{
  "id": "test-jj-prism-extended-2026-05-14",
  "type": "test",
  "title": "Test JJ Prism-Extended \u2014 Prism-Family Chebyshev Lock",
  "status": "confirmed",
  "project": "geometric_wave_compute",
  "date_published": "2026-05-14",
  "date_updated": "2026-05-14",
  "tags": [
    "test-jj",
    "prism-class",
    "chebyshev",
    "drive-invariant",
    "coupled-pair",
    "gwc",
    "fdtd",
    "prism-7fold",
    "prism-11fold",
    "prism-13fold"
  ],
  "author": "Jonathan Shelton",
  "log_subtype": "experiment_complete",
  "url": "https://prometheusresearch.tech/research/tests/test-jj-prism-extended-2026-05-14.html",
  "source_markdown_url": "https://prometheusresearch.tech/research/_src/tests/test-jj-prism-extended-2026-05-14.md.txt",
  "json_url": "https://prometheusresearch.tech/api/entries/test-jj-prism-extended-2026-05-14.json",
  "summary_excerpt": "",
  "frontmatter": {
    "id": "test-jj-prism-extended-2026-05-14",
    "type": "test",
    "title": "Test JJ Prism-Extended \u2014 Prism-Family Chebyshev Lock",
    "date_published": "2026-05-14",
    "date_updated": "2026-05-14",
    "project": "geometric_wave_compute",
    "status": "confirmed",
    "log_subtype": "experiment_complete",
    "tags": [
      "test-jj",
      "prism-class",
      "chebyshev",
      "drive-invariant",
      "coupled-pair",
      "gwc",
      "fdtd",
      "prism-7fold",
      "prism-11fold",
      "prism-13fold"
    ],
    "author": "Jonathan Shelton",
    "predicts": [
      "prism-class-spectral-lock",
      "chebyshev-attractor-2cos2pi-N"
    ],
    "data_supporting": [
      "hpc-039-heptagonal-resonance",
      "test-jj-joint-emergence-prereg"
    ]
  },
  "body_markdown": "\n## TL;DR\n\nGWC Test JJ phase-1 advanced from 341 \u2192 606 of 700 configurations\nbetween 2026-05-13 and 2026-05-14, closing the prism_7fold near_field\ngap and adding full prism_11fold + partial prism_13fold pair-coverage.\n**The single-cavity {7}-uniqueness of [HPC-039](/research/tests/hpc-039-heptagonal-resonance.html)\ngeneralizes to a prism-family Chebyshev attractor at the coupled-pair\nscale.** Each prism over-represents its own `2\u00b7cos(2\u03c0/N)` ratio; each\nprism shows a drive-and-decoherence-invariant joint-spectrum envelope\nof comparable tightness:\n\n| Pair | n | BW std/mean (pooled) | BW std/mean (near_field) |\n|---|---:|---:|---:|\n| prism_7fold \u00d7 prism_7fold | 150 | 4.4 % | **2.8 %** (tightest in dataset) |\n| prism_11fold \u00d7 prism_11fold | 150 | 4.9 % | **2.9 %** |\n| prism_13fold \u00d7 prism_13fold | 56 / 150 | 7.1 % | (partial) |\n| octahedron \u00d7 octahedron | 175 | 75.6 % (compare) | \u2014 |\n| bicone \u00d7 bicone | 150 | 59.2 % (compare) | \u2014 |\n\n## Headline findings\n\n- **Prism family is a Chebyshev attractor.** The dominant joint-spectrum\n  ratio is `2\u00b7cos(2\u03c0/N)` (second-order Chebyshev), generic across\n  N. Earlier \"{7}-fold Fibonacci attractor\" framing is superseded.\n- **prism_11fold near_field is a new compute primitive** \u2014 12 GHz\n  wideband locked (2.9 % CV), 25-peak high-density modulator. Distinct\n  from the narrowband prism_7fold near_field clock primitive and the\n  high-entropy octa near_field modulator.\n- **prism_13fold may be entering a Bessel/cylinder asymptotic regime**\n  \u2014 its first-order Chebyshev `2\u00b7cos(2\u03c0/13) = 1.942` is *suppressed*\n  (0.70 %) below octa baseline 1.41 %. PROVISIONAL pending the\n  remaining 94 of 150 configs (Hetzner phase-1 ETA late 2026-05-14).