{
  "meta": {
    "source": "fto.twistytools.com — authored FTO algorithm data",
    "description": "FTO algorithms grouped by subset, then by case. Face letters follow the community notation (Sonja Black's 'FTO Notation' doc + Ben Streeter's FTO Notes); {X,Y} bracket rotations, X2 ergonomic doubles and w-suffix wides are supported. Each subset declares the HOLD its algs execute from ('cif' or 'eif').",
    "notation": "streeter",
    "apostrophe": "normalized to ASCII '",
    "status": "TCP (last layer) imported 2026-07-10; 1L3T (one-look last 3 triples) imported 2026-07-13 from zwegner’s page by tools/import-1l3t.mjs; LBT (last bottom triple) imported 2026-07-13 from zwegner’s page by tools/import-lbt.mjs; 1LP (one-look pair formation) imported 2026-07-13 from the user-supplied sheet by tools/import-1lp.mjs; rotations respelled site-wide as {X,Y} re-orientation brackets 2026-07-14 (tools/lib/bracketize.mjs, machine-verified move-for-move).",
    "counts": {
      "cases": 302,
      "algs": 418
    }
  },
  "subsets": {
    "TCP": {
      "name": "TCP — Triangle + Corner Permutation (Last Layer)",
      "notation": "cif",
      "notation_note": "The sheet's header says its algs are written in EIF notation, but machine verification (case layer-locality, the filled-slot criterion, recognition structure) shows every alg executes from the CIF hold — matching the community notation doc's description of the TCP set ('presents its algorithms in CIF orientation, then begins many algs with a puzzle rotation'). Verified 2026-07-10; see tools/test-engine.mjs.",
      "description": "Solves the last layer's three triples (corner + two triangles each) and the filled slot in one look, after everything else is done. 18 cases in three groups: Even (even triangle permutation), Odd (odd triangle permutation, needs a starting AUF — cases 7-10's listed algs INCLUDE the AUF; cases 11-12 are written post-AUF, so do the AUF first), and 2-Flip (the filled slot's triangle already matches, i.e. two triples are flipped in place).",
      "groups": [
        "Even",
        "Odd",
        "2-Flip"
      ],
      "sources": [
        "Sheet: Edd Dibley, 'Triangle + Corner Permutation (TCP) Cases and Solutions' (New_Notation_TCP_Full_Diansheng_DaYan) — https://docs.google.com/document/d/16KaLlxaUujgYbCgs-QNCbJbA1Tgc23VsbgMrOhl8gig",
        "[2] Ben Streeter, '[FTO] Introduction to TCP + My Algorithms' — https://youtu.be/iyDDCHQn-T8",
        "[3] Ben Streeter, '[FTO] My Odd TCP Algorithms!' — https://youtu.be/NLJbzBDkGzI",
        "[4] A.B. 'Tipster Tickster', 'All of my FTO TCP algorithms and fingertricks!' — https://youtu.be/ohwcpjqFWb0",
        "[5] A.B. 'Tipster Tickster', 'FTO Algorithms' spreadsheet, sheet 'Full l3t' — https://docs.google.com/spreadsheets/d/11N8tEu0S8aXDUHAsDVJsrh3Uyr6YGn1Asvse4zfAzus"
      ],
      "cases": [
        {"name":"TCP 1","group":"Even","recognition":"Clockwise corners and clockwise triangles.","moves":4,"algs":[{"alg":"B' R B R'"}]},
        {"name":"TCP 2","group":"Even","recognition":"Anticlockwise corners and anticlockwise triangles.","moves":4,"algs":[{"alg":"{U,BR} R B' R' B"}]},
        {"name":"TCP 3","group":"Even","recognition":"Solved corners, clockwise triangles.","moves":8,"algs":[{"alg":"{B,U} (U' R' D R') (U R D' R)"}]},
        {"name":"TCP 4","group":"Even","recognition":"Solved corners, anticlockwise triangles.","moves":8,"algs":[{"alg":"{B,BL} (U R D' R) (U' R' D R2)"}]},
