SP2: physical project store - #53

Specs the fix for the SP2 defect filed in PR davidwt-com#53: graphdb_query's BFS
re-guesses which store each frontier node lives in, so a project with >=6
instances shadows bootstrap nref 6 and an environment-only path returns
{ok, no_path}.

Two halves. (A) arc-discovered nrefs route through a new pure
graphdb_ns:arc_target_namespace(Home, Kind, Char) keyed on
#relationship.kind, with the 29/30 membership pair distinguished by
characterization. (B) the BFS frontier, visited set, and target comparison
become Home-qualified -- without B, project-6 and environment-6 collapse
into one visited entry and the bare-nref target test reports a false found.

Corrects the fix direction recorded in the PR davidwt-com#53 comment and in TASKS.md,
which said to route via graphdb_ns:target_namespace/2 on the arc's
target_kind. Bootstrap arc labels 21-30 carry no target_kind AVP, and arcs
23/24 are the decisive hops in the repro, so that lookup fails exactly
where routing matters most.

Design only -- no code changes.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EWukKCbrN8GybaScJGU2kF

* Design: query-traversal Home routing for arc-discovered nrefs

Specs the fix for the SP2 defect filed in PR #53: graphdb_query's BFS
re-guesses which store each frontier node lives in, so a project with >=6
instances shadows bootstrap nref 6 and an environment-only path returns
{ok, no_path}.

Two halves. (A) arc-discovered nrefs route through a new pure
graphdb_ns:arc_target_namespace(Home, Kind, Char) keyed on
#relationship.kind, with the 29/30 membership pair distinguished by
characterization. (B) the BFS frontier, visited set, and target comparison
become Home-qualified -- without B, project-6 and environment-6 collapse
into one visited entry and the bare-nref target test reports a false found.

Corrects the fix direction recorded in the PR #53 comment and in TASKS.md,
which said to route via graphdb_ns:target_namespace/2 on the arc's
target_kind. Bootstrap arc labels 21-30 carry no target_kind AVP, and arcs
23/24 are the decisive hops in the repro, so that lookup fails exactly
where routing matters most.

Design only -- no code changes.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EWukKCbrN8GybaScJGU2kF

* Plan: query-traversal Home routing implementation

Five tasks, TDD throughout. T1 graphdb_ns:arc_target_namespace/3 + EUnit;
T2 Home-qualified BFS (the headline invariant + the false-found case);
T3 home key on cross-store edges; T4 resume/2 continuation-Home gate;
T5 docs + verification gate.

Records one deliberate deviation from the design: its T3 (visiting
project-6 must not suppress environment-6) is not constructible under
this scope, since reaching both keys in one walk needs a store crossing
and the only one available lands on a class, from which the environment
attribute subtree is unreachable by taxonomy. Replaced by T3', which
asserts the same Half-B property observably via #cont_path{} state.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EWukKCbrN8GybaScJGU2kF

* Half A: graphdb_ns:arc_target_namespace/3 routes arc-discovered nrefs

* Half B: Home-qualified BFS frontier, visited set and target

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EWukKCbrN8GybaScJGU2kF

* Disclose home_id on path edges that cross stores

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EWukKCbrN8GybaScJGU2kF

* resume/2 rejects continuations carrying a foreign project Home

Adds validate_cont_homes/2, a caller-side gate on resume/2 that runs
after validate_session_home/1 and before the gen_server:call. Every
home_id() a #cont_path{} carries (target + frontier) must resolve
against the resuming session's own bound project; a mismatch returns
{error, session_project_mismatch} instead of reaching home_of_id/2
inside the graphdb_query singleton.

Closes two review findings tracked from Task 2:
- a continuation resumed under a project-less session no longer risks
  maps:get(project, Session) raising {badkey, project} inside
  handle_call/3 and killing the singleton
- a continuation resumed under a *different* project is rejected
  instead of home_of_id/2 silently discarding the anchor and reading
  the wrong project's tables

Adds three regression tests: t3_continuation_state_is_home_qualified
and t6_resume_round_trip_under_project_session (pass on arrival --
Task 2 already delivered this shape) and
resume_rejects_foreign_project_continuation (drives this fix).

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EWukKCbrN8GybaScJGU2kF

* Docs: record query-traversal Home routing as implemented

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EWukKCbrN8GybaScJGU2kF

* Docs: fix stale resolve_home/2 duplicates and test count after review

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EWukKCbrN8GybaScJGU2kF

* Final review fix wave: docs corrections, dead-code removal, hardened frontier gate

Six findings from the whole-branch final review:

1. docs/Architecture.md: correct the false claim that bootstrap arc labels
   21-30 carry target_kind (they don't -- only runtime-created relationship-
   attribute pairs do); note arc-discovered traversal routes via
   graphdb_ns:arc_target_namespace/3 instead, and that target_namespace/2
   has no production caller.
2. graphdb_query.erl: rewrite resume/2's stale header comment -- it no
   longer dispatches through resolve_home/2; validate_session_home/1 is
   still load-bearing because validate_cont_homes/2 depends on it running
   first.
3. apps/graphdb/CLAUDE.md: document resume/2's {error, invalid_project}
   and {error, session_project_mismatch} returns alongside the existing
   {error, snapshot_expired}.
4. graphdb_query.erl: validate_cont_homes/2 folds a frontier-element shape
   check into its lists:all/2 pass, closing a gap where a wrong-arity
   frontier tuple was silently dropped by the old list-comprehension
   generator instead of failing the gate. Adds
   resume_rejects_malformed_frontier_continuation/1 to
   graphdb_query_SUITE's sp2_traversal_home_routing group, asserting both
   the clean error and that the graphdb_query singleton pid survives.
5. graphdb_ns.erl: Rev PA3 revision-history entry for arc_target_namespace/3.
6. graphdb_query.erl: remove the dead `[] -> []` arm in bfs/8's
   depth-exhausted clause -- unreachable because the first bfs/8 clause
   already matches an empty frontier for any depth.

Verification: rebar3 compile / as test compile zero warnings, rebar3 xref
clean, make test-ct-parallel 551/551, rebar3 eunit 151/151.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EWukKCbrN8GybaScJGU2kF

---------

Co-authored-by: Claude Opus 5 <noreply@anthropic.com>