\n- **bicone shared_wall hidden BW lock** \u2014 pooled 4.0 % CV, comparable\n  to a 7-fold prism, masked in pooled-shape views.\n\n## Math correction\n\nThe 2026-05-13 comprehensive doc labeled the dominant ratio\n`2\u00b7cos(\u03c0/7) = 1.247`. The correct label is **`2\u00b7cos(2\u03c0/7)`** \u2014\n`2\u00b7cos(\u03c0/7) \u2248 1.802` is a different number entirely. Minimal\npolynomial for `2\u00b7cos(2\u03c0/7)` is `x\u00b3 + x\u00b2 \u2212 2x \u2212 1 = 0`. The phenomenon\n(over-representation of the value 1.247) is real; only the symbolic\nidentification was wrong. Propagated to the GWC `tests/` corpus and\nthe GWC bibliography.\n\n## What this means for the framework\n\n- HPC-039's single-cavity {7}-uniformity result still holds as a\n  single-cavity property. Coupled-pair behavior generalizes.\n- Cipher v3 circuit-language Layer 1 should add a PRISM-CLASS family\n  with `bw_lock_cv` as a new readout, rather than proliferating\n  N-specific FRUSTRATE archetypes.\n- {7} is *first* in the cycle (lowest odd-prime frustration overtone),\n  not *unique* across it. Biology's preferential use of {7}-fold\n  rotational machines (ATP synthase, GroEL, proteasome) becomes an\n  open question for [Paper 9](/research/paper-status/paper-9-status-2026-05.html).\n\n## Source\n\nFindings doc and reproducibility artifacts are in the GWC project\ntree:\n\n- Findings: `geometric_wave_compute/tests/test_jj_prism_extended_2026-05-14.md`\n- Dataframe: `geometric_wave_compute/data/2026_05_14_pull/jj_fingerprints.pkl`\n  (681 records)\n- Build/analysis scripts: `geometric_wave_compute/data/2026_05_14_pull/{build_dataframe.py,analyze.py}`\n\nThe frequency-ratio analysis is in `analysis/ratios.json`; the\nshape \u00d7 topology cuts are in `analysis/cuts.json`.\n\n## Status\n\n**Confirmed for prism_7fold, prism_11fold.** Provisional for\nprism_13fold pending full sample (~94 more configurations finishing\non Hetzner late 2026-05-14). Bicone shared_wall hidden lock confirmed\nat the coupled-pair scale.\n",
  "body_html": "<h2>TL;DR</h2>\n<p>GWC Test JJ phase-1 advanced from 341 \u2192 606 of 700 configurations between 2026-05-13 and 2026-05-14, closing the prism_7fold near_field gap and adding full prism_11fold + partial prism_13fold pair-coverage. <strong>The single-cavity {7}-uniqueness of <a href=\"/research/tests/hpc-039-heptagonal-resonance.html\">HPC-039</a> generalizes to a prism-family Chebyshev attractor at the coupled-pair scale.</strong> Each prism over-represents its own <code>2\u00b7cos(2\u03c0/N)</code> ratio; each prism shows a drive-and-decoherence-invariant joint-spectrum envelope of comparable tightness:</p>\n<table class=\"entry-table\">\n<thead><tr>\n<th>Pair</th>\n<th>n</th>\n<th>BW std/mean (pooled)</th>\n<th>BW std/mean (near_field)</th>\n</tr></thead>\n<tbody>\n<tr>\n<td>prism_7fold \u00d7 prism_7fold</td>\n<td>150</td>\n<td>4.4 %</td>\n<td><strong>2.8 %</strong> (tightest in dataset)</td>\n</tr>\n<tr>\n<td>prism_11fold \u00d7 prism_11fold</td>\n<td>150</td>\n<td>4.9 %</td>\n<td><strong>2.9 %</strong></td>\n</tr>\n<tr>\n<td>prism_13fold \u00d7 prism_13fold</td>\n<td>56 / 150</td>\n<td>7.1 %</td>\n<td>(partial)</td>\n</tr>\n<tr>\n<td>octahedron \u00d7 octahedron</td>\n<td>175</td>\n<td>75.6 % (compare)</td>\n<td>\u2014</td>\n</tr>\n<tr>\n<td>bicone \u00d7 bicone</td>\n<td>150</td>\n<td>59.2 % (compare)</td>\n<td>\u2014</td>\n</tr>\n</tbody></table>\n<h2>Headline findings</h2>\n<ul>\n<li><strong>Prism family is a Chebyshev attractor.