docs: rename runs.md/runs.rs → writes and repoint all references (#131)

The Run state machine was removed in MR-771 (v0.4.0); `docs/dev/runs.md`
and `crates/omnigraph/tests/runs.rs` have since documented and tested the
direct-publish write path, so the "runs" name was misleading.

- git mv docs/dev/runs.md → docs/dev/writes.md (reframe H1 + intro;
  keep MR-771 history note)
- git mv crates/omnigraph/tests/runs.rs → tests/writes.rs (reframe header)
- repoint every runs.md / runs.rs reference across docs, AGENTS.md, and
  source comments
- fix four pre-existing broken `docs/runs.md` links (the file never lived
  at that path) to `docs/dev/writes.md`
- fix the stale v0.4.0 anchor to the live section

No behavior change: every source edit is a comment. Engine builds and the
renamed test passes 25/25; scripts/check-agents-md.sh passes.

The run-removal cleanup itself (run_registry.rs guard, __run__ prefix) is
deferred to MR-770.

docs/dev/architecture.md

@@ -207,7 +207,7 @@ contracts:
 This pattern realizes read-your-writes within a multi-statement mutation
 and keeps failure scope bounded for inserts/updates by construction at
 the writer layer. See [docs/dev/invariants.md](invariants.md) and
-[docs/dev/runs.md](runs.md) for the publisher CAS contract this builds on.
+[docs/dev/writes.md](writes.md) for the publisher CAS contract this builds on.
 
