PROBLEM / REVISION / SOURCES / AUTHORIZED SCOPE
  Problem: intersect (diagram title INTERSECTIONS).  Revision 6, 2026-11-10 (rev 5 2026-11-08; rev 4 2026-11-07; rev 3 2026-11-05; rev 2 consolidated 2026-11-04).
  Sources: doc/problems/intersect/intersect-diagram.png; symbol key from
  doc/problems/rumin-topo/diagram.png; user clarifications in dialogue 2026-11-04
  (apparatus offsets, starts, controls, goal, ladder LD1 added in dialogue);
  user corrections 2026-11-05 (L2 relocated, L8 removed, LD1 retargeted to L2);
  user addition 2026-11-07 (new L8 at (15,8), diagram updated);
  user addition 2026-11-08 (new L9 at (10,8), central room);
  solving-advisor reanalysis 2026-11-10 (new L10 at (8,1), L11 at (2,15); L4, L5 removed).
  Record: doc/problems/intersect/problem-analysis.txt.
  Scope: problem-advisor analysis only.  No spec, measurement, or search authorized.

AGREED PROBLEM DESCRIPTION  (agreed by user 2026-11-04)
  Single-floor talos puzzle, no elevation parameters.  Boundary rectangle (0,0)-(29,20).
  Walls / windows (beams pass windows; agent does not):
    x=5:  w1 y0-6, WIN4 y6-10, w9 y10-15.   x=8: w2 y3-6, WIN3 y6-10.
    w10 y=10 x5-8.   y=15: w8 x5-13, WIN2 x13-17, w7 x17-23.
    x=23: w6 y10-15, WIN1 y6-10, w5 y4-6.   w3 y=6 x8-14.   w4 x=17 y0-6.
    No wall along y=6 x5-8.  Faint erased circles (e.g. near (6,5)) are not locations.
  Gates: G1 y=6 x14-17; G2 x=23 y0-4; G3 x=18 y15-20; G4 y=6 x0-5.
  Ladder: LD1 positioned at L3; one-way climb L3 -> L2; empty-handed only.
  Areas (joined only by gates and LD1):
    lower room    x5-17 y0-6 plus cell x5-8 y6-10:          L1(15,5), L10(8,1), T1b, R1b
    central room  x8-23 y6-10, x5-23 y10-15, x17-23 y0-6:    L2(21,6), L8(15,8), L9(10,8), T2r, R2r
    east corridor x23-29 y0-20 and y15-20 x18-23:            L3(24,8), LD1
    west/north corridor x0-5 y6-20 and y15-20 x0-18:         L11(2,15), L6(1,7)+P1,
                                                             R3b, R4r
    SW room       x0-5 y0-6:                                 L7(3,4)
    G1 lower<->central; G2 central<->east; G3 east<->west/north; G4 west/north<->SW;
    LD1 east -> central (one way).
  Beam paths through windows: WIN3 lower-cell<->central; WIN4 lower-cell<->west corridor;
    WIN2 central<->north corridor; WIN1 central<->east corridor.
  Apparatus (one-sided, 1/10 off wall, facing):
    T1b (15,0.1) N; T2r (7,14.9) S; R1b (13,5.9) S; R2r (22.9,5) W;
    R3b (15,19.9) S; R4r (0.1,8) E.
  Controls (gate open only while condition holds): G1<-R1b; G2<-R2r; G3<-R3b;
    G4<-R4r AND P1.  P1 pressed by agent or a connector at L6.
  Start: agent1 at L1; C1 at L1; C2 at L2; C3 at L3; gates closed; connectors unlit,
    no links.
  Goal: agent1 at L7.

USER OBJECTIVE AND ANSWER IDENTITY
  Any plan reaching the goal; a shortest plan preferred (unit action cost).
  Plans are action sequences; only length matters for comparison.

