Refined Index Calculator

Installation

macOS

1. Download ManifoldIndex.zip from the download section above.
2. Open the zip — macOS expands it to ManifoldIndex.app. Drag the app into /Applications (or any folder you prefer).
3. Because the app is not notarised, Gatekeeper will block the first launch. Clear the quarantine flag with:
   xattr -cr /Applications/ManifoldIndex.app
   Then double-click the app as normal. This step is only required once.
4. If you skipped step 3 and already saw the "cannot be opened" dialog, open System Settings → Privacy & Security and click Open Anyway next to the ManifoldIndex entry.

The app bundles its own Python runtime and SnapPy — you do not need to install anything else.

Windows

1. Download ManifoldIndex.exe from the download section above (it's a single self-contained executable — no installer, no zip).
2. Move it anywhere you like (Desktop, Documents, a new folder — it's fine). Double-click to run.
3. On first launch, Windows SmartScreen may show a blue pop-up saying "Windows protected your PC" because the binary isn't signed by a recognised publisher. Click More info, then Run anyway. You will only see this once per download.
4. If Microsoft Defender or a third-party antivirus quarantines the file, add an exclusion for the folder you put ManifoldIndex.exe in. The installer-less format occasionally trips heuristic scanners.

Startup takes ~5–10 seconds on first launch while the embedded Python unpacks into %LOCALAPPDATA%\Temp. Subsequent launches are faster.

From Source

Requires Python 3.10 or newer. After cloning the repo:

Changelog

v1.1.4 — hard-edge basis info moves to the fill-info panel

• "opt K→K′" badge moved out of the NC cycle table. The Weyl-vectors-per-edge table in the Compute Filling info panel is the right home for it: $a_j$ / $b_j$ are attached to the hard-edge basis $W_j$, so the basis itself belongs immediately above that table. v1.1.4 adds a dedicated Hard-edge basis section that lists each $W_j$ as the per-tetrahedron triplet $(z_i, z'_i, z''_i)$, and carries the optimisation badge (refinement gain + $G$ matrix on hover) when the basis is non-default.

v1.1.3 — basis optimiser actually runs in the GUI

• Hard-edge basis optimisation now activates in the GUI. In v1.1.0 / v1.1.1 / v1.1.2 the per-NC-cycle worker thread silently swallowed an exception when it tried to reload the manifold via SnaPy — SnaPy's SQLite session is thread-bound and refuses cross-thread access, so the optimiser never ran. Symptom: 6_2 with NC=(1,0) and Dehn-filling slope (5,1) reported refinement = 1 instead of the expected 2. The fix stashes a thread-safe ManifoldData (raw=None) on the session at load time and uses that everywhere instead of re-loading via SnaPy from worker threads. Optimiser failures are now also printed to stderr instead of being silently swallowed.

v1.1.2 — fill workers honour the optimised basis; fresh dist-info

• Fill workers now use the optimised hard-edge basis. v1.1.0 / v1.1.1 optimised the basis for the per-NC-cycle Weyl check (and showed the green opt K→K′ badge) but the actual FillWorker / UnrefinedKernelFillWorker continued to compute on the default nz_data, so the η-indices didn't line up with the optimised incompat_edges and the filled-index series came out with the default refinement count. The launchers now rebuild nz_data from the optimised_easy_result emitted by NcCompatWorker, so the fill genuinely runs in the optimised basis.
• Stale dist-info on v1.1.0 / v1.1.1 macOS builds. importlib.metadata returned 1.0.8 in the bundled app because the build machine's editable install hadn't been refreshed since v1.0.8. release.sh now reinstalls the package immediately before invoking PyInstaller, so future binaries always carry the correct version.

v1.1.1 — multi-cusp basis optimisation, downloads page cleanup

• Multi-cusp hard-edge basis optimisation. ``MultiCuspNcCompatWorker`` now silently runs the optimiser before the joint adjoint check, mirroring the single-cusp behaviour from v1.1.0. Refinement is the count of edges j for which every per-cusp Weyl column has ``a_I[j] ∈ ℤ ∧ 2·b_I[j] ∈ ℤ``, and verification uses the multi-cusp adjoint formula.
• Downloads page cleanup. v1.1 is the latest stable series; v1.0 (final: v1.0.9) is now in Older Releases. The internal version-grouping IDs and JS were renamed accordingly.

