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  {\titlefont\fontsize{34pt}{38pt}\selectfont\color{epiphanyteal}\bfseries Epiphany}\\[10pt]
  {\Large\scshape\color{epiphanyslate}Operation Catalog}\\[6pt]
  {\large\itshape\color{epiphanyslate}A companion to the Core Specification}\\[14pt]
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  {\normalsize\color{epiphanyink}Version 0.2.0 --- Phase 2 (K0 representative + broad-K0 M2 groups)}\\[4pt]
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\tableofcontents

% ===========================================================================
\chapter{About This Companion}
\label{ch:about}

The \emph{Operation Catalog} is a companion to the Epiphany Core Specification.
It fulfils the open question the core specification raises in its
\emph{Operation Catalog Conformance} section (Chapter~6,
\sectionsc{Semantic Operations and Concurrent Reduction}, the
\texttt{sec:semops:catalog} open question), which states that the catalog
``is normative once published; this specification is non-final until the catalog
is delivered.'' This release delivers the catalog \emph{framework}, the
\textbf{K0 representative primitive set}, and the \textbf{M2 broad-K0 groups}
(the event/pitch leaf-field, cross-cutting CRUD, structural-container, and
score-settings operations the Phase~2 slice exercises) --- the operation kinds
the Phase~2 visible slice and binary format actually exercise, each fully
specified in Chapter~\ref{ch:k0}. The remaining items of the full
$60$--$80$-primitive catalog are drafted as framework slots
(Chapter~\ref{ch:k1}) and completed in Phase~3.

\section{Relationship to the Core Specification}

This companion does not restate the operation framework; it \emph{references} it.
The framework --- operation identity and stamps, the hybrid-logical-clock
monotonicity rule, the dotted-version-vector causal context, the
order-independent operation-slot model and equivocation, the canonical reduction
order, the four-phase lifecycle, conflict records and the conflict registry,
re-anchoring, transactions, forward undo, and the LWW discipline --- is the core
specification's Chapter~6. This companion defines, for each operation kind, the
\emph{payload schema} and how that kind \emph{instantiates} the framework's
reduction, conflict, undo, and re-anchoring rules.

It also consumes, rather than re-deriving, the \textbf{ratified byte-convention
baseline} (core specification Chapter~8, \sectionsc{Binary Format Companion},
requirement \texttt{req:format:codec-conventions}, and the
\sectionsc{Canonical Byte-Layout Reference} appendix): little-endian integers, a
single discriminant byte per tagged union, \texttt{u32} length prefixes on every
variable-width leaf, and raw UTF-8 free text. Operation-payload encodings are
expressed in terms of that baseline; the literal wire layout of each payload is
the Binary Format companion's (Agent~J's) to pin, in coordination with this
catalog.

\begin{rationale}
The catalog is versioned \emph{independently} of the core specification
(independent semver). Operation kinds are added over time; the catalog should
evolve --- adding primitives, refining conflict cases --- without forcing a core
specification revision. The core specification changes only when the
\emph{framework} changes.
\end{rationale}

\section{Conformance Profiles}

A \textbf{Phase-2 profile} implementation \MUST{} implement every primitive in
Chapter~\ref{ch:k0} --- the representative set and the M2 broad-K0 groups --- with
the schema, reduction rule, conflict cases, undo semantics, and re-anchoring
behaviour defined there. The remaining (Phase-3) framework slots of
Chapter~\ref{ch:k1} are \emph{unavailable} under the Phase-2 profile: an
implementation \MUST{} reject (not silently ignore) an operation whose kind is one
of those slots it does not implement.

% ===========================================================================
\chapter{The Catalog Framework}
\label{ch:framework}

\section{Value-Typed Payloads}
\label{sec:framework:value-typed}

Every operation payload in this catalog is \textbf{value-typed}: it carries the
real graph values its effect introduces, not identifiers that point at values in
some ambient graph. An \texttt{InsertEvent} carries the whole \texttt{Event}; a
\texttt{RespellPitch} carries the whole \texttt{PitchSpelling}; a
\texttt{CreateCrossCutting} carries the whole tie, slur, beam, or spanner.

\begin{rationale}
The v0 prototype carried \emph{identifier-only projections} --- an
\texttt{InsertEvent} held an \texttt{EventId} plus reduction-relevant scalars; a
\texttt{RespellPitch} held a content-hash \emph{fingerprint} of the new spelling.
That was sufficient to make an envelope hashable and to drive reduction, but it
is \textbf{not durable}: an operation replayed in a fresh context --- a backup
restore, a cross-tool round-trip --- needs the full value, which an
identifier-only payload cannot supply. Value-typed payloads are what make an
Epiphany document portable.
\end{rationale}

\begin{requirement}
\label{req:catalog:value-encoding}
A value-typed payload field \MUST{} be encoded by emitting the field's value
under the core specification's canonical value encoding
(\texttt{req:format:codec-conventions}), framed by a \texttt{u32} little-endian
length prefix. Decoding \MUST{} be the exact inverse and \MUST{} reject trailing
bytes within the framed region. The encoding introduces no byte layout beyond the
ratified baseline: a value's bytes here are byte-for-byte the bytes the whole
document codec emits for that value.
\end{requirement}

