Results
| Quantity | Result |
|---|---|
| Final sphere count | 1,000 |
| Final generation-event index | 999 |
| Contacting sphere pairs | 5,178 |
| Minimum separation between distinct centers | 2r |
| Minimum center distance from the fixed reference centroid | Approximately 1.224745r |
| Maximum center distance from the fixed reference centroid | Approximately 11.022704r |
| Spheres with 12 final contacts | 565 |
Here r=ℓP is the assigned sphere radius. These are geometric model quantities, not physical observations.
The run stopped at the approved endpoint. No placement rule or stopping rule was changed in response to the output.
What passed verification
The implementation checked:
- The prescribed first five positions.
- Distinct, integer-coordinate lattice sites and the correct inventory count.
- Non-overlap across every pair of final sphere centers.
- Contact with at least one earlier sphere at every non-seed insertion.
- Compliance with the nearest-fixed-centroid and coordinate tie-breaking rules from sphere 6 onward.
- Retention of previously assigned coordinates.
- Agreement between contact counts calculated in different ways.
- An identical ordered sequence on rerunning the generator.
Placement decisions used exact integer arithmetic—not rounded Cartesian coordinates.
For the selection audit, a separate replay explicitly minimized over the complete eligible-site frontier rather than relying on the generator’s priority queue. This is a useful cross-check, but not a fully independent implementation: both procedures share the mathematical definitions and selection key.
What this establishes
The result supports a narrow conclusion:
The specified FCC construction can be executed to 1,000 spheres reproducibly, and the resulting configuration satisfies the implemented construction checks.
It does not establish physical sphere generation, the finite–infinite interpretation, or any connection with Galois representations, Langlands, SU(2), or SU(3). HCP remained inactive, as agreed.
Also, I have not independently verified that the final approved analysis plan was frozen on the public page before execution. The report therefore records approval in this conversation without claiming a verified public registration timestamp. Specifying the plan prospectively—and clearly distinguishing subsequent changes—is the purpose of preregistration.cos
Prepared deliverables
The PDF report contains the method, results, verification details, limitations, and three figures.
The accompanying reproducibility bundle contains:
- The complete 1,000-sphere event table.
- Final contact-count distribution.
- Verification table and machine-readable summary.
- Python reproduction source.
- Figures and the PDF report.
The next documentation step is to preserve these as the first bounded-run results, separately from the protocol. Any further explorations can then be identified as follow-up work rather than folded retrospectively into this run.