---
id: sim-003-v6c-cone-cascade
type: test
title: SIM-003 v6c — Two-Curve Cone Cascade With Emergent Global r
date_published: 2026-04-02
date_updated: 2026-05-12
project: dimensional_cascade
status: open
log_subtype: experiment_in_progress
tags: [sim-003, cone-cascade, hetzner, pockets-voids, wave-reinjection, global-r-emergence]
author: Jonathan Shelton
predicts:
  - r-equals-half-derivable-from-cone-geometry
data_supporting: []
data_refuting: []
see_also:
  - cipher-v11-complete-self-derivation
attachments:
  - path: research/simulation-code/SIM-003_v6c_wave_reinjection.py.txt
    role: script
    description: v6c driver — pockets + voids dual-curve, wave re-injection, emergent global_r
---

## Author notes

SIM-003 is the long-running attempt to *derive* the framework's
foundational `r = 0.5` decoherence ceiling from cone geometry rather
than impose it. Earlier versions:

- **v3** introduced cascade + information-theoretic terms. Matched
  the linear coefficient of the quadratic capacity equation; missed
  the quadratic coefficient. Used p=2 norm and 3D spherical
  propagation — the latter failed.
- **v4** moved to cone-shaped propagation with pulsed overflow.
  Fixed v3's 3D failure. Reached 18% angular coefficient-of-variation
  on the unfolding-angle prediction — better but still wide.
- **v6** (skipped v5) added pockets + voids dual-curve representation.
  Stalled at global_r = 0.419 — close to 0.5 but persistently below,
  suggesting an architectural rather than parameter issue.
- **v6c** (current) adds wave re-injection: when a pulse reflects off
  the cone boundary, the reflected energy is re-injected into the
  cascade as a fresh input, with phase-aware addition. Hypothesis:
  the 0.419 stall in v6 was because reflected energy was being
  *absorbed* by the boundary; re-injecting it should drive global_r
  toward 0.5 cleanly.

**Architecture (v6c).**
- Two-curve dual representation:
  - "Pockets" curve = energy concentrated at cone-apex regions
    (small-r, high-density)
  - "Voids" curve = energy in cone-bulk regions (large-r, low-density)
- Emergent global_r = mean(r_local) across the full cone volume,
  where r_local is computed from the local pocket/void ratio.
- Wave re-injection: reflected pulses are reintroduced at the source
  plane with phase-aware superposition.
- Convergence criterion: global_r stable to within 1% over 1000
  cascade steps.

**Currently running on Hetzner** (5.78.189.153). Single-box CPU run,
~96 hours estimated. As of 2026-05-12: ~36 hours in, global_r currently
tracking ~0.487 (vs v6's stalled 0.419). The trend is moving toward
0.5, but it's premature to call convergence — the last 8 hours have
seen global_r drift from 0.480 to 0.487, which is the right direction
but not yet stable.

**Pre-registered outcomes.**
- **Success:** global_r converges to 0.500 ± 0.003 over the last 1000
  steps. This would *derive* the r=0.5 ceiling from cone geometry with
  no parameter tuning.
- **Partial success:** global_r converges to 0.49–0.51 but with wider
  variance. The framework's ceiling is approximately right but the
  derivation isn't tight enough to call canonical.
- **Failure:** global_r stalls below 0.49 or oscillates without
  converging. Indicates the wave-reinjection hypothesis is insufficient
  and a deeper architectural change is needed (likely moving to 6D
  cascade — see SIM-003 6D extension memo).

**What this is and is not.**
- IS: an attempt to derive r=0.5 (a load-bearing framework parameter)
  from first principles via cone-geometry cascade simulation.
- IS NOT: a fit. The r=0.5 ceiling was set in the framework BEFORE
  SIM-003 began. If the simulation converges to 0.5, that's a
  prediction-matches-observation result. If it stalls below, the
  framework either has the right ceiling but the wrong derivation
  path, or both.

**Why this matters.** r=0.5 is the most foundational parameter in
TLT. It governs the dimensional cascade, defines when overflow occurs,
and propagates into the energy boundaries, the framerate formula, and
the spiral coordinate. A clean derivation would close one of the
framework's biggest open derivation chains.

**Float64 precision concern.** Earlier SIM-003 runs hit float64
precision limits when r_local approached 0.5 (cancellation errors in
the pocket/voids ratio). v6c added compensated summation in the
relevant accumulators. The fix appears to be working — no precision
artifacts observed in the first 36 hours.

## Summary

SIM-003 v6c is the current version of a long-running simulation
attempting to *derive* the framework's foundational `r = 0.5`
decoherence ceiling from cone-cascade geometry, rather than impose
it as a parameter.

**Why this matters.** r=0.5 governs the entire dimensional cascade —
when overflow occurs, the energy boundaries, the framerate formula,
the spiral coordinate. A clean derivation closes one of the framework's
biggest open derivation chains.

**v6c architecture.** Two-curve dual representation (pockets at small-r,
voids at large-r), emergent global_r from local-r averaging, plus
wave re-injection of reflected pulses (the fix for v6's 0.419 stall).

**Status: in progress on Hetzner.** As of 2026-05-12, ~36 hours into
a ~96-hour run. global_r currently tracking ~0.487 and trending toward
0.5. Premature to call convergence.

**Pre-registered outcomes:**
- 0.500 ± 0.003 → derivation confirmed
- 0.49–0.51 with wider variance → ceiling approximately right but
  derivation not tight
- Stalls below 0.49 → wave-reinjection hypothesis insufficient,
  deeper architectural change needed (possibly 6D cascade extension)

**Not a fit.** r=0.5 was set in the framework BEFORE SIM-003 began.
The simulation tests whether cone-cascade geometry produces that
ceiling independently. Either outcome is a finding.