        {"name":"TCP 5","group":"Even","recognition":"Clockwise corners, anticlockwise triangles.","moves":12,"algs":[{"alg":"{B,BL} (U R' U') (R' D' R U R' D) (R U' R)"}]},
        {"name":"TCP 6","group":"Even","recognition":"Anticlockwise corners, clockwise triangles.","moves":12,"algs":[{"alg":"{B,U} (U' R U) (R D R' U' R D') (R' U R')"}]},
        {"name":"TCP 7","group":"Odd","recognition":"Solved corners, clockwise AUF.","moves":9,"moves_note":"excl. AUF; the listed alg includes it","algs":[{"alg":"U {B,BL} (R D R' U) (R D' R U') R"}]},
        {"name":"TCP 8","group":"Odd","recognition":"Solved corners, anticlockwise AUF.","moves":9,"moves_note":"excl. AUF; the listed alg includes it","algs":[{"alg":"U' {B,U} (R' D' R U') (R' D R' U) R'"}]},
        {"name":"TCP 9","group":"Odd","recognition":"Clockwise corners, clockwise AUF.","moves":11,"moves_note":"excl. AUF; the listed alg includes it","algs":[{"alg":"U {B,BL} (R D R' U) (R D R U') (R' D R2)"}]},
        {"name":"TCP 10","group":"Odd","recognition":"Anticlockwise corners, anticlockwise AUF.","moves":11,"moves_note":"excl. AUF; the listed alg includes it","algs":[{"alg":"U' {B,U} (R' D' R U') (R' D' R' U) (R D' R)"}]},
        {"name":"TCP 11","group":"Odd","recognition":"Anticlockwise corners, clockwise AUF.","moves":10,"moves_note":"unlike cases 7-10, this text does NOT include the starting AUF — apply it first (machine-verified: the text solves the post-AUF state)","algs":[{"alg":"{L,U} U' D (R' U R) D' {L,D} (R' U R U')"}]},
        {"name":"TCP 12","group":"Odd","recognition":"Clockwise corners, anticlockwise AUF.","moves":10,"moves_note":"unlike cases 7-10, this text does NOT include the starting AUF — apply it first (machine-verified: the text solves the post-AUF state)","algs":[{"alg":"{R,BR} U D' (R U' R') D {BR,F} (R B' R' B)"}]},
        {"name":"TCP 13","group":"2-Flip","recognition":"Solved corners, solved triangles.","moves":8,"algs":[{"alg":"(R B' R' B) (R' L R L')"}]},
        {"name":"TCP 14","group":"2-Flip","recognition":"Clockwise corners, solved triangles.","moves":10,"algs":[{"alg":"{R,BR} (R' U' Rw' R U') (R U Rw R' U)"}]},
        {"name":"TCP 15","group":"2-Flip","recognition":"Anticlockwise corners, solved triangles.","moves":10,"algs":[{"alg":"{L,U} (R U Rw R' U) (R' U' Rw' R U')"}]},
        {"name":"TCP 16","group":"2-Flip","recognition":"Solved corners, 2-swap triangles.","moves":11,"algs":[{"alg":"{B,BR} (R' U' R D') (R U' R' D) (R' U' R)"}]},
        {"name":"TCP 17","group":"2-Flip","recognition":"Clockwise corners, 2-swap triangles.","moves":9,"algs":[{"alg":"{R,BR} (U Rw' U' R) (U Rw R U') R"}]},
        {"name":"TCP 18","group":"2-Flip","recognition":"Anticlockwise corners, 2-swap triangles.","moves":9,"algs":[{"alg":"{L,U} (U' Rw U R') (U' Rw' R' U) R'"}]}
      ]
    },
    "1L3T": {
      "name": "1L3T — One-Look Last 3 Triples",
      "notation": "cif",
      "notation_note": "zwegner's page dialect, all machine-verified: S/H are the sledge (R' L R L') and hedge (R B' R' B) triggers (S'/H' their inverses), [U]/[U'] are pre-AUF marks executed as the plain move, {X,Y} bracket rotations as in the community notation. Two source algs are transcription errors (they do not solve last-layer states) and are excluded: 6b.E.5's only alg (the case is therefore omitted) and 4b.O.4's fourth alg. Case 1.E.1 is the solved state. Some algs are marked as working-slot variants or as ending one AUF short — hover their note tag.",