v1.1.0 — hard-edge basis optimisation

• Auto-optimise hard-edge basis per NC cycle. The per-cycle Weyl/adjoint check in Card ③ now searches integer-unimodular changes-of-basis on the hard subspace and silently swaps in a basis that yields a strictly larger refinement count subject to the adjoint q¹ projection passing with an integer value. For 6_2 NC=(1,0) this lifts the displayed refinement from 1 to 2 with adj_val = −1 (was −2 / refinement 1) — at < 2 s extra cost per cycle. Manifolds whose default basis is already optimal (m060, …) return immediately with no overhead.
• Bug fix: ν_internal in build_neumann_zagier no longer hard-codes RHS = 2. The RHS is now tracked per row via EasyEdgeResult, so any non-raw integer combination of edges produces the correct affine shift. The default flow (raw + Stage-1 easy edges, all RHS = 2 by construction) is unchanged.
• UI: a green opt 1→2 pill appears next to the γᵢ slope in the NC table when an optimised basis was used; hovering reveals the G-matrix and the refinement gain.

v1.0.9 — 6_2 (1, 0) undercounting fix, batched F_x2

• Fixed 6_2 (1, 0) regression introduced by v1.0.8 where the unrefined fill produced a spurious {0: −1} term and was incorrectly classified non-NC. Root cause: the v1.0.8 floor padding raised R[j] to ≥40, but the resulting initial box exceeded the 1M isotropic cap → R was clamped back to ~15 per axis → adaptive shell growth was skipped entirely, dropping ~192 valid sublevel points per kernel context. Fix: removed the early-exit on clamp, removed the inner _MAX_BOX_SIZE check inside shell growth, raised _MAX_SHELL_STEPS 32→80 with a 3-empty-shell convergence stop. 6_2 (1, 0) is now correctly stably zero at q_half ∈ {4, 6, 8, 10}; the v1.0.8 m060 (1, 1) refined fix is preserved.
• Batched F_x2 in _proj_min_fixed: the projection minimiser now evaluates ray-scan trial points in 32-point NumPy chunks instead of single calls, and the inner F_x2 always uses the vectorised path. ~2× speedup on the projection step; reduces total F_x2 overhead from ~180 s to ~40 s on m111 (1, 0).
• Known regression: m111 (1, 0) at q_half = 4 unrefined fill is ~1.5× slower (102 s → ~150 s) because shell growth now correctly walks out the genuinely large sublevel set instead of stopping at the isotropic cap. The result is unchanged. A principled fix that replaces _proj_min_fixed with an exact projection minimiser is planned for v1.1.0.

v1.0.8 — refined filling basis-independence, responsive Stop

• Refined Dehn-filling basis-dependence fix: the filled index via any NC cycle now agrees at η → 1 with the classical unrefined filling (previously m060 (1, 1) through NC = (−1, 0) or (0, 1) could give a different answer from NC = (1, 0)). Root cause was the per-axis bounding box in _exact_e0_candidates silently dropping valid lattice points; replaced with clip-to-floor + per-axis adaptive shell growth.
• Stop button in NC search is now responsive — aborts within a few seconds even on slow manifolds (was an AttributeError crash or an indefinite wait for the current slope to finish).
• _MAX_BOX_SIZE default lowered from 50M to 1M (env-overridable via _IREF_MAX_BOX_SIZE) — keeps per-slope runtime tractable on manifolds with highly-elongated sublevel sets (m111 etc.). Trade-off is silent correctness loss on those manifolds; raise the env var to re-validate.

v1.0.7 — first stable release

• Data Hub: 3-tab workflow (Download · Generate · Export & Share) with sequential multi-pack downloads, pause/resume/cancel generate queue, and a publish flow that infers category from file types.
• Offline KaTeX rendering: math views no longer require network access.
• Weyl compatibility diagnostic with collapsed-edge support, plus multi-cusp adjoint projection checks in the filling service.
• v0.4-style α/β notation throughout the UI, with γᵢ/δᵢ display for NC cycles.
• Cross-platform builds: macOS .app and Windows .exe from a unified release.sh, with GitHub Actions handling the Windows build.
• Repository layout flattened — src/, tests/, assets/, and build scripts now live at the repo root.

Contributors

The Refined Index Calculator was built alongside a forthcoming article that motivates its computations. The app exists so that the constructions in the article can be reproduced and extended without re-implementing them from scratch.

Get involved

• Found a bug or have a feature request? Open an issue.
• Have a computed data pack you want to share? Use the Export & Share tab in the Data Hub to package it, then open a PR adding the release URL to the registry.
• Citations and academic use: please cite the project URL and the specific version you used. A BibTeX snippet will be added once the accompanying paper is posted to arXiv.