\section{Per-Primitive Schema Template}
\label{sec:framework:template}

Each catalog primitive is specified under a fixed six-part template. A new
primitive is a schema-fill against this template, not a fresh design:

\begin{description}
  \item[Payload schema] The value-typed fields the operation carries, with their
    core-specification types.
  \item[Canonical encoding] The field order and framing, consuming
    Requirement~\ref{req:catalog:value-encoding}. (The literal byte layout is the
    Binary Format companion's; this catalog fixes the \emph{field set and order}.)
  \item[Reduction rule] How the operation mutates canonical state when it is
    reached in canonical reduction order --- the preconditions it checks, the
    objects it mints or tombstones, and the bookkeeping it records.
  \item[Conflict cases] The conflict records the operation can produce, by
    \texttt{ConflictKind}, and which participant materialises.
  \item[Undo semantics] The compensating effect of undoing a transaction that
    contains the operation, under each \texttt{UndoPolicy}
    (\texttt{StrictInverse} / \texttt{BestEffort} / \texttt{Cascade}).
  \item[Re-anchoring] The behaviour when an object the operation references is
    tombstoned before or concurrently with it.
\end{description}

\section{Reduction-Discipline Coverage}

The K0 representative set is chosen so that, between them, the primitives
exercise \emph{every} reduction discipline the framework defines:
position-keyed insert with system-voice promotion; delete-wins with tombstones,
tuplet compensation, and cross-cutting re-anchoring; field-overwrite with
last-writer-wins and structural-field-collision conflicts; set-union creation;
structural time-model migration; an LWW advisory; atomic transactions with
descriptor precedence; and the two meta-operations (conflict resolution and
forward undo). A primitive added later that reuses one of these disciplines
inherits its reduction, conflict, undo, and re-anchoring treatment.

% ===========================================================================
\chapter{K0 --- Representative Primitives}
\label{ch:k0}

This chapter is normative under the Phase-2 profile. Each primitive's reduction,
conflict, undo, and re-anchoring behaviour is the behaviour the core
specification's Chapter~6 defines for its discipline; the description here states
how the primitive instantiates it. The reference implementation is
\texttt{epiphany-ops} (the \texttt{payload}, \texttt{reduce}, and \texttt{migrate}
modules).

\section{InsertEvent}
\label{sec:k0:insert-event}

\textbf{Payload schema.} \texttt{InsertEventOp \{ staff\_instance:
StaffInstanceId, event: Event \}}. The voice, region-local position, duration,
and pitch identities are read from the \texttt{Event} value; the
\texttt{staff\_instance} is retained alongside it so the system-voice promotion
derivation is total without a containment walk.

\textbf{Canonical encoding.} \texttt{staff\_instance}, then the length-framed
canonical bytes of \texttt{event}.

\textbf{Reduction rule.} A position-keyed insert. Preconditions: the event's
duration is positive; the event id is neither live nor tombstoned; in graph-aware
reduction the target voice exists in a metric region and the event's pitch ids
are fresh. The event and its pitches are minted live; the voice is created on
first use. Concurrent inserts whose half-open duration intervals overlap in the
same voice are resolved by an order-independent promotion pre-pass: the
lower-\texttt{OperationId} insert is retained in the original voice, and each
overlapping loser is promoted to the deterministic system voice
\texttt{derive\_promoted\_voice\_id(staff\_instance, voice, winner, loser)} and
tagged \texttt{VoicePromoted}.

\textbf{Conflict cases.} None at reduction time; promotion is a deterministic
repair, not a conflict.

\textbf{Undo semantics.} Undoing the enclosing transaction tombstones the minted
event, its pitches, and any promoted voice. \texttt{StrictInverse} conflicts if
any was already tombstoned or modified; \texttt{BestEffort} tombstones the
survivors; \texttt{Cascade} is \texttt{StrictInverse} over the same minted set
(dependent-closure undo is a Phase-3 refinement).

\textbf{Re-anchoring.} Not applicable (the operation mints, it does not
reference a pre-existing object that could be tombstoned).

\section{DeleteEvent}
\label{sec:k0:delete-event}

\textbf{Payload schema.} \texttt{DeleteEventOp \{ event: EventId,
tuplet\_compensation: TupletCompensation \}}, where \texttt{TupletCompensation}
is \texttt{NotInTuplet}, \texttt{ReplaceWithRest \{ rest: Rest \}} (value-typed
replacement rest), \texttt{RewriteTuplets \{ tuplets \}}, or
\texttt{CascadeDeleteTuplets \{ tuplets \}}.

