indicating the cascade structure is
  grid-discretization-artifactual.

### Why this matters for Paper 7

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 —
which could push Paper 7's release back significantly.

### Why this matters for the framework more broadly

Grid-independence at 256³ 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 64³ findings) may need to be re-checked at
higher resolution.

The
[HPC-024 sphere-artifact discovery](/research/tests/hpc-024-angular-deficit.html)
is the precedent here: small grid-resolution artifacts can produce
misleading signals. The 256³ test is the framework's commitment
to checking that this isn't happening to its cosmological
predictions.

## Summary

The **256³ pulsed FDTD simulation** is the grid-convergence test
for [Paper 7's](/research/paper-status/paper-7-status-2026-05.html)
universe-birth cascade prediction. Tests whether the framework's
predicted shell perturbation amplitude (10⁻⁶, matching CMB
observation) is grid-resolution-independent or is an artifact of
the simulation discretization.

**Compute:** 256³ pulsed FDTD on Hetzner. ~84 hours per run, ~3-4
weeks for full sweep, ~120 GB per run.

**As of 2026-05-12:** first 256³ run in progress, completing in
~2-3 days.

**Pre-registered confirmation thresholds:**
- 256³ amplitude in (0.8 to 1.2) × 10⁻⁶ range
- 256³ within 15% of 128³ amplitude (grid-independent)
- Shell-position distribution matches across resolutions

**Pre-registered falsification:**
- 256³ differs from 128³ by >50% (grid-dependent prediction)
- 256³ amplitude off CMB observation by >2×
- Shell-position distribution differs across grids

**Why this matters:** 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.

**Status: open.** Simulation in progress on Hetzner. First result
expected ~2-3 days from filing date.

**Precedent:** the
[HPC-024 sphere-artifact discovery](/research/tests/hpc-024-angular-deficit.html)
showed how 64³ grid artifacts can produce misleading signals.
This 256³ test is the framework's commitment to checking that the
cosmological predictions aren't subject to the same issue.