      "description": "One-look last 3 triples: all 179 cases of the Bencisco last layer solved in a single look. Cases are sorted by OLP (where the top face’s stickers are), then triangle permutation (E = even, O = odd), then corner permutation. Set 6c is the TCP set. Sourced from zwegner’s page; algs by Aedan Bryant, with the 6c algs largely from Edd Dibley’s document.",
      "groups": [
        "OLP 1",
        "OLP 2",
        "OLP 3",
        "OLP 4a",
        "OLP 4b",
        "OLP 4c",
        "OLP 5",
        "OLP 6a",
        "OLP 6b",
        "OLP 6c",
        "OLP 7",
        "OLP 8"
      ],
      "sources": [
        "zwegner, '1L3T' — https://zwegner.github.io/cubing/fto/1l3t.html (snapshot: data/sources/1l3t-zwegner.html, fetched 2026-07-13)",
        "Aedan Bryant, original alg sheet — https://docs.google.com/spreadsheets/d/1ERlQ5R1m5UGBCi65WTi4IBVyIKj60oVWjOFknFA3Pcs",
        "Edd Dibley, TCP document (set 6c) — https://docs.google.com/document/d/16KaLlxaUujgYbCgs-QNCbJbA1Tgc23VsbgMrOhl8gig"
      ],
      "cases": [
        {"name":"1.E.2","group":"OLP 1","algs":[{"alg":"{L,F} R' U R' D' R U' R' D R'"}]},
        {"name":"1.E.3","group":"OLP 1","algs":[{"alg":"{L,F} R D' R U R' D R U' R"}]},
        {"name":"1.E.4","group":"OLP 1","algs":[{"alg":"{L,F} U' Rs' U' R' U Rs U' R U'"},{"alg":"{R,F} U' R U Rw' U' R U Rw' U' R U"}]},
        {"name":"1.E.5","group":"OLP 1","algs":[{"alg":"L R' L' R' B' R' B"}]},
        {"name":"1.E.6","group":"OLP 1","algs":[{"alg":"{B,U} R U' R' U' {U,BL} R D' R U' R' D R'"}]},
        {"name":"1.E.7","group":"OLP 1","algs":[{"alg":"{R,F} U R' U' Rw U R' U' Rw U R' U'"},{"alg":"{L,F} U R' U Rs' U' R U Rs U"}]},
        {"name":"1.E.8","group":"OLP 1","algs":[{"alg":"L' B L B {B,U} R' D R' U R D' R"}]},
        {"name":"1.E.9","group":"OLP 1","algs":[{"alg":"B' R B R L R L'"}]},
        {"name":"1.O.1","group":"OLP 1","algs":[{"alg":"{B,BR} Rw U R' U' Rs' U R U' R'"}]},
        {"name":"1.O.2","group":"OLP 1","algs":[{"alg":"BRw' U R' B L' B' L R U' BRw"},{"alg":"{BL,F} R' U B' S' B U' R"}]},
        {"name":"1.O.3","group":"OLP 1","algs":[{"alg":"BLw U' L H' L' U R'"}]},
        {"name":"2.E.1","group":"OLP 2","algs":[{"alg":"{R,D} D' R' U' H S U R D"}]},
        {"name":"2.E.2","group":"OLP 2","algs":[{"alg":"[U] S U S U S U S"}]},
        {"name":"2.E.3","group":"OLP 2","algs":[{"alg":"[U'] S' U' S' U' S' U' S'"}]},
        {"name":"2.E.4","group":"OLP 2","algs":[{"alg":"[U] S' U S U' S U S'"}]},
        {"name":"2.E.5","group":"OLP 2","algs":[{"alg":"R' U' R' L R L' U R L R' L' B' R B"}]},
        {"name":"2.E.6","group":"OLP 2","algs":[{"alg":"[U] B' BLw U S U S U L BLw'"},{"alg":"[U] S U S U S U H"}]},
        {"name":"2.E.7","group":"OLP 2","algs":[{"alg":"[U'] S U' S' U S' U' S"}]},
        {"name":"2.E.8","group":"OLP 2","algs":[{"alg":"BLw L' U' S' U' S' U' BLw' B"},{"alg":"[U'] B BRw' U' S' U' S' U' R' BRw","note":"as printed this ends one AUF short of the case — append U (machine-verified)"},{"alg":"H U' H U' H U' S","note":"as printed this ends one AUF short of the case — append U' (machine-verified)"},{"alg":"{U,BL} BR' R' U' R U R B' R' B U' R' U R BR"}]},
        {"name":"2.E.9","group":"OLP 2","algs":[{"alg":"L U L R' L' R U' L' R' L R B L' B'"}]},
        {"name":"2.O.1","group":"OLP 2","algs":[{"alg":"[U] {U,BR} Rw' L R L' Rw R' U S'"}]},