INTENDED RULES AND EXAMPLES
  Standard talos tech rules (talos-reference 1.4, 1.8), confirmed by user:
  - Agent walks freely within an area; walls, windows, closed gates block it.
  - No reach through any window: the agent cannot pick up or place a connector across a
    window (all windows effectively barred); beams still pass windows.  (User, 2026-11-05.)
  - LD1 climb L3->L2 only, only when empty-handed.  Allowed: empty agent at L3 climbs to L2.
    Forbidden: agent holding a connector climbs; any descent L2->L3.
  - Agent carries one connector.  Pickup either drops links or keeps them (game option).
  - A connector has at most 3 links at any time, counting links it made and links other
    connectors made to it; links kept through a pickup still count.  (User, 2026-11-05.)
  - Connect: place held connector and link to 1-3 termini (transmitters, receivers, other
    connectors) structurally visible from any currently walkable location.
  - Connector takes the hue reaching it; two hues in the same layer -> unlit.
  - Receiver active while a beam of its own hue reaches it from a paired relay.
  - Any two crossing beams, of any hues, cut each other at the intersection.
  - Agent and connectors block beams passing within 1/2 unit.
  - Example: an unlinked connector put at L6 holds P1; G4 then opens iff R4r is also active.

CURRENT IMPLEMENTATION
  None (new problem).

STRUCTURE AND GROWTH
  Structural fact (deduction from layout): the only agent route into L7 is
  L1 -G1-> central -G2-> east -G3-> west/north -G4-> L7.  LD1 only returns the agent
  from east to central.  Every plan therefore passes G1, G2, G3, G4 in that order, each
  open at its time of passage.  C2 (at L2) is unreachable before G1 is first opened; C3 (at L3)
  before G2 is first opened.
  Size: 1 agent, 3 connectors, 9 locations, 6 apparatus, 4 gates, 1 plate, 1 ladder.
  History irrelevant to future legality: state fully determines continuations.
  Growth: connect branching = reachable locations x link subsets (92 for 8 termini, cap 3);
  subsets grow ~cubically in termini; locations, gates grow linearly.

JUSTIFIED DESIGN  (all agreed by user 2026-11-04)
  D1 State: agent location; held connector; connector locations; link set.  Derived after
     every action by tech: hues, crossings, receiver activity, gate status, plate status.
     Alternative: store gate/receiver status as fluents -- rejected, derived is faithful.
  D2 Graph search (merge equal states).  Premise: no history dependence (D1).  Sound for
     shortest plans.
  D3 Actions: move (incl. LD1 climb), pickup-connector, pickup-connector-retaining-pairings,
     put-connector, connect-connector.  All cost 1.
     Retaining pickup kept: game-faithful; offered only with links; proving it unneeded
     would require solving.  Reconsider: search advisor may test omission as a speed-up.
     put-connector needed (cheapest way to hold P1 with an unlinked connector).
  D4 *max-connector-pairings* 3 (user: probably needed; one input + two outputs).
  D5 Locations L1-L3, L6-L11 as given (L8 added by user 2026-11-07 for the third subgoal leg;
     L9 added 2026-11-08 for the red feed to the west room).
     L10, L11 added and L4, L5 removed 2026-11-10 (rev 6).
     Reconsider if a needed beam line has no location.
  D6 Coordinate-derived geometry (walls, windows, gates, fixtures, locations), as in
     rumin-topo; required for exact crossings.
  D7 No pruning of hue-mismatched links: a non-activating link beam can still cut other
     beams, possibly intentionally.  No action omitted as useless.
  D8 Optional topo-lower-bound (admissible); benefit deferred to search advisor.

WOULDWORK MAPPING  (source-checked 2026-11-04 unless noted)
  D1/D3 connector actions, lighting, crossings: B, tech/beam-relay.lisp, beam-crossing.lisp.
  D3 move/climb: B, tech/-mobility-action.lisp, tech/ladder.lisp (climb via traverse-via>,
     ladder has-position at source; empty-handed via -passability per talos-reference 1.4).
  Gates, plate: B, gate and plate tech (documented in talos-reference; not re-read here).
  D6 geometry: B derivation (-beam-los-coordinates) + S coordinates, as in rumin-topo.
  Controls G1-G4 wiring incl. G4 = R4r AND P1: S (verify the AND form is expressible in
     gate tech at spec time -- documented only).
  Goal: S.
  Tech set: gate, plate, beam-relay, walkability, visibility, reachability, ladder;
     elevation possibly required as a dependency (rumin includes it) -- spec advisor checks.

INITIAL SETTINGS AND DEFERRED MEASUREMENTS
  Semantic: *problem-type* planning; *solution-type* min-length; *tree-or-graph* graph;
    *max-connector-pairings* 3.
  Provisional: *threads* 16 (other talos specs run so; compatibility with this tech set to
    be confirmed against source at spec time); depth cutoff supplied by user.
  Deferred to search advisor: omission of retaining pickup; topo-lower-bound benefit.