\textbf{Canonical encoding.} \texttt{event}, then the tuplet-compensation
discriminant and its payload (a length-framed \texttt{Rest} value for
\texttt{ReplaceWithRest}).

\textbf{Reduction rule.} Delete-wins: the event and its contained pitches are
tombstoned (retaining their identifiers). Tuplet compensation, when present, adds
the replacement rest live or tombstones the cascaded tuplet group. Concurrent
deletes of the same event are idempotent.

\textbf{Conflict cases.} None for the delete itself. Graph-aware reduction
refuses an ill-formed tuplet compensation as a precondition failure (no-op).

\textbf{Undo semantics.} An insert-shaped compensation re-introduces the
tombstoned content; for the prototype's minted-object model this is the inverse
of the tombstone set, with the policy treatment described under InsertEvent.

\textbf{Re-anchoring.} Tombstoning the event runs the framework's re-anchoring
rule table over every cross-cutting structure that referenced it: a tie
cascade-deletes; a comment or analytical annotation orphans (user content is
never silently deleted); a beam truncates while $\geq 2$ members survive and
otherwise cascade-deletes; a slur or spanner re-anchors to the nearest surviving
endpoint while $\geq 1$ survives and otherwise cascade-deletes.

\section{RespellPitch}
\label{sec:k0:respell-pitch}

\textbf{Payload schema.} \texttt{RespellPitchOp \{ pitch: PitchId, spelling:
PitchSpelling \}} --- the full spelling value (v1), not a fingerprint.

\textbf{Canonical encoding.} \texttt{pitch}, then the length-framed canonical
bytes of \texttt{spelling}.

\textbf{Reduction rule.} A last-writer-wins field overwrite, keyed by pitch.
Precondition: the pitch is live. The resolved spelling is the one carried by the
operation latest in canonical order. Two respellings of one pitch that are
causally ordered overwrite intentionally; two \emph{concurrent} respellings with
\emph{equal} spelling reduce idempotently.

\textbf{Conflict cases.} Two concurrent respellings of one pitch with
\emph{differing} spellings produce a \texttt{StructuralFieldCollision} conflict
recording the winner (later in canonical order), the loser, and the field
\texttt{spelling}. The winner materialises and carries the \texttt{Conflicted}
effect tag.

\textbf{Undo semantics.} Undo restores the pre-operation spelling (or removes the
spelling if the operation introduced the first one), under the active policy.

\textbf{Re-anchoring.} If the target pitch is tombstoned, the respelling is a
no-op (\texttt{TargetTombstoned}).

\begin{openquestion}
\textbf{P12-K1.} A v0 \texttt{RespellPitch} carried only a content-hash \emph{fingerprint} of the
spelling. The fingerprint cannot be inverted to a \texttt{PitchSpelling} without
a side table, so the v0$\rightarrow$v1 migration (Chapter~\ref{ch:migration})
recovers the spelling from the score graph context --- an explicit per-pitch
spelling attachment whose canonical bytes hash to the fingerprint --- and, when
the context lacks it, declares the envelope unmigratable (the bundle opens
read-only). This is the one representative payload that is not self-contained
under migration; the disposition (whether a richer v0 corpus, or a documented
read-only fallback, is the long-term answer) is a Pass-12 question.
\end{openquestion}

\section{ModifyEvent}
\label{sec:k0:modify-event}

\textbf{Payload schema.} \texttt{ModifyEventOp \{ event: Event \}} --- the full
replacement \texttt{Event} value (v1). The identity (and therefore the LWW key)
is read from the value.

\textbf{Canonical encoding.} The length-framed canonical bytes of \texttt{event}.

\textbf{Reduction rule.} A last-writer-wins field overwrite keyed by event id.
Precondition: the event is live. The resolved value is the one carried by the
operation latest in canonical order; two causally ordered modifications overwrite
intentionally, and two \emph{concurrent} modifications with \emph{equal} value
reduce idempotently. Graph-aware reduction overwrites the event in place. A
modification that \emph{moves} the event (a different region-local position or
duration) is recorded in the bookkeeping but its placement change is \emph{not}
applied to the graph: re-sorting a voice on a placement change is a deferred
refinement, and an in-place move would break \texttt{VoiceEventsSortedNonOverlap}
(Chapter~5 invariant~3). A malformed (empty pitched) replacement is likewise
recorded but not materialised.

\textbf{Conflict cases.} Two concurrent modifications of one event with
\emph{differing} values produce a \texttt{StructuralFieldCollision} on the field
\texttt{event}, recording the winner (later in canonical order) and the loser.