        {"name":"2.O.2","group":"OLP 2","algs":[{"alg":"[U'] BLw L' U H' U' BLw' B"},{"alg":"[U] {U,BL} H U' S U S","note":"as printed this ends one AUF short of the case — append U (machine-verified)"}]},
        {"name":"2.O.3","group":"OLP 2","algs":[{"alg":"B' BLw U H U' L BLw'"},{"alg":"[U'] S U H U' H","note":"as printed this ends one AUF short of the case — append U (machine-verified)"}]},
        {"name":"3.E.1","group":"OLP 3","algs":[{"alg":"[U] {L,F} R U R' U' Rw R' U R U' Rw'"}]},
        {"name":"3.E.2","group":"OLP 3","algs":[{"alg":"[U'] {U,BR} H U' S'"}]},
        {"name":"3.E.3","group":"OLP 3","algs":[{"alg":"[U] {U,BR} S U H'"}]},
        {"name":"3.E.4","group":"OLP 3","algs":[{"alg":"[U] H' U S'"}]},
        {"name":"3.E.5","group":"OLP 3","algs":[{"alg":"[U'] {B,U} U' R' D R' U R D' R U' R U R'"}]},
        {"name":"3.E.6","group":"OLP 3","algs":[{"alg":"[U'] {U,BR} S U' S"}]},
        {"name":"3.E.7","group":"OLP 3","algs":[{"alg":"[U'] {U,BR}S U' H"}]},
        {"name":"3.E.8","group":"OLP 3","algs":[{"alg":"[U] {U,BL} S' U S'"}]},
        {"name":"3.E.9","group":"OLP 3","algs":[{"alg":"[U] {L,U} R U' R' U R' D R' U' R D' R U"}]},
        {"name":"3.O.1","group":"OLP 3","algs":[{"alg":"[U] {R,U} U' R BR' U R' U' R BR' U R' U' R BR' U R'"}]},
        {"name":"3.O.2","group":"OLP 3","algs":[{"alg":"{B,U} U R BR' R' U' R U BR R' U'"}]},
        {"name":"3.O.3","group":"OLP 3","algs":[{"alg":"{R,D} R U R' U Rw BR Rw' U R U' R'"}]},
        {"name":"3.O.4","group":"OLP 3","algs":[{"alg":"[U] {R,U} U R Rw' U' R U R' Rw U' R'"}]},
        {"name":"3.O.5","group":"OLP 3","algs":[{"alg":"{U,BL} S U S' U S"}]},
        {"name":"3.O.6","group":"OLP 3","algs":[{"alg":"S U' L Rw' R L' R' L Rw L'"}]},
        {"name":"3.O.7","group":"OLP 3","algs":[{"alg":"[U'] {L,U} R U Rw' R U' R' U Rw R' U'"}]},
        {"name":"3.O.8","group":"OLP 3","algs":[{"alg":"[U] {B,BL} U Rw' U' R U R' Rw U' BR U R' U' R"}]},
        {"name":"3.O.9","group":"OLP 3","algs":[{"alg":"{U,BR} S' U' S U' S'"}]},
        {"name":"4a.E.1","group":"OLP 4a","algs":[{"alg":"[U'] {L,U} R U' BR Rw' R U R' U' Rw BR' R' U"},{"alg":"[U'] {B,BL} Rw' U R U' R' Rw BR Rw' R U R' U' Rw","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"},{"alg":"{F,BL} R' BR' R B' R' B R' L R L' BR R","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"},{"alg":"{U,BL} R U B R' L R' L' R B' R U' R'","note":"as printed this ends one AUF short of the case — append U' (machine-verified)"}]},
        {"name":"4a.E.2","group":"OLP 4a","algs":[{"alg":"[U] {B,L} Rw U' Rw' R BR R' Rw U Rw' R BR'"},{"alg":"H U' S U' S","note":"as printed this ends one AUF short of the case — append U (machine-verified)"}]},
        {"name":"4a.E.3","group":"OLP 4a","algs":[{"alg":"[U] {L,U} R' D' R U' R' D R U"},{"alg":"[U] {R,BR} U R D R' U' R D' R'"}]},
        {"name":"4a.E.4","group":"OLP 4a","algs":[{"alg":"{R,U} Rw' R U' R' D R' U R D' Rw"},{"alg":"{U,BR} S' U S' U S'","note":"as printed this ends one AUF short of the case — append U (machine-verified)"}]},
        {"name":"4a.E.5","group":"OLP 4a","algs":[{"alg":"[U] {BL,F} B R' U R' L R L' U' B' R"},{"alg":"[U'] L R' L' R U' R Rw' U' R B' R' B U Rw R'"}]},
        {"name":"4a.E.6","group":"OLP 4a","algs":[{"alg":"{U,BR} S' U' S' U' H'"},{"alg":"H U' S U' H"}]},
        {"name":"4a.E.7","group":"OLP 4a","algs":[{"alg":"[U'] {L,F} Rw D R' U R D' R U' Rw' R'"},{"alg":"H U' H U' S'","note":"as printed this ends one AUF short of the case — append U (machine-verified)"},{"alg":"S U' H' U' H'","note":"as printed this ends one AUF short of the case — append U (machine-verified)"}]},