</strong> The dominant joint-spectrum</li>\n<p>ratio is <code>2\u00b7cos(2\u03c0/N)</code> (second-order Chebyshev), generic across N. Earlier \"{7}-fold Fibonacci attractor\" framing is superseded.</p>\n<li><strong>prism_11fold near_field is a new compute primitive</strong> \u2014 12 GHz</li>\n<p>wideband locked (2.9 % CV), 25-peak high-density modulator. Distinct from the narrowband prism_7fold near_field clock primitive and the high-entropy octa near_field modulator.</p>\n<li><strong>prism_13fold may be entering a Bessel/cylinder asymptotic regime</strong></li>\n<p>\u2014 its first-order Chebyshev <code>2\u00b7cos(2\u03c0/13) = 1.942</code> is *suppressed* (0.70 %) below octa baseline 1.41 %. PROVISIONAL pending the remaining 94 of 150 configs (Hetzner phase-1 ETA late 2026-05-14).</p>\n<li><strong>bicone shared_wall hidden BW lock</strong> \u2014 pooled 4.0 % CV, comparable</li>\n<p>to a 7-fold prism, masked in pooled-shape views.</p>\n</ul>\n<h2>Math correction</h2>\n<p>The 2026-05-13 comprehensive doc labeled the dominant ratio <code>2\u00b7cos(\u03c0/7) = 1.247</code>. The correct label is <strong><code>2\u00b7cos(2\u03c0/7)</code></strong> \u2014 <code>2\u00b7cos(\u03c0/7) \u2248 1.802</code> is a different number entirely. Minimal polynomial for <code>2\u00b7cos(2\u03c0/7)</code> is <code>x\u00b3 + x\u00b2 \u2212 2x \u2212 1 = 0</code>. The phenomenon (over-representation of the value 1.247) is real; only the symbolic identification was wrong. Propagated to the GWC <code>tests/</code> corpus and the GWC bibliography.</p>\n<h2>What this means for the framework</h2>\n<ul>\n<li>HPC-039's single-cavity {7}-uniformity result still holds as a</li>\n<p>single-cavity property. Coupled-pair behavior generalizes.</p>\n<li>Cipher v3 circuit-language Layer 1 should add a PRISM-CLASS family</li>\n<p>with <code>bw_lock_cv</code> as a new readout, rather than proliferating N-specific FRUSTRATE archetypes.</p>\n<li>{7} is *first* in the cycle (lowest odd-prime frustration overtone),</li>\n<p>not *unique* across it. Biology's preferential use of {7}-fold rotational machines (ATP synthase, GroEL, proteasome) becomes an open question for <a href=\"/research/paper-status/paper-9-status-2026-05.html\">Paper 9</a>.</p>\n</ul>\n<h2>Source</h2>\n<p>Findings doc and reproducibility artifacts are in the GWC project tree:</p>\n<ul>\n<li>Findings: <code>geometric_wave_compute/tests/test_jj_prism_extended_2026-05-14.md</code></li>\n<li>Dataframe: <code>geometric_wave_compute/data/2026_05_14_pull/jj_fingerprints.pkl</code></li>\n<p>(681 records)</p>\n<li>Build/analysis scripts: <code>geometric_wave_compute/data/2026_05_14_pull/{build_dataframe.py,analyze.py}</code></li>\n</ul>\n<p>The frequency-ratio analysis is in <code>analysis/ratios.json</code>; the shape \u00d7 topology cuts are in <code>analysis/cuts.json</code>.</p>\n<h2>Status</h2>\n<p><strong>Confirmed for prism_7fold, prism_11fold.</strong> Provisional for prism_13fold pending full sample (~94 more configurations finishing on Hetzner late 2026-05-14). Bicone shared_wall hidden lock confirmed at the coupled-pair scale.</p>",
  "see_also": [],
  "cited_by": [],
  "attachments": [],
  "schema_version": "1.0",
  "generated_at": "2026-05-14T15:56:01.670847Z"
}