\textbf{Undo semantics.} Under the prototype's minted-object undo
(Section~\ref{sec:k0:undo}) a field overwrite mints nothing, so undoing the
enclosing transaction does not restore the prior event value; a snapshot-and-
restore inverse is a Phase-3 refinement (P11-C8).

\textbf{Re-anchoring.} If the target event is tombstoned, the modification is a
no-op (\texttt{TargetTombstoned}/\texttt{TargetMissing}).

\section{Identified-Pitch Operations}
\label{sec:k0:identified-pitch}

\textbf{Payload schema.} \texttt{InsertIdentifiedPitchOp \{ event: EventId,
pitch: IdentifiedPitch \}} mints a pitch into a live event;
\texttt{DeleteIdentifiedPitchOp \{ pitch: PitchId \}} tombstones one;
\texttt{ModifyIdentifiedPitchOp \{ pitch: PitchId, value: Pitch \}} overwrites a
pitch's acoustic / scale-position value (distinct from \texttt{RespellPitch},
which overwrites only the \emph{spelling}).

\textbf{Canonical encoding.} Insert: \texttt{event}, then the length-framed
\texttt{pitch} value. Delete: \texttt{pitch}. Modify: \texttt{pitch}, then the
length-framed \texttt{value}.

\textbf{Reduction rule.} The pitch-level analogues of the event-level mint,
delete, and field overwrite, inheriting their disciplines
(Sections~\ref{sec:k0:insert-event}, \ref{sec:k0:delete-event}, and this
chapter's field-overwrite treatment). \textbf{A note and a rest are the same slot
under pitch add/remove} (normative): deleting the \emph{only} pitch of a
single-pitch note degrades the event to a \texttt{Rest} of the same
id/voice/position/duration rather than leaving an empty pitched event (Chapter~5
forbids the empty chord, \texttt{ArenaError::EmptyPitchedEvent}); inserting a
pitch into a rest is the dual, promoting it to a one-pitch note. This preserves
the delete-wins / mint disciplines and keeps the graph consistent with the
bookkeeping, which tombstones or mints the pitch object either way.

\textbf{Conflict cases.} Insert and delete: none (mint is set-union; delete-wins
is idempotent). Modify: two concurrent differing writes of one pitch produce a
\texttt{StructuralFieldCollision} on the field \texttt{pitch}.

\textbf{Undo semantics.} Insert is the only minting member: undoing the enclosing
transaction tombstones the minted pitch, re-resting the event if it was the only
one (Section~\ref{sec:k0:undo}). The prototype's minted-object undo has nothing
to tombstone for delete or modify, so neither is inverted under it (re-introducing
a tombstoned pitch or restoring a prior value is a Phase-3 refinement, P11-C8).

\textbf{Re-anchoring.} An operation whose target event or pitch is tombstoned is
a no-op; tombstoning a pitch runs the cross-cutting re-anchoring table over any
structure that referenced it (see DeleteEvent).

\section{Transpose}
\label{sec:k0:transpose}

\textbf{Payload schema.} \texttt{TransposeOp \{ targets: Vec<PitchId>,
chromatic\_steps: i32 \}}. Pitch identifiers are preserved; only acoustic content
changes.

\textbf{Canonical encoding.} The canonically-ordered \texttt{targets} set, then
\texttt{chromatic\_steps} as a little-endian \texttt{i32}.

\textbf{Reduction rule.} An order-dependent content overwrite. Each live target
pitch is shifted by \texttt{chromatic\_steps}; reduction is order-dependent in the
general case (interval composition need not commute), so the resolved value is
the composition in canonical reduction order. In this prototype
\texttt{chromatic\_steps} is a minimal CMN alteration shift that commutes except
at the alteration's \texttt{i8} saturation bound; rich interval algebra is
deferred (Chapter~4 tuning catalog; P12-K2).

\textbf{Conflict cases.} None --- composition is deterministic in canonical order
(a deterministic repair, not a conflict).

\textbf{Undo semantics.} Transpose mints nothing, so the prototype's minted-object
undo (Section~\ref{sec:k0:undo}) does not negate it; an inverse-interval undo is a
Phase-3 refinement (P11-C8).

\textbf{Re-anchoring.} Tombstoned targets are skipped (the transpose applies only
to live pitches).

\section{CreateCrossCutting}
\label{sec:k0:create-cross-cutting}

\textbf{Payload schema.} \texttt{CreateCrossCuttingOp \{ structure:
CrossCuttingValue \}}, where \texttt{CrossCuttingValue} is the typed value of a
\texttt{Tie}, \texttt{Slur}, \texttt{Beam}, or \texttt{Spanner}. Its identity and
referenced endpoints are read from the value.