        {"name":"4a.E.8","group":"OLP 4a","algs":[{"alg":"[U'] {U,BL} H U S U S"},{"alg":"H U S U H'","note":"as printed this ends one AUF short of the case — append U' (machine-verified)"},{"alg":"S U H' U S'","note":"as printed this ends one AUF short of the case — append U' (machine-verified)"},{"alg":"{L,F} U R D R' U' R D' R' BR U R' U' R"}]},
        {"name":"4a.E.9","group":"OLP 4a","algs":[{"alg":"[U] {F,BR} R' B U L R' L' R U' R B'"}]},
        {"name":"4a.O.1","group":"OLP 4a","algs":[{"alg":"R' U R B' R B R' L R' L' U' R"},{"alg":"R' U L R L' R B' R' B R' U' R"},{"alg":"{F,BL} B' Rw B' R' B R' L R L' R Rw' B"}]},
        {"name":"4a.O.2","group":"OLP 4a","algs":[{"alg":"[U] {U,BR} S' U H"}]},
        {"name":"4a.O.3","group":"OLP 4a","algs":[{"alg":"[U] {R,U} U' Rs U R U' Rw' U"},{"alg":"[U'] Rs' U' S' U Rs","note":"as printed this ends one AUF short of the case — append U' (machine-verified)"}]},
        {"name":"4a.O.4","group":"OLP 4a","algs":[{"alg":"[U] S U S'"}]},
        {"name":"4a.O.5","group":"OLP 4a","algs":[{"alg":"[U] {L,BL} U R' D R U R' D' R U"}]},
        {"name":"4a.O.6","group":"OLP 4a","algs":[{"alg":"[U'] {B,U} U' R BR' U R' U' R BR U R'"}]},
        {"name":"4a.O.7","group":"OLP 4a","algs":[{"alg":"[U] {R,BR} L R' U R D' R U' R' D L'"},{"alg":"[U] {L,U} BR' D' R U' R' D R' U R BR","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"},{"alg":"[U] {R,B} U' R' BR Rw' U' R U' Rw BR U"},{"alg":"{B,L} U Rw U Rw' B Rw' BR' Rw B' U'"}]},
        {"name":"4a.O.8","group":"OLP 4a","algs":[{"alg":"[U'] {R,U} R U' BR' R' U R U' BR R' U"}]},
        {"name":"4a.O.9","group":"OLP 4a","algs":[{"alg":"[U] {U,BL} H' U S"}]},
        {"name":"4b.E.1","group":"OLP 4b","algs":[{"alg":"[U] {L,U} U' R BR Rw' U R U' Rw R' BR' U R'"},{"alg":"R' U' L' R B' R B R' L R' U R","note":"as printed this ends one AUF short of the case — append U (machine-verified)"},{"alg":"D Rw R B' R' B R' L R L' Rw' D'","note":"as printed this ends one AUF short of the case — append U (machine-verified)"}]},
        {"name":"4b.E.2","group":"OLP 4b","algs":[{"alg":"[U'] {L,U} U' R' D' R U R' D R"}]},
        {"name":"4b.E.3","group":"OLP 4b","algs":[{"alg":"{U,BL} S U H U H"},{"alg":"[U'] {B,L} BR R' Rw U' Rw' R BR' R' Rw U Rw'","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"}]},
        {"name":"4b.E.4","group":"OLP 4b","algs":[{"alg":"[U] {R,U} Rw' D' R U' R' D R' U R Rw"}]},
        {"name":"4b.E.5","group":"OLP 4b","algs":[{"alg":"[U'] {U,BL} BLw L' U' H' U BLw' B"}]},
        {"name":"4b.E.6","group":"OLP 4b","algs":[{"alg":"[U] S U' H U' H"}]},
        {"name":"4b.E.7","group":"OLP 4b","algs":[{"alg":"{L,F} Rw R' U R D' R U' R' D Rw'"}]},
        {"name":"4b.E.8","group":"OLP 4b","algs":[{"alg":"{R,U} U' R U Rw' U' R' D R' U R D' Rw"}]},
        {"name":"4b.E.9","group":"OLP 4b","algs":[{"alg":"[U'] B' BLw U' H U L BLw'"}]},
        {"name":"4b.O.1","group":"OLP 4b","algs":[{"alg":"{U,BL} R U' R' L R' L' R B' R B U R'"}]},
        {"name":"4b.O.2","group":"OLP 4b","algs":[{"alg":"[U'] {L,F} U Rw' R U' R' U Rw U'"}]},
        {"name":"4b.O.3","group":"OLP 4b","algs":[{"alg":"[U'] {U,BR} H' U' S"}]},
