fix(session): persist the delegation depth in the session header

A subagent child's recursion depth lived only in runtime AgentOptions,
so a persisted child came back from resume counted as top-level and
maxDepth stopped binding after every restart. Add
SessionHeader.delegationDepth, round-trip it through the JSONL and
SQLite backends (SQLite schema v5), restore it on agent-loop resume,
and write it when the in-process backends create a child. The seam now
owns the shared depth vocabulary (delegationDepthOf): the persisted
header is authoritative and monotone — runtime options may deepen it
but never lower it.

website/zh-CN/api/harness/agents.md

@@ -7,7 +7,7 @@
 Agent service (`ctx.agents`): tracks live agents and carries the initiating Agent through one process-local asynchronous driver chain. Agent *creation* is provided by whichever plugin implements the AgentFactory (`@deepseek-ai/dsh-agent-loop`), registered via setFactory.
 Initiator methods provide same-process causal attribution only. Ambient presence is neither liveness proof nor authorization; subjects and owners remain explicit, as does identity at worker, process, persistence, and wire boundaries. Returned Promise boundaries drain during teardown, except a nested lineage that starts an owning-fiber unload is excluded from its own drain.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L217)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L223)
 
 ### ctx.agents.currentInitiator()
 
@@ -28,7 +28,7 @@ Read the Agent that initiated the inherited asynchronous driver chain. Use this
 
 **Returns** the inherited Agent, or `undefined` outside an initiator boundary and inside an explicit clearing boundary.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L256)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L262)
 
 ### ctx.agents.requireInitiator()
 
@@ -48,7 +48,7 @@ Read the initiating Agent and fail when no initiator boundary is active. Use thi
 
 **Returns** the inherited Agent.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L269)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L275)
 
 ### ctx.agents.withInitiator(agent, operation)
 
@@ -76,7 +76,7 @@ Run an operation with one exact Agent as its process-local initiator. The exact
 
 **Returns** the exact value returned by `operation`.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L288)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L294)
 
 ### ctx.agents.withoutInitiator(operation)
 
@@ -101,7 +101,7 @@ Run an operation inside a boundary that hides any inherited initiating Agent. Th
 
 **Returns** the exact value returned by `operation`.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L303)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L309)
 
 ### ctx.agents.setFactory(factory)
 
@@ -127,7 +127,7 @@ Register the agent-creation factory (the loop calls this on construction, effect
 
 **Returns** the disposer that clears the factory slot. The exact Cordis effect disposer (single-shot): composite (generator) effects may yield it directly — exact identity nests the teardown in order.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L319)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L325)
 
 ### ctx.agents.create(options)
 
@@ -150,7 +150,7 @@ Create and publish a new agent through the registered factory. Distinct from reg
 
 **Returns** the handle after setup, rollback-covered publication, and loop start complete.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L352)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L358)
 
 ### ctx.agents.resume(options)
 
@@ -171,7 +171,7 @@ Load a persisted session and resume an agent on it through the registered factor
 
 **Returns** the handle after setup, rollback-covered publication, and loop start complete.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L371)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L377)
 
 ### ctx.agents.register(agent)
 
@@ -203,7 +203,7 @@ Register a live agent. Throws if an agent with the same id is already registered
 
 **Returns** the EXACT Cordis effect disposer (single-shot; a repeat call returns undefined without awaiting an in-flight teardown). Exact identity is load-bearing: a composite (generator) effect that owns a teardown ORDER — the agent factory's lifecycle chain — must yield THIS function so Cordis nests the unregistration at that yield position; yielding a wrapper would leave it disposing as a concurrent sibling on owner unload, unregistering the agent (and emitting `agent/disposed`) while its final turn is still draining.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L397)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L403)
 
 ### ctx.agents.enter(agent, owner)
 
@@ -233,7 +233,7 @@ Insert an already-constructed agent without announcing it. This is the advanced
 
 **Returns** an idempotent closure that removes this exact entry and emits `agent/disposed` with listener failures contained. When called from a synchronous `agent/created` listener, removal and disposal wait until that creation dispatch unwinds.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L421)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L427)
 
 ### ctx.agents.announce(agent)
 
@@ -252,7 +252,7 @@ Announce an agent previously inserted with enter.
 
 - `agent` — the live inserted agent to announce.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L496)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L502)
 
 ### ctx.agents.get(id)
 
@@ -271,7 +271,7 @@ Look up a live agent.
 
 **Returns** the agent, or undefined when no live agent has that id.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L530)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L536)
 
 ### ctx.agents.isOwnedBy(id, owner)
 
@@ -294,7 +294,7 @@ Test whether a live agent was created through one exact parent agent's scoped co
 
 **Returns** true only while the exact child entry is live under that owner.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L542)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L548)
 
 ### ctx.agents.list()
 
@@ -310,7 +310,7 @@ All live agents, in registration order.
 
