+++ title = “The Viewer” section = “features” +++

The Viewer

The spectral sequence viewer is the main interface for exploring computations in htpy. It displays the $E_r$ pages of a spectral sequence as a chart in the $(t-s, s)$ plane.

Pan — click and drag the chart background
Zoom — scroll wheel or pinch gesture
Select a class — click on a dot to open the detail panel. When multiple generators sit at the same bidegree, the dot closest to your click is selected

The detail panel

Clicking a class opens a panel showing:

The bidegree $(t-s, s)$ and the internal degree $t$
The dimension of the group at that bidegree
Generator names — one input per generator. User-entered names override automatically inferred names (from product propagation)
Named combinations — named linear combinations of basis elements, defined by selecting coefficients
Differentials — known $d_r$ differentials originating from or landing in this bidegree, with delete buttons for user-entered ones
Products — nontrivial products with named generators
Massey products — computed brackets and their indeterminacy
Detects — record which stable homotopy element a generator detects (e.g., $h_0$ detects 2, $h_1$ detects $\eta$)
Annotations — sticky notes with tags (question, todo, proof, reference)

Clicking differentials and structlines

You can click differential lines and product structlines in the chart. Clicking a differential shows its page, source, target, origin (base computation or user-entered), and the dimension of source and target groups on each page. Clicking a structline shows the product name, shift, and relation formula.

Both detail views include buttons to navigate to the source or target class.

Page selection

The page scrubber at the top selects the $E_r$ page. Use the left/right arrow keys to step through pages, Home for $E_2$, and End for $E_\infty$. The viewer shows the surviving classes and differentials for the selected page.

Tabs

The tab bar lets you switch between multiple open modules. Click a module in the dropdown to open it in a new tab; click a tab to switch. Tab state (scroll position, zoom, selected class) is preserved.

Visual indicators

Green diamonds mark classes identified as permanent cycles (surviving to $E_\infty$)
Hollow circles mark $\tau$-torsion generators (motivic modules)
Vanishing lines are drawn as dashed lines
Orange ring on a class in differential entry mode
Orange “?” marker for unknown differentials

Motivic features

For modules with motivic weight data:

Weight filter dropdown: View a single weight slice at a time, filtering all nodes, structlines, and differentials by weight.
Weight annotations: The detail panel shows the weight of each generator.
$\tau$-torsion order: Shown in the detail panel; hollow circles in the chart distinguish torsion from non-torsion generators.

Export

Export JSON — download the full computation data in htpy’s v2 archive format
Lean certificate — download a Lean 4 file that formally verifies the Ext computation (available for resolvable modules)

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