        {"name":"4b.O.4","group":"OLP 4b","algs":[{"alg":"[U'] {B,BL} L' D' R U R' D R' U' R L"},{"alg":"[U'] L U R' D R U' R D' R' L'"},{"alg":"[U'] {B,D} U' Rw' BR' Rw B' Rw U Rw' B U"}],"moves_note":"the sheet lists a fourth alg here that does not solve a last-layer state (transcription error, machine-verified) — excluded; see data/sources/1l3t-zwegner.html"},
        {"name":"4b.O.5","group":"OLP 4b","algs":[{"alg":"[U'] S' U' H"}]},
        {"name":"4b.O.6","group":"OLP 4b","algs":[{"alg":"[U] {R,U} U' R BR U R' U' R BR' U R'"}]},
        {"name":"4b.O.7","group":"OLP 4b","algs":[{"alg":"[U'] S' U' S"}]},
        {"name":"4b.O.8","group":"OLP 4b","algs":[{"alg":"[U] {L,U} R U' BR R' U R U' BR' R' U"}]},
        {"name":"4b.O.9","group":"OLP 4b","algs":[{"alg":"[U'] {R,F} U' R D' R' U' R D R' U'"}]},
        {"name":"4c.E.1","group":"OLP 4c","algs":[{"alg":"[U] S' U H U' {U,BL} S'"}]},
        {"name":"4c.E.2","group":"OLP 4c","algs":[{"alg":"[U] {B,U} BR' R' U' R D R' U R D' BR"},{"alg":"[U] {BR,U} U' R' U' R D R' U R D' U"}]},
        {"name":"4c.E.3","group":"OLP 4c","algs":[{"alg":"[U'] {BL,F} U R U R' D' R U' R' U' D"},{"alg":"[U'] {F,U} BR R D R' U' R D' R' U BR'"}]},
        {"name":"4c.E.4","group":"OLP 4c","algs":[{"alg":"[U'] {B,U} R U' R' U R U' BR' R' U R U' BR R' U"},{"alg":"[U'] {B,U} U' R U R' U' R BR' R' U R U' BR R' U"},{"alg":"[U'] {R,U} U' R U R' U' R BR' U R' U' R BR U R'"},{"alg":"[U'] {R,U} R U' R' U R U' BR' U R' U' R BR U R'"}]},
        {"name":"4c.E.5","group":"OLP 4c","algs":[{"alg":"[U'] S U' S' U S"}]},
        {"name":"4c.E.6","group":"OLP 4c","algs":[{"alg":"[U'] Rw' L R L' U' B' R B R' U Rw R'"},{"alg":"[U] {F,U} R L' R B' R' B U L R' L' R U' L R'","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"},{"alg":"[U'] {L,U} R U' BR R' U R U' BR' Rw' R U R' U' Rw R' U"},{"alg":"[U] {U,BL} S U' S U S U S'"}]},
        {"name":"4c.E.7","group":"OLP 4c","algs":[{"alg":"[U] {R,U} R U' R' U R U' BR R' U R U' BR' R' U"},{"alg":"[U] {L,U} R U' R' U R U' BR U R' U' R BR' U R'"},{"alg":"[U] {L,U} U' R U R' U' R BR U R' U' R BR' U R'"},{"alg":"[U] {R,U} U' R U R' U' R BR R' U R U' BR' R' U"},{"alg":"[U] {R,U} R U' R' U R U' BR R' U R U' BR' R' U"}]},
        {"name":"4c.E.8","group":"OLP 4c","algs":[{"alg":"[U] {U,BL} Rw B' R' B U S' U' Rs'"}]},
        {"name":"4c.E.9","group":"OLP 4c","algs":[{"alg":"[U] S' U S U' S'"}]},
        {"name":"4c.O.1","group":"OLP 4c","algs":[{"alg":"[U'] H' U S U S"}]},
        {"name":"4c.O.2","group":"OLP 4c","algs":[{"alg":"[U'] {U,BR} BR' R U' S' U R' BR"},{"alg":"[U'] {R,BR} D' R BR' U R' U' R BR R' D"},{"alg":"[U] {L,BL} D R' BR U' R' U R BR' R D'","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"},{"alg":"[U] {L,F} U Rw' U' Rw R' U R U' Rw' U Rw U'","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"}]},
        {"name":"4c.O.3","group":"OLP 4c","algs":[{"alg":"[U] {U,BL} BL L' U S U' L BL'"},{"alg":"[U] {R,U} Rw U' BR R' U R U' BR' U Rw'"},{"alg":"{L,F} Rw' R BR' Rw' R U R' U' Rw BR Rw R'","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"}]},
        {"name":"4c.O.4","group":"OLP 4c","algs":[{"alg":"[U] {B,U} U' Rw' R' U R D' R U' R' D Rw U"},{"alg":"[U] {R,U} U' R U R' Rw U BR U' R' U R BR' U' Rw'"},{"alg":"[U] {L,F} Rw' R U' R' U Rw U BR R' U' R U BR' U'"},{"alg":"[U] {B,U} R U' R' U Rw U BR R' U' R U BR' U' Rw'"}]},
        {"name":"4c.O.5","group":"OLP 4c","algs":[{"alg":"{U,BL} Rs' U S' U' L R' L' Rw"},{"alg":"{U,BL} R Rw' U L R' L' R U' L R' L' Rw"},{"alg":"[U] {L,BL} U R' U R U Rw' D' U R' U' R D"}]},