 **Returns** a fresh array; mutating it does not affect the registry.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L550)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L556)
 
 ### ctx.agents.roots()
 
@@ -328,4 +328,4 @@ All live top-level agents in registration order. A top-level agent was created w
 
 **Returns** a fresh array; mutating it does not affect the registry.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L560)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/agent/src/index.ts#L566)

website/zh-CN/api/harness/events.md

@@ -614,7 +614,7 @@ A ready child settled. Scope-filtered dispatch uses the same delegating parent c
 
 - `info` — the run identity and terminal outcome.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L112)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L138)
 
 ### subagent/provider-added
 
@@ -633,7 +633,7 @@ A provider became resolvable in the registry.
 
 - `provider` — the registered provider.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L86)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L112)
 
 ### subagent/provider-removed
 
@@ -652,7 +652,7 @@ A provider left the registry. Accepted runs remain holder-owned.
 
 - `name` — the provider name that no longer resolves.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L92)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L118)
 
 ### subagent/start
 
@@ -676,7 +676,7 @@ A provider established a ready child. For in-process providers, `ctx.agents.get(
 
 - `info` — the provider and ready child identity.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L103)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L129)
 
 ## system-prompt/*
 

website/zh-CN/api/harness/sessions.md

@@ -7,7 +7,7 @@
 In-memory session store (`ctx.sessions`).
 Persistence is intentionally not implemented here — persistence plugins subscribe to `session/event` and flush on `session/flush` / dispose.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L577)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L581)
 
 ### ctx.sessions.create(id?, options?)
 
@@ -44,7 +44,7 @@ For an agent whose session must be torn down IN ORDER with its loop (so the loop
 
 **Returns** the live session, already entered and announced.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L606)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L610)
 
 ### ctx.sessions.prepare(id?, options?)
 
@@ -75,7 +75,7 @@ Build a session WITHOUT entering it into the store — validate the id/cwd and c
 
 **Returns** the constructed session, NOT yet in the store.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L635)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L639)
 
 ### ctx.sessions.enter(session)
 
@@ -112,7 +112,7 @@ Re-checks the id for a duplicate: `prepare` and `enter` are public cross-package
 
 **Returns** the detach disposer (publication hooks + store removal). When called from a synchronous `session/created` listener, removal and disposal wait until that creation dispatch unwinds.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L679)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L684)
 
 ### ctx.sessions.announce(session)
 
@@ -131,7 +131,7 @@ Emit `session/created` exactly once for an entered session (with the carrier ent
 
 - `session` — the entered session to announce to listeners.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L734)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L739)
 
 ### ctx.sessions.flush(session)
 
@@ -156,7 +156,7 @@ Dispatch the awaited `session/flush` durability checkpoint for `session`, with t
 
 **Returns** resolves when every flush listener has settled; after all settle, rejects with the first registered listener failure if any listener failed.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L786)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L791)
 
 ### ctx.sessions.get(id)
 
@@ -175,7 +175,7 @@ Look up a live session.
 
 **Returns** the session, or undefined when no live session has that id.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L818)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L823)
 
 ### ctx.sessions.list()
 
@@ -191,7 +191,7 @@ All live sessions, in creation order.
 
 **Returns** a fresh array; mutating it does not affect the store.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L826)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L831)
 
 ### ctx.sessions.fork(source, boundary?, childSessionId?)
 
@@ -220,4 +220,4 @@ Create a live child session from a turn-enclosed prefix of a live source. `bound
 
 **Returns** The created live child session.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L843)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/core/session/src/index.ts#L848)

website/zh-CN/api/harness/subagents.md

@@ -6,7 +6,7 @@
 
 Named provider registry and capability-checked start surface.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L153)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L179)
 
 ### ctx.subagents.registerProvider(provider)
 
@@ -27,7 +27,7 @@ Register a provider under its name. Registration is effect-scoped and HMR safe;
 
 **Returns** the exact Cordis effect disposer.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L167)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L193)
 
 ### ctx.subagents.getProvider(name)
 
@@ -46,7 +46,7 @@ Look up a provider by name.
 
 **Returns** the provider, or undefined when absent.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L190)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L216)
 
 ### ctx.subagents.list()
 
@@ -62,7 +62,7 @@ List registered provider names in insertion order.
 
 **Returns** the registered names.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L198)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L224)
 
 ### ctx.subagents.start(name, request)
 
@@ -86,4 +86,4 @@ Establish a ready child on the named provider. Capability and semantic checks ru
 
 **Returns** the ready holder-owned run.
 
-[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L211)
+[Source](https://github.com/deepseek-harness/deepseek-harness/blob/master/packages/subagent/subagent/src/index.ts#L237)