 ### Storage trait — today vs. roadmap
 
@@ -278,7 +278,7 @@ flowchart LR
     eng --> wq
 ```
 
-The server applies Cedar policy at the HTTP boundary today. The roadmap, called out in [docs/dev/invariants.md](invariants.md) as a known gap, is to push policy into the planner as predicates. After Cedar, mutating handlers go through `WorkloadController` (per-actor admission cap + byte budget; PR 2 / MR-686) before reaching the engine. The engine itself holds an `Arc<WriteQueueManager>` so concurrent mutations on the same `(table, branch)` serialize at the queue, while disjoint keys run in parallel — see [docs/user/server.md](../user/server.md) "Per-actor admission control" and [docs/dev/runs.md](runs.md). The CLI bypasses the HTTP layer (and admission) and calls the engine API directly.
+The server applies Cedar policy at the HTTP boundary today. The roadmap, called out in [docs/dev/invariants.md](invariants.md) as a known gap, is to push policy into the planner as predicates. After Cedar, mutating handlers go through `WorkloadController` (per-actor admission cap + byte budget; PR 2 / MR-686) before reaching the engine. The engine itself holds an `Arc<WriteQueueManager>` so concurrent mutations on the same `(table, branch)` serialize at the queue, while disjoint keys run in parallel — see [docs/user/server.md](../user/server.md) "Per-actor admission control" and [docs/dev/writes.md](writes.md). The CLI bypasses the HTTP layer (and admission) and calls the engine API directly.
 
 Code paths:
 

docs/dev/execution.md

@@ -147,7 +147,7 @@ sequenceDiagram
 - End-of-query Lance commit: `TableStore::stage_append`, `stage_merge_insert`, `commit_staged` at `crates/omnigraph/src/table_store.rs`
 - Manifest commit primitive: `commit_updates_on_branch_with_expected` at `crates/omnigraph/src/db/omnigraph/table_ops.rs`
 
-Atomicity guarantee for multi-statement mutations: a mid-query failure leaves Lance HEAD untouched on staged tables (no inline commit happened during op execution), so the next mutation proceeds normally with no `ExpectedVersionMismatch`. The publisher CAS at the very end either succeeds (manifest advances atomically across all touched sub-tables) or fails with a typed `ManifestConflictDetails::ExpectedVersionMismatch` (no partial publish). See [docs/dev/invariants.md](invariants.md) and [docs/dev/runs.md](runs.md).
+Atomicity guarantee for multi-statement mutations: a mid-query failure leaves Lance HEAD untouched on staged tables (no inline commit happened during op execution), so the next mutation proceeds normally with no `ExpectedVersionMismatch`. The publisher CAS at the very end either succeeds (manifest advances atomically across all touched sub-tables) or fails with a typed `ManifestConflictDetails::ExpectedVersionMismatch` (no partial publish). See [docs/dev/invariants.md](invariants.md) and [docs/dev/writes.md](writes.md).
 
 ## Bulk loader (`loader/mod.rs`)
 

docs/dev/index.md

@@ -21,7 +21,7 @@ constraints. User-facing behavior should still be documented through
 |---|---|
 | System structure, L1/L2 framing, component diagrams | [architecture.md](architecture.md) |
 | On-disk layout, manifest schema, URI behavior | [storage.md](../user/storage.md) |
-| Direct-publish writes, D2, staged writes, recovery sidecars | [runs.md](runs.md) |
+| Direct-publish writes, D2, staged writes, recovery sidecars | [writes.md](writes.md) |
 | Query execution, mutation execution, loader flow | [execution.md](execution.md) |
 | Index lifecycle and graph topology indexes | [indexes.md](../user/indexes.md) |
 | Branch and commit internals | [branches-commits.md](../user/branches-commits.md) |

docs/dev/invariants.md

@@ -38,7 +38,7 @@ Use it this way:
    publishes one manifest update. Do not commit per statement. Delete-only
    queries are the documented inline residual; the parse-time D2 rule prevents
    mixing deletes with insert/update until Lance exposes two-phase delete.
-   Read [runs.md](runs.md) and [execution.md](execution.md).
+   Read [writes.md](writes.md) and [execution.md](execution.md).
 
 5. **Recovery is part of the commit protocol.** Writers that can advance Lance
    HEAD before manifest publish must write `__recovery/{ulid}.json` sidecars.
@@ -56,7 +56,7 @@ Use it this way:
    branch they read even when index coverage is partial. Expensive index work
    should converge from manifest state instead of extending the critical write
    path. Scalar staged index builds and vector inline residuals are documented
-   in [runs.md](runs.md) and [indexes.md](../user/indexes.md).
+   in [writes.md](writes.md) and [indexes.md](../user/indexes.md).
 
 8. **Schema identity survives renames.** Accepted schema identity must remain
    stable across type and property renames. Rename support belongs in migration
@@ -96,12 +96,12 @@ Use it this way:
 
 | Area | Current state | Source |
 |---|---|---|
-| Multi-table commit | Manifest CAS plus recovery sidecars; not a single Lance primitive | [runs.md](runs.md), [architecture.md](architecture.md) |
-| Constructive mutations | In-memory `MutationStaging`, one end-of-query table commit per touched table, then one manifest publish | [runs.md](runs.md), [execution.md](execution.md) |