\textbf{Canonical encoding.} A discriminant for the structure kind, then the
length-framed canonical bytes of the structure value.

\textbf{Reduction rule.} Set-union creation: the structure is minted live if its
id is not already live and every referenced endpoint is live; a second create of
a live id is idempotent. Graph-aware reduction materialises the structure with
its full fields.

\textbf{Conflict cases.} None (all-or-nothing creation; union is deterministic).

\textbf{Undo semantics.} Undo tombstones the minted structure, under the active
policy.

\textbf{Re-anchoring.} The structure participates in the re-anchoring rule table
when one of its endpoints is later tombstoned (see DeleteEvent).

\textbf{Migration coverage.} The v0$\rightarrow$v1 migration
(Chapter~\ref{ch:migration}) reconstructs the event-anchored \texttt{Tie},
\texttt{Slur}, and \texttt{Beam} from the v0 reference (id plus event endpoints).
A \texttt{Spanner} is anchored by \texttt{TimeAnchor}s rather than a fixed pair
of event endpoints, so its full value is not reconstructable from the v0
event-reference projection; a \texttt{Spanner}-create is therefore reported
unmigratable (read-only), alongside the respell case of P12-K1, and remains so.
A faithful spanner migration awaits a richer v0 projection that carries the
anchors --- a Phase-3 / Pass-12 extension, not yet implemented.

\section{DeleteCrossCutting}
\label{sec:k0:delete-cross-cutting}

\textbf{Payload schema.} \texttt{DeleteCrossCuttingOp \{ structure: TypedObjectId
\}} --- the structure named by the same key the set-union creation and the
re-anchoring table use; it \MUST{} be a cross-cutting kind
(\texttt{Tie}/\texttt{Slur}/\texttt{Beam}/\texttt{Spanner}).

\textbf{Canonical encoding.} The canonical bytes of \texttt{structure}.

\textbf{Reduction rule.} Delete-wins: the structure is tombstoned (its identifier
retained). A second delete of the same structure is idempotent; deleting a
missing or non-cross-cutting id is a no-op precondition failure. Graph-aware
reduction removes the structure from the score.

\textbf{Conflict cases.} None (delete-wins is idempotent).

\textbf{Undo semantics.} A delete mints nothing, so the prototype's minted-object
undo (Section~\ref{sec:k0:undo}) does not re-introduce the tombstoned structure
(P11-C8).

\textbf{Re-anchoring.} The deletion is direct (the structure is the target, not a
referenced endpoint); it does not itself trigger the endpoint re-anchoring table.

\section{ModifyCrossCutting}
\label{sec:k0:modify-cross-cutting}

\textbf{Payload schema.} \texttt{ModifyCrossCuttingOp \{ structure:
CrossCuttingValue \}} --- the full replacement value (v1). The replacement keeps
the structure's identity but may change its endpoints and per-kind fields; the
LWW key is the structure's \texttt{CrossCuttingValue::id}.

\textbf{Canonical encoding.} The discriminant and length-framed bytes of the
\texttt{CrossCuttingValue} (as for CreateCrossCutting).

\textbf{Reduction rule.} A last-writer-wins field overwrite keyed by structure
id. Precondition: the structure is live. The reduction re-derives the structure's
endpoints from the new value, so a later re-anchoring sees them. A malformed
replacement is a precondition no-op --- in particular a beam whose membership
falls below the two-member minimum is refused rather than materialised.
Graph-aware reduction overwrites the structure in place.

\textbf{Conflict cases.} Two concurrent differing modifications of one structure
produce a \texttt{StructuralFieldCollision} on the field \texttt{cross\_cutting}.

\textbf{Undo semantics.} A modification mints nothing, so the prototype's
minted-object undo (Section~\ref{sec:k0:undo}) does not restore the prior
structure value (a snapshot-and-restore inverse is Phase-3, P11-C8).

\textbf{Re-anchoring.} If the target structure is tombstoned, the modification is
a no-op; re-deriving the endpoints lets a subsequent endpoint tombstone re-anchor
the structure through the standard table (see DeleteEvent).

\section{ChangeRegionTimeModel}
\label{sec:k0:change-region-time-model}

\textbf{Payload schema.} \texttt{ChangeRegionTimeModelOp \{ region: RegionId,
new\_time\_model: RegionTimeModel, declared\_incompatible: Vec<EventId>,
remapping: PositionRemapping \}} --- the full target model value (v1).

\textbf{Canonical encoding.} \texttt{region}, the length-framed
\texttt{new\_time\_model} value, the canonically-ordered
\texttt{declared\_incompatible} set, then \texttt{remapping}.

\textbf{Reduction rule.} Structural migration. The region adopts the target time
model. Graph-aware reduction derives coordinate-kind incompatibilities from the
region's events (and from the remapping coverage) and refuses a migration that
would violate the coordinate discipline.

