{ "id": "dimensional-progression-cycle-restart", "type": "log", "title": "Dimensional Progression v2 \u2014 Cycle Restart Model, Not Single-Peak Cascade", "status": "superseded", "project": "cipher_v9", "date_published": "2026-03-28", "date_updated": "2026-05-12", "tags": [ "dimensional-progression", "cycle-restart", "single-peak-retired", "pi-scaling", "meta-cycle" ], "author": "Jonathan Shelton", "log_subtype": "framework_revision", "url": "https://prometheusresearch.tech/research/notes/dimensional-progression-cycle-restart.html", "source_markdown_url": "https://prometheusresearch.tech/research/_src/notes/dimensional-progression-cycle-restart.md.txt", "json_url": "https://prometheusresearch.tech/api/entries/dimensional-progression-cycle-restart.json", "summary_excerpt": "Earlier framework formulations described dimensions as a single-peak monotonic progression. This entry documents the revision to a cycle-restart model (3-dimension cycles with parameters scaled by \u03c0 between adjacent cycles' analogous slots) and its eventual subsumption into the Tribonacci cycle-spec...", "frontmatter": { "id": "dimensional-progression-cycle-restart", "type": "log", "title": "Dimensional Progression v2 \u2014 Cycle Restart Model, Not Single-Peak Cascade", "date_published": "2026-03-28", "date_updated": "2026-05-12", "project": "cipher_v9", "status": "superseded", "log_subtype": "framework_revision", "tags": [ "dimensional-progression", "cycle-restart", "single-peak-retired", "pi-scaling", "meta-cycle" ], "author": "Jonathan Shelton", "superseded_by": "fibonacci-to-tribonacci-c-ladder-correction", "see_also": [ "fibonacci-to-tribonacci-c-ladder-correction", "tribonacci-refinement-audit" ] }, "body_markdown": "\n## Author notes\n\nEarlier framework formulations described the dimensional cascade\nas a **single-peak progression** \u2014 one monotonic curve from\ndim 1 through dim N, with framework parameters varying smoothly\nalong it. This entry documents the *revision* to a **cycle-restart**\nmodel and its eventual subsumption into the Tribonacci-cycle\nframework.\n\n### The earlier model\n\nThe original framework treated dimensions as a single sequence\nwith parameters (framerate, c-value, spiral ratio) varying\nmonotonically. The implicit assumption: dim 4 is just \"one step\npast dim 3\" with the same machinery extended.\n\nThis was *partially* correct (parameters do vary along the\nsequence) but *missed the cycle structure*: dimensions don't form\none monotonic ladder \u2014 they form **cycles of three** (seed \u2192 flat\n\u2192 volumetric) with the meta-pattern *restarting* at each cycle\nboundary.\n\n### The cycle-restart insight\n\nThe framework's discovery:\n- Cycle 1 = dims 1, 2, 3. Pattern: seed (1D, linear) \u2192 flat (2D,\n planar) \u2192 volumetric (3D, solid).\n- Cycle 2 = dims 4, 5, 6. Pattern repeats: seed (4D, 4D-linear\n analog) \u2192 flat (5D, 5D-planar analog) \u2192 volumetric (6D, 6D-solid\n analog).\n- Cycle 3 = dims 7, 8, 9. Pattern repeats again.\n\nWithin each cycle, parameters scale by \u03c0 relative to the previous\ncycle's analogous slot. The 2D\u21923D boundary energy and the 5D\u21926D\nboundary energy differ by a factor close to \u03c0 (predicted ~3.14).\n\n### Why the single-peak model was wrong\n\nThe single-peak model didn't predict the cycle structure. It\npredicted *smooth* parameter variation across the entire sequence\n\u2014 so framework parameters at dim 4 should look like extrapolations\nof dim 3.\n\nBut the cipher's empirical results (and the magic-numbers\nderivation, the c-ladder findings) showed that dim 4 parameters\nare *not* simple extrapolations of dim 3. They're *analogs* at\nthe next cycle level. The single-peak model was missing the cycle\nrestart.