9/2127 the staircase

OPEN Survived every test within its budgets. No box tiling through volume 128. No periodic tiling through lattice index 72. Wraps itself 2 times, with a verified witness. Whether it wraps 3 times is undecided.

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cells
9, bounding box 1×4×4
symmetry order
2
chiral
no, its own mirror image
Heesch number
≥ 2
record
data/9/2127/shape.json

Stages

stageoutcomeat
boxexhausted128
torusexhausted72
coronawitnessed2
coronaattempted3

Downloads

The record, as stored 
{
  "id": "9/2127",
  "n": 9,
  "cells": [[0, 0, 0], [0, 0, 1], [0, 0, 2], [0, 0, 3], [0, 1, 0], [0, 1, 2], [0, 2, 0], [0, 2, 1], [0, 3, 0]],
  "symmetry_order": 2,
  "chiral": false,
  "mirror_id": "9/2127",
  "verdict": "open",
  "tiles_rotations_only": null,
  "tiles_with_reflections": null,
  "certificate": null,
  "heesch": null,
  "budgets": { "box_max_volume": 128, "corona_depth": 3, "torus_max_index": 72 },
  "credits": { "prior_art": null, "solved_by": "polycube-census v0.1.0", "verified_by": null },
  "reached": { "corona_sat": 2 },
  "attempts": [
    {
      "as_of": "2026-10-07",
      "core_hours": 3350,
      "depth": 3,
      "notes": "approximate total: kissat 4.0.4 and cadical 3 (source builds) one core each on the colo from 2026-08-12 to 2026-10-07, 1,347 hours each, stopped by hand with no verdict and no proof output (1.34 and 1.54 billion conflicts, glue drifting up, elimination flat); kissat on the laptop 128.4 hours, stopped 2026-08-16; three cube-and-conquer campaigns (4,096-way, 192-way, 25,920-way) through 2026-08-14, ledgers kept; solver logs kept under cnf/colo-logs/",
      "status": "stopped"
    }
  ],
  "stages": [
    { "outcome": "exhausted", "stage": "box", "volume": 128 },
    { "index": 72, "outcome": "exhausted", "stage": "torus" },
    { "depth": 2, "outcome": "witnessed", "stage": "corona" },
    { "depth": 3, "outcome": "attempted", "stage": "corona" }
  ]
}