PROBLEM / REVISION / SOURCES / AUTHORIZED SCOPE
  Problem: corner-topo-advisor (reanalysis of corner-topo; lives alongside it).
  Revision: 2, 2026-10-12. Status: analysis complete; ready for the spec advisor.
  Record: doc/problems/corner-topo-advisor/problem-analysis.txt
  Snapshot: deleted at spec wrap-up 2026-10-12 (see spec-analysis.txt history).
  Sources: user description; doc/problems/corner-topo/diagram.jpg; probs/problem-corner-topo.lisp;
    doc/problems/corner-topo/{Briefing.md, Handoff.md, Actions.lisp, Validation.txt} (reference only);
    tech/ and src/ source as cited below.
  Prior exposure: the old corner-topo spec, analysis and validated 15-action plan were read for reference at
    the user's direction, so no blind comparison boundary applies.
  Scope: problem analysis only. Spec writing, staging, replay and search are not authorized by this record.

AGREED PROBLEM DESCRIPTION (agreed by user 2026-10-12)
  Geometry (fixed givens, from the diagram and old spec): boundary rectangle (0,0)-(12,11). A partition at
    x=8, bottom to top: wall2 (8,0)-(8,3), gate1 (8,3)-(8,11/2), wall1 (8,11/2)-(8,8), window1 (8,8)-(8,11).
    Walls block walking and sight; window1 blocks walking only; gate1 blocks both while closed.
  Sides: east = location1 (9,1), location2 (9,8), location3 (10,9); west = location4 (6,8).
    gate1 is the only walking route between the sides, and it is open exactly while receiver1 is active.
  Apparatus (fixed): transmitter1 red (11,1/10); transmitter2 blue (10,1/10); receiver1 red (81/10,1);
    receiver2 red (7,109/10); receiver3 blue (1,109/10).
  Movable: agent1 starts at location1; connector1/2/3 start unpaired at location1/2/3.
  Operations: exactly as tech/ defines them (doc/talos-reference.md section 1.8): move,
    pickup-connector, pickup-connector-retaining-pairings, put-connector, connect-connector.
  Beam rules: cut model -- two live beams that cross are both cut (tech/beam-crossing.lisp); bodies occlude.
  Standing locations: location1-4 as above (D4). Adding locations is permitted in principle as a modeling
    choice; none is proposed.
  Goal (final state only): agent1 at location4, receiver2 active (red), receiver3 active (blue). What
    agent1 holds and the states of receiver1/gate1 are irrelevant.

USER OBJECTIVE AND ANSWER IDENTITY
  A minimum-length action sequence; any one shortest plan is acceptable. Each action costs 1; a move to any
  currently walkable location is one action regardless of route. Connector names are irrelevant to answer
  identity.
  Underlying aim (user): structure the representation so a minimal solution can be found efficiently.
  A validated 15-action plan exists (old corner-topo); its minimality has not been established.

INTENDED RULES AND EXAMPLES
  Allowed:
    A1 With nothing else paired, connector3 at location3 connected to {transmitter1, receiver2, receiver1}
       lights receiver2 and receiver1 red and opens gate1 (no crossing among those three beams).
    A2 A connector picked up with pickup-connector-retaining-pairings and put down again relights through
       its retained pairings, if they are still visible and uncut.
    A3 A connect pairs termini visible from any location agent1 can currently walk to; the beam carries a
       hue only if live visibility from the placement holds.
    A4 A move from location2 to location4 through an open gate1 is one action.
  Forbidden / no effect:
    F1 Picking up or connecting a connector anywhere but agent1's own location.
    F2 Connecting at a location that already holds a lit connector.
    F3 Walking through window1, or through gate1 while closed.
    F4 Crossing beams: connector at location1 paired {transmitter1} and connector at location2 paired
       {transmitter2} cut each other at (9.94,0.58); neither connector is lit by that beam.
    F5 A relay reached by red and blue in the same lighting layer stays unlit; a later-arriving hue is
       ignored.
  Invariant (D1): no goal state has receiver1 lit or gate1 open.

