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:
the linear coefficient of the quadratic capacity equation; missed the quadratic coefficient. Used p=2 norm and 3D spherical propagation \u2014 the latter failed.
\nFixed v3's 3D failure. Reached 18% angular coefficient-of-variation on the unfolding-angle prediction \u2014 better but still wide.
\nStalled at global_r = 0.419 \u2014 close to 0.5 but persistently below, suggesting an architectural rather than parameter issue.
\nthe 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.
\nArchitecture (v6c).
\n(small-r, high-density)
\nwhere r_local is computed from the local pocket/void ratio.
\nplane with phase-aware superposition.
\ncascade steps.
\nCurrently 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 \u2014 the last 8 hours have seen global_r drift from 0.480 to 0.487, which is the right direction but not yet stable.
\nPre-registered outcomes.
\nsteps. This would *derive* the r=0.5 ceiling from cone geometry with no parameter tuning.
\nvariance. The framework's ceiling is approximately right but the derivation isn't tight enough to call canonical.
\nconverging. Indicates the wave-reinjection hypothesis is insufficient and a deeper architectural change is needed (likely moving to 6D cascade \u2014 see SIM-003 6D extension memo).
\nWhat this is and is not.
\nfrom first principles via cone-geometry cascade simulation.
\nSIM-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.
\nWhy 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.
\nFloat64 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 \u2014 no precision artifacts observed in the first 36 hours.
\nSIM-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 \u2014 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.
\nv6c 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).
\nStatus: 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.
\nPre-registered outcomes:
\nderivation not tight
\ndeeper architectural change needed (possibly 6D cascade extension)
\nNot 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.
", "see_also": [ "cipher-v11-complete-self-derivation" ], "cited_by": [ "paper-7-status-2026-05", "sim-256-cubed-pulsed-cmb", "spiral-self-derivation-prereg" ], "attachments": [ { "path": "research/simulation-code/SIM-003_v6c_wave_reinjection.py.txt", "role": "script", "description": "v6c driver \u2014 pockets + voids dual-curve, wave re-injection, emergent global_r" } ], "schema_version": "1.0", "generated_at": "2026-05-12T03:27:18.533879Z" }