EVIDENCE
  - tech/beam-relay.lisp (2026-11-04): retaining pickup + put-connector restores prior links;
    connect-connector links only termini structurally visible from the agent's walkable
    area, needs no lit connector at the placement, branches over subsets <=3.
  - tech/ladder.lisp (2026-11-04): climb is directed, ladder positioned at source.
  - Area/route fact: deduction from the agreed layout.

OPEN ISSUES AND CAPABILITY GAPS
  No analysis blockers.  Spec-time checks: G4 AND-wiring form; required tech dependencies;
  *threads* 16 compatibility.

VALIDATION PLAN
  Fidelity checks for the spec advisor:
  - From start, connect C1 at L1 to T1b and R1b; check C1 hue, R1b, G1 (agent also at L1:
    confirm whether an agent at the relay location occludes its beams).
  - Holding a connector at L3, the agent cannot reach L2 by LD1; empty-handed it can.
  - No move from L2 to L3 except through G2.
  - A connector at L6 with R4r inactive leaves G4 closed.
  - Two crossing link beams (any hues) both cut.
  Growth: measure branching of connect-connector at cap 3 (search advisor).

HINTS FOR DOWNSTREAM ADVISORS
  - Gate order G1 -> G2 -> G3 -> G4 is forced (deduction); natural milestones and a
    minimum plan length.  Unverified as a solution route.
  - C2 and C3 become available only after G1 and G2 respectively; LD1 allows return to
    the central room empty-handed only.

AGREEMENT AND HANDOFF
  User confirmed description and design D1-D8, 2026-11-04.
  Status: Analysis complete and ready for the spec advisor.
  Snapshot: problem-analysis-2026-11-04-before-spec.txt (removed at wrap-up 2026-11-10;
  in git history).
  Next step (not yet authorized): spec-advisor consultation to write problem-intersect.lisp.

CORRECTIONS
  - Structural route fact first stated without LD1 (rev 1).  LD1 added; one-way L3->L8
    leaves the forced gate order unchanged.  Retained.
  - Central room extent rev 1 omitted x5-8 y10-15 (T2r's corner); corrected.
  - Rev 3 (user, 2026-11-05): L2 relocated from (14,9) to (21,6), still in the central
    room; L8 removed; LD1 now climbs L3 -> L2 (one way, empty-handed).  Area membership
    and the forced gate order G1 -> G2 -> G3 -> G4 are unchanged.  Locations now L1-L7.
  - Rev 3 addendum (user, 2026-11-05): windows bar reach as well as walking.
  - Rev 3 addendum (user, 2026-11-05): C2 starts at L2, not L3.
  - Rev 3 addendum (user, 2026-11-05): C3 starts at L3, not L5.
  - Rev 3 addendum (user, 2026-11-05): link cap of 3 is per connector, total, at any time.
  - Rev 4 (user, 2026-11-07): new location L8 at (15,8) in the central room, added to the
    diagram; the user needs it for the third leg of subgoaling (L3 -> L5).  Area membership
    and the forced gate order are unchanged.  Locations now L1-L8.
  - Rev 5 (user, 2026-11-08): new location L9 at (10,8) in the central room, west of the
    x=15 blue line.  Found by the solving advisor (SG3): with L1-L8 every red feed to the
    west room (from L2, L3 or L8) stops blue reaching R3b, so G3 cannot be recrossed.
    From L9 a connector sees T2r and, through WIN3 and WIN4, L6 and R4r, without crossing
    x=15.  The user confirms a connector can be placed there in the level.  Area membership
    and the forced gate order are unchanged.  Locations now L1-L9.
  - Rev 6 (solving advisor, user-approved 2026-11-10): new L10 at (8,1) in the lower room,
    in the opening south of w2, and new L11 at (2,15) in the west/north corridor.  A
    connector at L10 sees T1b and R1b and, through WIN4, L11; L11 sees R3b.  Blue then
    reaches R3b without entering the central room, so red there no longer competes with it
    (the user confirmed the sight lines in the level).  L4 and L5 removed: with 11 locations
    the crossing records exceed the engine's 999-object limit, and no plan step needs them.
    Area membership and the forced gate order are unchanged.  Locations now L1-L3, L6-L11.
    A 40-action plan replays to the goal (Briefing, SG3 2026-11-10).