\textbf{Conflict cases.} Concurrent same-region migrations produce a
\texttt{StructuralFieldCollision} on the field \texttt{time\_model}; a migration
with incompatible events produces a \texttt{TimeModelMigrationFailure} naming the
region and the incompatible events. A causally-later migration is re-evaluated
against the first migration's graph rather than conflicting.

\textbf{Undo semantics.} Undo restores the region's prior time model under the
active policy.

\textbf{Re-anchoring.} Not applicable.

\begin{openquestion}
\textbf{P11-C6.} The rich migration payload --- a coordinate converter rather than a
\texttt{declared\_incompatible} list plus a \texttt{PositionRemapping} --- remains
the catalog's to design when graph-aware migration is the only reduction path.
\end{openquestion}

\section{Structural Containers}
\label{sec:k0:structural-containers}

\textbf{Payload schema.} Three create/delete pairs over the region hierarchy:
\texttt{CreateRegionOp \{ region: Region \}} /
\texttt{DeleteRegionOp \{ region: RegionId \}};
\texttt{CreateStaffInstanceOp \{ region: RegionId, instance: StaffInstance \}} /
\texttt{DeleteStaffInstanceOp \{ staff\_instance: StaffInstanceId \}};
\texttt{CreateVoiceOp \{ staff\_instance: StaffInstanceId, voice: Voice \}} /
\texttt{DeleteVoiceOp \{ voice: VoiceId \}}. Each create carries the full
container value (v1); the reduction preconditions it bears \emph{no typed child
object} --- an empty container.

\textbf{Canonical encoding.} Create: the parent id (where the schema names one),
then the length-framed canonical bytes of the container value. Delete: the
container id.

\textbf{Reduction rule.} Set-union creation of an \emph{empty} container, and an
\emph{empty-only} delete-wins tombstone. A create mints the container live if its
id is fresh and (for staff instance and voice) its parent is live; it
preconditions the carried value to bear no typed child object (a region: no staff
instances, barline-alignment groups, or graphic objects; a staff instance: no
voices or measures; a voice: no events), since those carry distinct
\texttt{TypedObjectId}s the reducer mints separately --- so contents are added by
subsequent operations. A delete is a delete-wins tombstone, but a
\emph{precondition no-op} (\texttt{ContainerNotEmpty}) unless the container has no
live children --- the caller deletes contents first. Graph-aware reduction adds
or removes the container and maintains the region's staff extent so
\texttt{RegionExtents} stays satisfied.

\textbf{Conflict cases.} None at reduction time: creation is set-union (a repeat
create is idempotent), and the empty-only delete is a deterministic precondition
gate, not a conflict.

\textbf{Undo semantics.} Undo of a \emph{create} tombstones the minted container
(Section~\ref{sec:k0:undo}); \texttt{StrictInverse} conflicts if it was
concurrently mutated, with the policy treatment as for InsertEvent. A
\emph{delete} mints nothing, so the prototype's minted-object undo does not
re-introduce it (P11-C8).

\textbf{Re-anchoring.} Not applicable (the containers are minted/tombstoned by id;
the empty-only precondition means a delete never strands live children).

\section{SetUserSystemBreak}
\label{sec:k0:set-user-system-break}

\textbf{Payload schema.} \texttt{SetUserSystemBreakOp \{ region: RegionId,
anchor: TimeAnchor, present: bool \}} --- the full anchor value (v1).

\textbf{Canonical encoding.} \texttt{region}, the length-framed \texttt{anchor}
value, then the boolean.

\textbf{Reduction rule.} A last-writer-wins advisory. The break preference is
recorded for the region keyed by the anchor's \emph{resolved musical position};
graph-aware reduction adds or removes the anchor from the region's user
system-break list.

\textbf{Conflict cases.} None (LWW advisory).

\textbf{Undo semantics.} Undo restores the prior advisory value for the
\texttt{(region, resolved-position)} key.

\textbf{Re-anchoring.} Not applicable in the prototype (the advisory is keyed by
resolved position; a tombstoned anchor target degrades to the region origin).

\section{Score Settings}
\label{sec:k0:score-settings}

\textbf{Payload schema.} Three score-level field overwrites:
\texttt{SetMetadataOp \{ metadata: ScoreMetadata \}} overwrites the score
singleton; \texttt{SetMetricGridOp \{ region: RegionId, grid: Option<MetricGrid>
\}} overwrites (or clears) a region's default metric grid;
\texttt{SetUserPageBreakOp \{ region: RegionId, anchor: TimeAnchor, present: bool
\}} is the page-break sibling of SetUserSystemBreak.