\n\n### How this evolved into the Tribonacci framework\n\nThe cycle-restart model was the framework's intermediate step\nbetween the single-peak model and the full\n[Tribonacci cycle-specific framework](/research/notes/fibonacci-to-tribonacci-c-ladder-correction.html).\n\n- Single-peak \u2192 predicts smooth monotonic variation. Wrong.\n- Cycle-restart \u2192 predicts the same machinery restarts at each\n cycle boundary, with parameters scaled by \u03c0. Closer but\n incomplete.\n- Tribonacci \u2192 predicts each cycle has its *own* recurrence engine\n (Fibonacci for cycle 1, Tribonacci for cycle 2, Pentanacci for\n cycle 3). The cycle structure is real and the cycle *content*\n is different per cycle.\n\nThe cycle-restart model identified the structure; the Tribonacci\nframework identified the per-cycle mechanism.\n\n### Why this entry is preserved as superseded\n\nThe cycle-restart model is no longer canonical \u2014 the\nTribonacci framework supersedes it. But:\n1. The cycle structure itself (3-dimension cycles, meta-pattern\n restart) is correct and preserved in the Tribonacci framework.\n2. The \u03c0 scaling between analogous slots in adjacent cycles is\n approximately correct, though the Tribonacci framework gives a\n sharper derivation.\n3. The framework's intellectual-honesty discipline preserves\n intermediate-step documents as the audit trail. This entry is\n that audit trail for the single-peak \u2192 cycle-restart \u2192\n Tribonacci progression.\n\n### What this entry retains as solid\n\n- The cycle structure (three dimensions per cycle).\n- The meta-pattern restart at cycle boundaries.\n- The approximate \u03c0 scaling between adjacent cycle slots.\n- The recognition that the framework's machinery applies\n cycle-by-cycle, not monotonically.\n\n### What this entry retracts\n\n- The claim that the same recurrence engine governs all cycles.\n- The implicit equivalence of \"dim 4\" and \"dim 3 + 1.\" Dim 4 is\n the seed of cycle 2, structurally analogous to dim 1 (the seed\n of cycle 1), not a continuation of dim 3.\n\n## Summary\n\nEarlier framework formulations described dimensions as a\n**single-peak monotonic progression**. This entry documents the\nrevision to a **cycle-restart model** (3-dimension cycles with\nparameters scaled by \u03c0 between adjacent cycles' analogous slots)\nand its eventual subsumption into the\n[Tribonacci cycle-specific framework](/research/notes/fibonacci-to-tribonacci-c-ladder-correction.html).\n\n**Progression of framework versions:**\n1. **Single-peak** (early) \u2014 dims 1, 2, 3, 4, 5, \u2026 in one monotonic\n sequence. *Wrong:* didn't predict cycle structure.\n2. **Cycle-restart** (intermediate) \u2014 dims grouped into cycles of\n three (seed \u2192 flat \u2192 volumetric), with parameters scaled by \u03c0\n between adjacent cycles' analogous slots. *Better but incomplete.*\n3. **Tribonacci** (current canonical) \u2014 each cycle has its own\n recurrence engine (Fibonacci \u2192 Tribonacci \u2192 Pentanacci \u2192\n Octanacci). Cycle structure is real *and* the cycle content\n differs per cycle.\n\n**What this entry retains as solid:**\n- Cycle structure (three dimensions per cycle).\n- Meta-pattern restart at cycle boundaries.\n- Approximate \u03c0 scaling between adjacent cycle slots.\n\n**What this entry retracts:**\n- Single recurrence engine across all cycles.\n- Equivalence of \"dim 4\" and \"dim 3 + 1.\"\n\n**Status: superseded.** Preserved as the audit-trail record of how\nthe framework's understanding of dimensional progression evolved\nfrom monotonic to cycle-structured to cycle-specific.\n", "body_html": "