-| Deletes | Inline-commit residual; delete-only queries allowed, mixed insert/update/delete rejected by D2 | [query-language.md](../user/query-language.md), [runs.md](runs.md) |
+| Multi-table commit | Manifest CAS plus recovery sidecars; not a single Lance primitive | [writes.md](writes.md), [architecture.md](architecture.md) |
+| Constructive mutations | In-memory `MutationStaging`, one end-of-query table commit per touched table, then one manifest publish | [writes.md](writes.md), [execution.md](execution.md) |
+| Deletes | Inline-commit residual; delete-only queries allowed, mixed insert/update/delete rejected by D2 | [query-language.md](../user/query-language.md), [writes.md](writes.md) |
 | Schema validation | Type checks, required fields, defaults, edge endpoint checks, and edge cardinality are enforced on write paths | [schema-language.md](../user/schema-language.md), [execution.md](execution.md) |
 | Unique constraints | Intra-batch and write-path checks exist; full cross-version uniqueness is still a gap | [schema-language.md](../user/schema-language.md) |
-| Storage trait | `TableStorage` exists as the sealed staged-write surface; full call-site migration and capability/stat surfaces are incomplete | [runs.md](runs.md), [architecture.md](architecture.md) |
+| Storage trait | `TableStorage` exists as the sealed staged-write surface; full call-site migration and capability/stat surfaces are incomplete | [writes.md](writes.md), [architecture.md](architecture.md) |
 | Index lifecycle | `ensure_indices` is explicit today; reconciler-based convergence is roadmap | [indexes.md](../user/indexes.md), [maintenance.md](../user/maintenance.md) |
 | Traversal IDs | Runtime still builds `TypeIndex`; Lance stable row-id based graph IDs are roadmap | [architecture.md](architecture.md), [query-language.md](../user/query-language.md) |
 | Auth | Bearer token hashing and server-side actor resolution are implemented at the HTTP boundary | [server.md](../user/server.md), [policy.md](../user/policy.md) |

docs/dev/testing.md

@@ -20,7 +20,7 @@ The engine's `tests/` is the principal coverage surface; most graph-shaped behav
 | `end_to_end.rs` | Full init → load → query/mutate flow |
 | `branching.rs` | Branch create / list / delete, lazy fork |
 | `merge_truth_table.rs` | Merge-pair truth table (MR-786): all 9×9 `(left_op, right_op)` cells from `{noop, addNode, removeNode, addEdge, removeEdge, setProperty, dropProperty, addLabel, removeLabel}`. Adding a new op to `OpVariant` forces a compile error in `build_case` until the new row + column are dispositioned. 36 executable cells run through real `branch_merge` with a structured oracle (`MergeOutcome` / `MergeConflictKind` + graph-state assert); 45 cells involving `dropProperty`/`addLabel`/`removeLabel` are recorded as `Unsupported` until the mutation grammar grows. |
-| `runs.rs` | Direct-publish writes: cancellation, concurrent-writer CAS, multi-statement atomicity, MR-794 staged-write rewire (D₂ rejection, insert+update coalesce, multi-append coalesce, partial-failure recovery, load RI/cardinality recovery) |
+| `writes.rs` | Direct-publish writes: cancellation, concurrent-writer CAS, multi-statement atomicity, MR-794 staged-write rewire (D₂ rejection, insert+update coalesce, multi-append coalesce, partial-failure recovery, load RI/cardinality recovery) |
 | `staged_writes.rs` | TableStore staged-write primitives (`stage_append`, `stage_merge_insert`, `commit_staged`, `scan_with_staged`, `count_rows_with_staged`) — primitive-level only; engine code uses the in-memory `MutationStaging` accumulator instead |
 | `lifecycle.rs` | Graph lifecycle, schema state |
 | `point_in_time.rs` | Snapshots, time travel (`snapshot_at_version`, `entity_at`) |
@@ -89,7 +89,7 @@ If introducing coverage tooling is in scope for your task, the natural first ste
 
 How to check:
 
-1. **Map the change to an area** — use the engine integration-test table above (`branching.rs`, `runs.rs`, `search.rs`, etc.). The filename usually names the area.
+1. **Map the change to an area** — use the engine integration-test table above (`branching.rs`, `writes.rs`, `search.rs`, etc.). The filename usually names the area.
 2. **Open the file and skim every test fn name.** Test fn names are the index — read them all, not just the first few.
 3. **Grep for the symbol or path you're changing.** `rg <FunctionName>` or `rg <enum_variant>` across all `tests/` directories surfaces existing coverage you might miss.
 4. **Decide one of three outcomes**, in this order of preference:

docs/dev/writes.md

@@ -1,7 +1,10 @@
-# Runs — REMOVED (MR-771)
+# Direct-Publish Write Path
 
-The Run state machine and `__run__<id>` staging branches were removed in
-MR-771. `mutate_as` and `load` now write **directly to the target table**
+> History: the Run state machine and `__run__<id>` staging branches were
+> removed in MR-771 (shipped v0.4.0). Writes now go directly to the target
+> table; this document specifies that direct-publish path.
+
+`mutate_as` and `load` write **directly to the target table**
 and call `ManifestBatchPublisher::publish` once at the end with
 `expected_table_versions` (the per-table manifest versions captured before
 the first write). Cross-table OCC is enforced inside the publisher; the