\textbf{Canonical encoding.} Metadata: the length-framed \texttt{metadata} value.
Metric grid: \texttt{region}, then an \texttt{Option} discriminant and (when
present) the length-framed \texttt{grid} value. Page break: \texttt{region}, the
length-framed \texttt{anchor} value, then the boolean.

\textbf{Reduction rule.} Three field overwrites differing only in discipline.
\emph{SetMetadata} is an \textbf{advisory} last-writer-wins: the latest write in
canonical order silently wins and the operation always applies --- no working
state and no conflict (the same discipline as SetUserSystemBreak, on the score
singleton). \emph{SetMetricGrid} is a \textbf{structural} field overwrite keyed
by region: precondition the region is live and staff-based (a FreeGraphic region
has no metric-grid slot --- the op is a no-op there), and reject a grid whose
meter sequence names a time signature that is not live (the Chapter~5 invariant
forbids installing such a grid). \emph{SetUserPageBreak} is a canonical LWW
advisory keyed by the anchor's resolved musical position, with the same
staff-based precondition. Graph-aware reduction overwrites the metadata singleton,
sets the region's default metric grid, or adds/removes the page-break anchor
under its resolved-position key (so two anchors resolving to one position occupy a
single slot).

\textbf{Conflict cases.} SetMetadata and SetUserPageBreak: none (advisory LWW).
SetMetricGrid: two concurrent differing grids for one region produce a
\texttt{StructuralFieldCollision} on the field \texttt{metric\_grid}.

\textbf{Undo semantics.} All three are field overwrites that mint nothing, so the
prototype's minted-object undo (Section~\ref{sec:k0:undo}) does not restore the
prior metadata, grid, or break preference (a snapshot-and-restore inverse is a
Phase-3 refinement, P11-C8).

\textbf{Re-anchoring.} The advisory breaks degrade as for SetUserSystemBreak; the
metric grid and metadata are keyed by region / singleton and do not re-anchor (a
deleted region's settings are no-ops --- \texttt{TargetMissing}).

\section{DeclareTransaction}
\label{sec:k0:declare-transaction}

\textbf{Payload schema.} \texttt{TransactionDescriptor \{ id: TransactionId,
label: String, category: Option<TransactionCategory> \}}. Value-complete in v0
and unchanged.

\textbf{Reduction rule.} Records the descriptor. Member primitives reference the
transaction id and \MUST{} causally depend on the descriptor; the members reduce
atomically (all-or-nothing) in canonical order.

\textbf{Conflict cases.} A missing descriptor or a member that does not causally
follow it produces a \texttt{TransactionConflict}; any member failure rolls back
the whole transaction and all members read \texttt{NoOp\{TransactionConflict\}}.

\textbf{Undo / re-anchoring.} Transactions are the unit of undo
(Section~\ref{sec:k0:undo}); re-anchoring is per member.

\section{ResolveConflict (meta-operation)}
\label{sec:k0:resolve-conflict}

\textbf{Payload schema.} \texttt{ResolveConflictPayload \{ target: ConflictId,
action: ResolutionAction \}}. Value-complete.

\textbf{Reduction rule.} Transitions the target conflict's resolution state. An
action of \texttt{Dismiss} reaches the \texttt{Dismissed} state; any other action
reaches \texttt{Resolved}. Re-resolving with the same action is idempotent; two
concurrent resolves with differing actions produce a meta-conflict.

\begin{rationale}
Pass~11 added \texttt{ResolutionAction::Dismiss} (item 2.5) precisely so the
\texttt{Dismissed} state is reachable by an authored operation rather than merely
representable. The catalog records that \texttt{Dismiss} is the action that
selects it (resolving the v0 ambiguity P11-C10).
\end{rationale}

\section{UndoTransaction (meta-operation)}
\label{sec:k0:undo}

\textbf{Payload schema.} \texttt{UndoTransactionPayload \{ target: TransactionId,
policy: UndoPolicy \}}, with \texttt{UndoPolicy} one of \texttt{StrictInverse},
\texttt{BestEffort}, \texttt{Cascade}. Value-complete.

\textbf{Reduction rule.} A forward compensating edit computed against the
materialised state at the undo's canonical position (never literal time travel).
The prototype models the compensation as tombstoning the objects the target
transaction minted: \texttt{StrictInverse} conflicts (\texttt{TombstonedTarget})
if any minted object was already tombstoned; \texttt{BestEffort} tombstones the
survivors; \texttt{Cascade} is \texttt{StrictInverse} over the same set
(dependent-closure undo is a Phase-3 refinement, P11-C8).