Author notes

\n

Earlier framework formulations described the dimensional cascade as a single-peak progression \u2014 one monotonic curve from dim 1 through dim N, with framework parameters varying smoothly along it. This entry documents the *revision* to a cycle-restart model and its eventual subsumption into the Tribonacci-cycle framework.

\n

The earlier model

\n

The original framework treated dimensions as a single sequence with parameters (framerate, c-value, spiral ratio) varying monotonically. The implicit assumption: dim 4 is just \"one step past dim 3\" with the same machinery extended.

\n

This was *partially* correct (parameters do vary along the sequence) but *missed the cycle structure*: dimensions don't form one monotonic ladder \u2014 they form cycles of three (seed \u2192 flat \u2192 volumetric) with the meta-pattern *restarting* at each cycle boundary.

\n

The cycle-restart insight

\n

The framework's discovery:

\n\n

Within each cycle, parameters scale by \u03c0 relative to the previous cycle's analogous slot. The 2D\u21923D boundary energy and the 5D\u21926D boundary energy differ by a factor close to \u03c0 (predicted ~3.14).

\n

Why the single-peak model was wrong

\n

The single-peak model didn't predict the cycle structure. It predicted *smooth* parameter variation across the entire sequence \u2014 so framework parameters at dim 4 should look like extrapolations of dim 3.

\n

But the cipher's empirical results (and the magic-numbers derivation, the c-ladder findings) showed that dim 4 parameters are *not* simple extrapolations of dim 3. They're *analogs* at the next cycle level. The single-peak model was missing the cycle restart.

\n

How this evolved into the Tribonacci framework

\n

The cycle-restart model was the framework's intermediate step between the single-peak model and the full Tribonacci cycle-specific framework.

\n\n

The cycle-restart model identified the structure; the Tribonacci framework identified the per-cycle mechanism.

\n

Why this entry is preserved as superseded

\n

The cycle-restart model is no longer canonical \u2014 the Tribonacci framework supersedes it. But: 1. The cycle structure itself (3-dimension cycles, meta-pattern restart) is correct and preserved in the Tribonacci framework. 2. The \u03c0 scaling between analogous slots in adjacent cycles is approximately correct, though the Tribonacci framework gives a sharper derivation. 3. The framework's intellectual-honesty discipline preserves intermediate-step documents as the audit trail. This entry is that audit trail for the single-peak \u2192 cycle-restart \u2192 Tribonacci progression.

\n

What this entry retains as solid

\n\n

What this entry retracts

\n\n

Summary

\n

Earlier framework formulations described dimensions as a single-peak monotonic progression. This entry documents the revision to a cycle-restart model (3-dimension cycles with parameters scaled by \u03c0 between adjacent cycles' analogous slots) and its eventual subsumption into the Tribonacci cycle-specific framework.

\n

Progression of framework versions: 1. Single-peak (early) \u2014 dims 1, 2, 3, 4, 5, \u2026 in one monotonic sequence. *Wrong:* didn't predict cycle structure. 2. Cycle-restart (intermediate) \u2014 dims grouped into cycles of three (seed \u2192 flat \u2192 volumetric), with parameters scaled by \u03c0 between adjacent cycles' analogous slots. *Better but incomplete.* 3. Tribonacci (current canonical) \u2014 each cycle has its own recurrence engine (Fibonacci \u2192 Tribonacci \u2192 Pentanacci \u2192 Octanacci). Cycle structure is real *and* the cycle content differs per cycle.

\n

What this entry retains as solid:

\n\n

What this entry retracts:

\n\n

Status: superseded. Preserved as the audit-trail record of how the framework's understanding of dimensional progression evolved from monotonic to cycle-structured to cycle-specific.

", "see_also": [ "fibonacci-to-tribonacci-c-ladder-correction", "tribonacci-refinement-audit" ], "cited_by": [], "attachments": [], "schema_version": "1.0", "generated_at": "2026-05-12T03:27:18.533879Z" }