underneath

Make this tape from left to right. Cup is initially the seam. Square brackets below show the atoms of each segment; its closing seam is omitted from the brackets.

The stitch identifies slash and cup globally. Every slash now acts as punctuation, including the untouched fourth mark. Empty segments are visible faults. This changes the parse of unchanged ink; it is more than a change of name or colour.

Undo that stitch. A stitch from the first slash to the last fork is refused: its anchors cross the cup seam. Appoint fork as seam instead. The reading becomes [slash] [cup slash]. Now the middle cup and the following slash share a segment and can be stitched. A changed parse has changed permission to rewrite the grammar.

On the same original tape, teach slash fork → cup by selecting a slash, a fork and a cup as the rule's two inputs and result, then activating that proposal. Selecting alone changes nothing. Every matching pair in a segment becomes one compound.

The new cups are compound atoms, with their children retained. They do not split the tape again: punctuation is resolved before reduction. Every new reading starts from the raw ink, which decides the segments. The stage order matters. Rules match current equivalence classes, so a stitch can also change which pairs match a rule.

Reduction always takes the leftmost matching adjacent pair. Two rules for that pair with different current results produce a visible conflict; the machine does not choose a winner. Equivalent results agree. Cutting a rule removes that production. Each successful reduction replaces two atoms with one, so it must stop.

What is kept?

Raw mark kinds, positions, paths and identities; an equivalence partition; an appointed seam kind; reading direction; and the authored pair rules. The chosen pen fixes the kind; your exact path is retained as ink, not guessed by a shape recognizer.

What is read?

Order the marks horizontally, reverse for a turned reading, identify equivalent kinds, split at the seam class, then reduce pairs within each segment. Generated atoms retain their child trees.

Where may a stitch land?

Both anchors must belong to the same segment before the operation. Its closing seam belongs to that segment. This is permission to choose rewrite anchors, not variable scope.

What counts as a fault?

An empty sheet, a segment without atoms, or a reached pair with conflicting rule results. An initial or consecutive seam can make an empty segment. A final seam creates no extra empty segment. A nonempty segment may remain open at the end.

What is the current ideal family?

Readings with no such faults under the current grammar. Membership says neither that the original marks returned nor that their original reading returned.

The served kernel is the executable specification. It fixes the decoding and stage order; the marks alter the data those stages interpret. There is no hidden evaluation of drawn source code.

Start with the stitched tape in the first trace. Cup and slash now share the seam class; the reading has two empty-segment faults. Appoint fork as seam. The faults disappear. The current ideal admits the result, but neither the original grammar nor the original reading has returned.

The frozen witness asks a different question. It preserves the starting state and grammar, or the last checkpoint you explicitly chose to keep. Inspection compares the current reading with that witness, and also reads current ink under the frozen grammar. Reading agreement compares compound trees and faults; merely obtaining the same final word is weaker. Exact restoration checks the full mark-and-grammar state, including geometry. Keeping a new witness changes the comparison target; it does not repair the old one.

Turning twice is an inverse operation. Cutting a particular rule removes it. A stitch retains the raw marks but its internal union has no split operator; undo can retrieve the earlier partition because the journal remembers it. Repair from the witness is an explicit external restoration. None of these should be mistaken for recovery from information that has been discarded.

The journal retains up to 128 events. Undo moves its cursor and remains available at the limit. Undone future events stay in an export until a new edit replaces that future branch. Save the journal first if you want to preserve an abandoned branch.

The full journal keeps source distinctions. A released reading is a separate artifact: canonical tokens and grammar, without raw kinds, geometry, IDs or the operation history.

The raw first and second kinds differ, but their equivalence class is identical. The releases are identical. An algorithm given only that release receives exactly the same input in both cases; it cannot always return both different originals correctly. Choosing a plausible representative recovers a member of a family, not the exact source.

This is an elementary many-to-one map, not a new impossibility theorem. A saved full journal or an external witness can distinguish the sources and restore them. Release does not destroy those copies. The claim concerns only recovery from the released artifact alone.

The trusted machinery remains: three decoded mark kinds, finite state, fixed reading stages, bounded input and history, terminating pair reductions, and explicit conflict reporting. There is no recursive expansion, arbitrary program execution, network service or claim that computation escapes its own rules.

Stopping, resetting, navigation and exporting remain ordinary controls. The full journal export preserves local work. A release preserves less. Keep the journal when exact restoration matters.

Earlier geometric research asked whether a whole family admits a coherent repair under continuity, symmetry and information constraints. This small language isolates the information question and makes the target itself editable. It does not prove a geometric no-retraction result, and it does not claim mathematical novelty.