CURRENT IMPLEMENTATION
  Old spec probs/problem-corner-topo.lisp encodes the same geometry and technologies; corner-topo-advisor has
  no spec yet. Whether to copy and rename it (problem-corner-topo-advisor.lisp) or write anew is the spec
  advisor's decision.

STRUCTURE AND GROWTH
  Single fixed instance; no larger family expected.
  Plans are long (a 15-action plan is known; see hints), so sequence length is the main difficulty.
  State: agent location and holding; connector locations and PAIRED facts; derived color, crossing-active,
  receiver activity and gate status. No time or history dependence.

JUSTIFIED DESIGN (agreed by user 2026-10-12)
  D1 Separation (deduction, geometry-dependent): receiver1 lit red and a complete blue chain
    transmitter2 -> ... -> receiver3 can never coexist. Any red chain from transmitter1 to receiver1 together
    with the floor encloses transmitter2, so every blue chain leaving transmitter2 crosses it and the
    crossing cuts both. Consequences for every plan:
    - In every goal state gate1 is closed; the final red and blue chains cannot route through gate1.
    - The last walk west happens with blue incomplete; every action after it is taken at location4
      (identity reach).
    Role: a property of the rules, used as a fidelity check, not as an added constraint.
  D4 Standing locations: location1-3 must remain standing spots because connectors start there and pickup
    requires the agent at the connector's location; location4 is the goal location. Whether added locations
    could shorten a plan is left to the solving advisor.

WOULDWORK MAPPING (agreed by user 2026-10-12; source-checked that date)
  M1 Walking, partition, gate route -> walkability (derived from wall/gate/window segments). B; S: authored
     segment and location coordinates.
  M2 gate1 open exactly while receiver1 active -> gate tech (controls ((receiver1)) gate1 normal). B; S: fact.
  M3 Connector actions incl. retaining pickup -> tech/beam-relay.lisp define-actions pickup-connector,
     pickup-connector-retaining-pairings, put-connector, connect-connector; all present whenever beam-relay
     is included. B.
  M4 Cut model and body occlusion -> beam-crossing with -beam-crossing-coordinates (crossing pool minted at
     init from coordinates); *beam-occlusion-tolerance* 1/2. B; S: apparatus/location coordinates.
  M5 Lighting order and hue conflicts -> compute-relay-lighting. B.
  M6 Goal -> define-goal. S.
  M7 Shortest plan -> *solution-type* min-length with depth-first graph search; src/ww-searcher.lisp
     better-than-closed reopens a closed state revisited at a shallower depth, so merging states keeps
     shortest plans. B.
  M8 Interchangeable connectors -> *symmetry-pruning* t (src/ww-symmetry.lisp). Sound for this answer
     identity. B; detection for this spec not yet confirmed (validation item V3).
  M9 D1 -> no mapping required.
  No capability gaps.

INITIAL SETTINGS AND DEFERRED MEASUREMENTS
  Semantic: *problem-type* planning; *solution-type* min-length; *tree-or-graph* graph.
  Provisional: *symmetry-pruning* t; *max-connector-pairings* 3 (tech default); *depth-cutoff* set by the
    user from the problem's maximum search depth.
  Parallel: (ww-set *threads* 16) baseline. Compatible: depth-first graph search runs in parallel, the
    crossing cache is registered as a worker read memo (beam-crossing.lisp), and no serial-only feature is
    required. Exception: chained one-argument solve-subgoal, if the solving advisor uses it, must be serial.
  Deferred to the search advisor: the depth at which a single search is practical, and whether a milestone
    decomposition or a lower bound (topo-lower-bound) is needed.

EVIDENCE
  Source behavior (2026-10-12): tech/beam-relay.lisp, tech/beam-crossing.lisp, tech/-pickup.lisp,
    tech/-mobility-action.lisp, tech/-beam-occlusion.lisp (summarized in doc/talos-reference.md 1.8);
    src/ww-searcher.lisp (closed-state reopening).
  Deduction (2026-10-12): segment intersections computed exactly from the coordinates above, e.g.
    T1-L4 x T2-L2 (9.75,2.08); T1-L4 x L3-R1 (8.74,3.68); T1-L4 x L2-R1 (8.49,4.06); L1-L4 x L3-R1
    (8.42,2.35); T2-L4 x L3-R1 (8.56,2.94); T1-L1 x T2-L2 (9.94,0.58); T2-L2 x L3-R1 (9.27,5.91);
    no crossing among T1-L3, L3-R2, L2-R3, T2-L2, L3-L2. D1 rests on this geometry.
  Prior measurement (old spec, 2026-09-30): the 15-action plan replays to the goal under
    probs/problem-corner-topo.lisp. Not yet repeated for corner-topo-advisor.
  Limits: no staging, replay or search of corner-topo-advisor; occlusion margins not checked.