% ===========================================================================
\chapter{v0 \texorpdfstring{$\rightarrow$}{->} v1 Payload Migration}
\label{ch:migration}

A v0 envelope carries an identifier-only payload; a v1 envelope carries the
value-typed payload this catalog defines. The two forms do not coexist as
permanent dialects (that would double the reducer surface forever); instead the
catalog ships a \textbf{one-time migration} that lifts a v0 envelope to v1 using
the score graph as context, applied once on read. Production code carries only v1
payloads; v0 envelopes survive only as a regression corpus.

\begin{requirement}
\label{req:migration:properties}
The migration \texttt{migrate\_v0\_envelope(v0, context: \&Score)} \MUST{} be
\textbf{deterministic} (two implementations migrating the same v0 envelope
against the same context produce byte-identical v1 envelopes) and
\textbf{equivalence-preserving} (a v0 envelope and its v1 migration reduce to
byte-identical canonical \texttt{MaterializedState}). When a value cannot be
reconstructed from the v0 projection plus the context, the migration \MUST{}
report the envelope unmigratable rather than fabricate a value, and the bundle
opens read-only.
\end{requirement}

The reference implementation (\texttt{epiphany-ops::migrate}) reconstructs the
\texttt{InsertEvent} event, the \texttt{DeleteEvent} compensation, the
\texttt{ChangeRegionTimeModel} model, the \texttt{SetUserSystemBreak} anchor, and
the event-anchored cross-cutting structures (\texttt{Tie} / \texttt{Slur} /
\texttt{Beam}) self-containedly from the v0 projection; a \texttt{Spanner},
anchored by \texttt{TimeAnchor}s rather than event endpoints, remains unmigratable
until the projection carries them. It recovers a \texttt{RespellPitch} spelling
from the context (P12-K1,
Section~\ref{sec:k0:respell-pitch}). The migration's merge gate
(\texttt{epiphany-testkit::migration}) drives the inverse direction --- projecting
a v1 corpus to v0 and migrating it back --- and asserts byte-identical reduction
plus a non-vacuity guard.

% ===========================================================================
\chapter{K1 --- Framework Slots (Phase 3)}
\label{ch:k1}

This chapter drafted the remaining catalogue items as framework slots. The
Phase-2 \textbf{M2} expansion (the broad-K0 groups in \texttt{epiphany-ops})
implemented four groups of them; with the \textbf{M2e} catalogue expansion their
full per-primitive schemas now appear in Chapter~\ref{ch:k0}, so they are
\emph{normative under the Phase-2 profile} and an implementation \MUST{}
\emph{not} reject them. They are cross-referenced first. The genuinely Phase-3
slots that remain \textbf{unavailable} are listed second: an implementation
\MUST{} reject an operation of one of \emph{those} kinds. Each remaining slot is a
schema-fill against the template of Chapter~\ref{ch:framework}; adding one is not
a fresh design.

\section*{Implemented since M2 (now in Chapter~\ref{ch:k0})}

\begin{description}
  \item[Modify event; identified-pitch operations; transpose]
    M2 Group~1 --- Sections~\ref{sec:k0:modify-event},
    \ref{sec:k0:identified-pitch}, and \ref{sec:k0:transpose}.
  \item[Delete / modify cross-cutting]
    M2 Group~2 --- Sections~\ref{sec:k0:delete-cross-cutting} and
    \ref{sec:k0:modify-cross-cutting} (creation is
    Section~\ref{sec:k0:create-cross-cutting}).
  \item[Create / delete region / staff instance / voice]
    M2 Group~3 --- Section~\ref{sec:k0:structural-containers} (set-union creation
    and the empty-only delete).
  \item[Set metadata / metric grid / user page break]
    M2 Group~4 --- Section~\ref{sec:k0:score-settings} (advisory metadata,
    structural metric grid, advisory page break).
\end{description}

\section*{Remaining framework slots (Phase 3 --- unavailable, MUST reject)}

\begin{description}
  \item[Create score / canvas / staff]
    The remaining structural mints (the document root, the canvas, and global
    staves) the Phase-2 slice does not exercise. Discipline: set-union creation.
  \item[Set time signature / tempo segment]
    The finer-grained metric-model overwrites beneath the whole-grid
    \texttt{SetMetricGrid} (Section~\ref{sec:k0:score-settings}): a single meter
    change or tempo segment rather than the region's entire grid. Discipline:
    last-writer-wins structural overwrite.
  \item[Set layout]
    The non-break layout advisories (the page/system-break advisories themselves
    are implemented --- Sections~\ref{sec:k0:set-user-system-break} and
    \ref{sec:k0:score-settings}). Discipline: LWW advisory.
\end{description}

\begin{nongoal}
The full $60$--$80$-primitive catalogue is not a Phase-2 deliverable. The
framework (Chapter~\ref{ch:framework}) and the K0 representative set
(Chapter~\ref{ch:k0}) are sufficient to exercise every reduction discipline; the
remaining primitives are Phase-3 schema-fill.
\end{nongoal}

\end{document}