        {"name":"4c.O.6","group":"OLP 4c","algs":[{"alg":"[U] {U,BR} S U' S' U' S'"}]},
        {"name":"4c.O.7","group":"OLP 4c","algs":[{"alg":"[U] Rs' L R' L' Rw U' Rw' L R L' Rs"},{"alg":"[U] {L,F} Rw' R U R' U' Rw BR' Rw' U R U' Rw R'"},{"alg":"{B,U} Rw R' U' R BR' R' U R U' BR U Rw'"}]},
        {"name":"4c.O.8","group":"OLP 4c","algs":[{"alg":"[U'] {U,BL} S' U S U S"}]},
        {"name":"4c.O.9","group":"OLP 4c","algs":[{"alg":"Rs U' H' U B' R B Rw'"},{"alg":"Rw R' U' B' R B R' U B' R B Rw'"}]},
        {"name":"5.E.1","group":"OLP 5","algs":[{"alg":"[U] H U H U' S U' S"}]},
        {"name":"5.E.2","group":"OLP 5","algs":[{"alg":"[U] {U,BL} S U S U H"}]},
        {"name":"5.E.3","group":"OLP 5","algs":[{"alg":"[U'] H U' H U' S"}]},
        {"name":"5.E.4","group":"OLP 5","algs":[{"alg":"[U'] {U,BR} S' U' S' U' S'"}]},
        {"name":"5.E.5","group":"OLP 5","algs":[{"alg":"[U] {F,U} U' BLw' U' R L R' L' U BLw U"}]},
        {"name":"5.E.6","group":"OLP 5","algs":[{"alg":"[U] {U,BL} S U H U S'"}]},
        {"name":"5.E.7","group":"OLP 5","algs":[{"alg":"[U] {U,BL} S U S U S"}]},
        {"name":"5.E.8","group":"OLP 5","algs":[{"alg":"[U] S' U Rw R' L R' L' Rw' R'"}]},
        {"name":"5.E.9","group":"OLP 5","algs":[{"alg":"[U] {BR,U} U' BLw' U' L R L' R' U BLw U"}]},
        {"name":"5.O.1","group":"OLP 5","algs":[{"alg":"S' U' H U S'"}]},
        {"name":"5.O.2","group":"OLP 5","algs":[{"alg":"[U] {U,BL} BR' R' U' Rw L R' L' R Rw' U R BR"}]},
        {"name":"5.O.3","group":"OLP 5","algs":[{"alg":"S U Rw' R B' R B Rw R"}]},
        {"name":"5.O.4","group":"OLP 5","algs":[{"alg":"[U'] BLw L' U B L' B' L U' BLw' B"}]},
        {"name":"5.O.5","group":"OLP 5","algs":[{"alg":"{U,BL} B' BLw U S' U' BLw' B"}]},
        {"name":"5.O.6","group":"OLP 5","algs":[{"alg":"[U] {U,BR} S' U' S' U S"}]},
        {"name":"5.O.7","group":"OLP 5","algs":[{"alg":"BLw' B U S U' BLw L'"}]},
        {"name":"5.O.8","group":"OLP 5","algs":[{"alg":"S' U' S U S"}]},
        {"name":"5.O.9","group":"OLP 5","algs":[{"alg":"[U'] {U,BR} B' BLw U S U' BLw' B"}]},
        {"name":"6a.E.1","group":"OLP 6a","algs":[{"alg":"[U'] {L,U} U' R U R D' R U' R' D R U"}]},
        {"name":"6a.E.2","group":"OLP 6a","algs":[{"alg":"[U] {B,U} R U BR R BR' U BR R' BR' R' U"}]},
        {"name":"6a.E.3","group":"OLP 6a","algs":[{"alg":"[U] {U,BR} H U' S' U S"},{"alg":"[U'] {L,BL} U' D R U R Rw' U R' U' R' Rw D'","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"}]},
        {"name":"6a.E.4","group":"OLP 6a","algs":[{"alg":"{B,U} U' R BR U R' F' R U' BR U R'"}]},
        {"name":"6a.E.5","group":"OLP 6a","algs":[{"alg":"[U] {U,BL} L BL' U S' U' BL L'"}]},
        {"name":"6a.E.6","group":"OLP 6a","algs":[{"alg":"[U'] {B,U} R U' BR R' U R U' BR' U R'"},{"alg":"[U] {B,U} U' R BR' R' U R U' BR R' U","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"}]},
        {"name":"6a.E.7","group":"OLP 6a","algs":[{"alg":"[U] L BLw' U' S' U B' R"},{"alg":"[U'] BLw L' U H U' R' L","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"}]},
        {"name":"6a.E.8","group":"OLP 6a","algs":[{"alg":"[U'] {B,L} U' R' BR Rw' U' R' U' Rw BR R' U"}]},
        {"name":"6a.E.9","group":"OLP 6a","algs":[{"alg":"[U'] {U,BR} R B' BR' R' BR B R' U R"}]},
        {"name":"6a.O.1","group":"OLP 6a","algs":[{"alg":"{R,U} U' R BR' R' U R U' BR U R'"}]},
        {"name":"6a.O.2","group":"OLP 6a","algs":[{"alg":"[U'] {BL,BR} B' R' U' L' R' L R U R B"},{"alg":"[U'] {B,L} U' Rw R' BR U BR' U' Rw' R U"},{"alg":"[U'] {B,U} R U' R' U' Rw' U' R' U' R U' Rw U'"}]},