OPEN ISSUES AND CAPABILITY GAPS
  No analysis blockers.
  Deferred (solving advisor): whether added standing locations could shorten a plan.
  Deferred (search advisor): search depth practicality, milestones, lower bound.

VALIDATION PLAN (for the spec advisor; requires its own authorization)
  V1 Fidelity examples: reproduce A1-A4 and F1-F5 on the staged spec.
  V2 Crossing pool: confirm the minted crossings include the intersections listed under EVIDENCE.
  V3 Symmetry: confirm connector1-3 form one symmetry group (M8).
  V4 Replay the old 15-action plan (doc/problems/corner-topo/Actions.lisp) as an allowed example; check that
     its final state has gate1 closed (D1).
  V5 Occlusion: confirm which body positions block which beams within tolerance 1/2.

HINTS FOR DOWNSTREAM ADVISORS
  Unverified deductions; reviewed by user 2026-10-12, not checked by replay or search. Not developed further
  here (problem-advisor scope).
  H-terminal: the only mechanism found for completing blue from location4 is picking up a connector at
    location4 whose transmitter1->location4 beam cuts transmitter2->location2 at (9.75,2.08), east of gate1,
    so the cut holds while gate1 is closed. Rejected alternatives: a relay at location4 fed through window1
    (its feed is always cut first by the red chain to receiver1); a fourth relay role (needs 4 connectors).
  H-trips: the cutter must be placed on an earlier trip, giving walks west, east, west. While it is in
    place, the only current opener avoiding its beam is a connector at location1 paired {transmitter1,
    receiver1}, which must later move because transmitter1->location1 cuts the blue feed at (9.94,0.58).
  H-length: counting required pickups, connects and moves gives 15 for the current locations, matching the
    old validated plan. Candidate milestones: cutter set at location4; agent back east; final east setup.
  H-locations: under H-terminal and H-trips, added locations do not appear to shorten a plan.

AGREEMENT AND HANDOFF
  User-confirmed: problem description, objective and answer identity, D1, D4, Wouldwork mapping and settings
    (all 2026-10-12).
  Readiness: all eight criteria met; no analysis blockers. Covered scope: the whole problem.
  Requirement-to-design obligations for the spec advisor:
    R1 Encode the agreed geometry and initial state exactly (coordinates above); no added locations.
    R2 Include gate, beam-relay, beam-crossing, walkability and visibility techs, so all five actions and the
       cut model are available (M1-M5).
    R3 Goal is final-state only: agent1 at location4, receiver2 and receiver3 active.
    R4 Settings per INITIAL SETTINGS; depth cutoff from the user.
    R5 Pass V1-V5 before the spec is accepted.
  Persistence: record and dated snapshot saved 2026-10-12.
  Next step (needs separate authorization): spec advisor consultation for corner-topo-advisor.

DIALOGUE EVALUATION
  - Scope drift: the analysis moved into solution mechanisms and length bounds (solving/search advisor
    work). Resolved by moving them to hints and adding a scope paragraph to problem-advisor.md
    (user-approved 2026-10-12).
  - Friction: the beam-relay and crossing operations had to be rederived from source; resolved by adding
    doc/talos-reference.md section 1.8 (user-approved 2026-10-12).
  - Comparison boundary: not applicable; the old spec was read up front at the user's direction.

CORRECTIONS
  2026-10-12: earlier D2 (terminal mechanism) and D3 (lower bound 15) were removed from the design and
    moved to hints as out of scope; D4's justification no longer relies on them. Content retained under
    HINTS FOR DOWNSTREAM ADVISORS.
