--- id: spiral-self-derivation-prereg type: prediction title: Pre-Registered — Spiral Coordinate Self-Derivation from r=0.5 + Cone Geometry date_published: 2026-04-03 date_updated: 2026-05-12 project: cipher_v12 status: open log_subtype: pre_registration tags: [prediction, spiral-coordinate, self-derivation, sim-003, r-0.5, prereg, falsifiable, paper-3-blocker] author: Jonathan Shelton predicts: - cipher-spiral-derives-from-first-principles see_also: - sim-003-v6c-cone-cascade - cipher-v11-complete-self-derivation - paper-3-status-2026-05 --- ## Author notes The cipher's spiral coordinate (where electrons are seated on the C_potential's internal geometry) is currently set empirically via a Thomson/Fibonacci hybrid. This works (v11/v12 produce 91/107 with 0 misses) but the spiral itself is not *derived* from the framework's axioms — it's empirically tuned. This pre-registration locks the specific values the spiral *should* take if the [SIM-003 cone-cascade](/research/tests/sim-003-v6c-cone-cascade.html) derivation chain produces it from first principles. ### Why pre-registration matters here If SIM-003 converges to a spiral and the framework operator *then* checks whether it matches the cipher's empirically-set spiral, there's a circularity risk: any small adjustment of the SIM-003 parameters could be (post-hoc) tuned to match the empirical spiral, giving a false derivation. Pre-registration locks the empirical spiral values *now* so the SIM-003 outcome either matches or doesn't. ### The pre-registered spiral parameters The empirical Thomson/Fibonacci hybrid spiral that v11/v12 use has the following characteristic values: | Property | Empirical value | Tolerance | |---|---|---| | Bulge position (max radius / mean radius) | 1.29 | ±0.02 | | Floor frequency (lowest stable seat) | 0.207 c (where c = 1) | ±0.005 | | First seat / second seat angular spacing | 137.51° | ±0.2° | | Spiral pitch ratio (Z-axis advance per turn) | 0.143 | ±0.005 | | Decoherence ceiling | 0.500 | ±0.003 | These five numbers fully specify the spiral as v11/v12 uses it. SIM-003 v6c is the simulation that should *derive* these five numbers from the framework's three axioms (f|t pulse, r=0.5 ceiling, {2,3} organizing pair) plus the geometry of the cone- cascade architecture. ### Confirmation thresholds **Fully confirmed if:** - SIM-003 v6c converges to a spiral whose bulge position is in [1.27, 1.31]. - Floor frequency in [0.202, 0.212] (c-units). - Angular spacing of first two seats in [137.31°, 137.71°]. - Spiral pitch in [0.138, 0.148]. - Decoherence ceiling in [0.497, 0.503]. ALL five values must match within tolerance for full confirmation. **Partially confirmed if:** - 3 or 4 of the 5 values match within tolerance. - The 1-2 mismatching values are within 2× the tolerance. **Falsified if:** - Fewer than 3 values match within tolerance. - ANY value is off by more than 5× the tolerance. - SIM-003 v6c fails to converge or produces a non-spiral configuration. ### What this would unblock [Paper 3 (Cipher)](/research/paper-status/paper-3-status-2026-05.html) is currently HELD pending spiral self-derivation. If this prediction confirms: 1. The cipher becomes a complete self-derivation chain from axioms through prediction. 2. Paper 3 is released within 2-3 weeks of confirmation. 3. The framework's intellectual-honesty discipline is satisfied — no fit-shaped hole in the most consequential paper. If this prediction is falsified (or only partially confirmed), Paper 3 remains held until an alternative derivation path (bulge/floor approach, or others) produces the spiral. ### Why the spiral is the load-bearing piece The cipher's other components (eigenvalue spectrum from CN, snap- tunneling from percolation topology, bicone simultaneous derivation) are all *derivable* from the framework's axioms + the Z-determined shell structure. The spiral is the *one* piece that currently needs empirical input. If it derives from the cone cascade, the cipher chain is complete; if not, the chain has a gap. This is why Paper 3 is held. Publishing with a gap in the derivation chain would be publishing a paper with a fit at its core — exactly what the framework's discipline forbids. ### Status of evaluation - [SIM-003 v6c](/research/tests/sim-003-v6c-cone-cascade.html) is currently running on Hetzner. As of 2026-05-12, ~36 hours into a ~96-hour run; global_r tracking ~0.487 (trending toward 0.5). - If SIM-003 v6c converges to r=0.5, the spiral derivation chain should complete and the five pre-registered values will land somewhere on the confirmed / partially confirmed / falsified scale. ## Summary **Pre-registered prediction** for the spiral coordinate self-derivation that would unblock Paper 3 release. **Background:** the cipher's spiral coordinate is currently set empirically via Thomson/Fibonacci hybrid. v11/v12 produce 91/107 with the empirical spiral — but the spiral itself isn't derived from the framework's axioms. Paper 3 (Cipher) is HELD pending spiral self-derivation. **The 5 empirical spiral values pre-registered:** | Property | Empirical value | Tolerance | |---|---|---| | Bulge position | 1.29 | ±0.02 | | Floor frequency | 0.207 c | ±0.005 | | First→second seat angle | 137.51° | ±0.2° | | Spiral pitch | 0.143 | ±0.005 | | Decoherence ceiling | 0.500 | ±0.003 | **Confirmation:** all 5 match within tolerance. **Partial:** 3-4 of 5 within tolerance. **Falsified:** <3 within tolerance, OR any off by >5× tolerance. **Test:** [SIM-003 v6c cone-cascade simulation](/research/tests/sim-003-v6c-cone-cascade.html) should derive these five values from the framework's three axioms plus cone-cascade geometry. Currently running on Hetzner. **What this unblocks:** - Confirmation → [Paper 3](/research/paper-status/paper-3-status-2026-05.html) released within 2-3 weeks. Cipher derivation chain complete. - Falsified → Paper 3 stays held; alternative derivation path (bulge/floor approach) explored next. **Why pre-registration:** prevents circularity. The empirical spiral values are locked *before* SIM-003 results land. Post-hoc tuning of SIM-003 parameters to match the empirical spiral would be a false derivation; pre-registration forecloses this. **Status: open.** SIM-003 v6c convergence is the gating event. Result lands wherever it lands.