        {"name":"6a.O.3","group":"OLP 6a","algs":[{"alg":"[U'] S U S"}]},
        {"name":"6a.O.4","group":"OLP 6a","algs":[{"alg":"[U'] {U,BR} S U S U' S"},{"alg":"[U'] {L,U} L' U L Rw' U' R' U' R U' Rw U'"}]},
        {"name":"6a.O.5","group":"OLP 6a","algs":[{"alg":"[U'] H U S'"}]},
        {"name":"6a.O.6","group":"OLP 6a","algs":[{"alg":"[U'] {U,BL} Rs L R' L' Rw2 R'"}]},
        {"name":"6a.O.7","group":"OLP 6a","algs":[{"alg":"[U'] S U H"},{"alg":"[U'] {U,BR} S' U H'"}]},
        {"name":"6a.O.8","group":"OLP 6a","algs":[{"alg":"{U,BL} L BLw' U' S' U BLw L'"}]},
        {"name":"6a.O.9","group":"OLP 6a","algs":[{"alg":"[U'] {BR,U} U R U' R' L' R L U R' U'"}]},
        {"name":"6b.E.1","group":"OLP 6b","algs":[{"alg":"[U] {R,BR} U R' U' R' D R' U R D' R' U'"}]},
        {"name":"6b.E.2","group":"OLP 6b","algs":[{"alg":"[U'] H' U S' U' S"},{"alg":"{R,F} D' U R' U' R' Rw U' R U R Rw' D","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"},{"alg":"{R,U} U Rw' U BR' R' U R U' BR U' Rw U'","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"}]},
        {"name":"6b.E.3","group":"OLP 6b","algs":[{"alg":"{BR,U} Rw' B R' U R' L' R L U' R B' Rw"}]},
        {"name":"6b.E.4","group":"OLP 6b","algs":[{"alg":"[U] {U,BL} BLw' B U' S U BLw L'"}]},
        {"name":"6b.E.6","group":"OLP 6b","algs":[{"alg":"[U] {BL,U} U' R' L' U S' U' L R U"}]},
        {"name":"6b.E.7","group":"OLP 6b","algs":[{"alg":"{L,U} R U' BR' R' U F U' R BR' R' U"}]},
        {"name":"6b.E.8","group":"OLP 6b","algs":[{"alg":"[U] {L,U} U' R BR' U R' U' R BR R' U"}]},
        {"name":"6b.E.9","group":"OLP 6b","algs":[{"alg":"[U'] {U,BR} R' BR U' S U BR' R"}]},
        {"name":"6b.O.1","group":"OLP 6b","algs":[{"alg":"{U,BL} BLw L' U S' U' BLw' B"}]},
        {"name":"6b.O.2","group":"OLP 6b","algs":[{"alg":"[U] S' U' S'"}]},
        {"name":"6b.O.3","group":"OLP 6b","algs":[{"alg":"[U] {BR,F} L R U B R B' R' U' R' L'"},{"alg":"[U] {L,F} U R' U' R BR' U R D' R U' R' D R'","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"}]},
        {"name":"6b.O.4","group":"OLP 6b","algs":[{"alg":"{U,BR} H' U' S'"},{"alg":"{U,BL} H U' S"}]},
        {"name":"6b.O.5","group":"OLP 6b","algs":[{"alg":"[U] {BL,F} U' R' U R B R' B' U' R U"}]},
        {"name":"6b.O.6","group":"OLP 6b","algs":[{"alg":"B' BLw U H' U' BLw' B"}]},
        {"name":"6b.O.7","group":"OLP 6b","algs":[{"alg":"[U] {U,BL} S' U' S' U S'"}]},
        {"name":"6b.O.8","group":"OLP 6b","algs":[{"alg":"[U] {B,U} Rw' R U' R U Rw R2'"}]},
        {"name":"6b.O.9","group":"OLP 6b","algs":[{"alg":"[U] {U,BL} S U' H'"}]},
        {"name":"6c.E.1","group":"OLP 6c","algs":[{"alg":"H S"}]},
        {"name":"6c.E.2","group":"OLP 6c","algs":[{"alg":"{R,BR} R' U' Rw' R U' R U Rw R' U"}]},
        {"name":"6c.E.3","group":"OLP 6c","algs":[{"alg":"{L,U} R U Rw R' U R' U' Rw' R U'"}]},
        {"name":"6c.E.4","group":"OLP 6c","algs":[{"alg":"{B,U} U' R' D R' U R D' R"}]},
        {"name":"6c.E.5","group":"OLP 6c","algs":[{"alg":"H'"}]},
        {"name":"6c.E.6","group":"OLP 6c","algs":[{"alg":"{B,U} U' R U R D R' U' R D' R' U R'"}]},
        {"name":"6c.E.7","group":"OLP 6c","algs":[{"alg":"{B,BL} U R D' R U' R' D R'"}]},
        {"name":"6c.E.8","group":"OLP 6c","algs":[{"alg":"{B,BL} U R' U' R' D' R U R' D R U' R"}]},
        {"name":"6c.E.9","group":"OLP 6c","algs":[{"alg":"{U,BL} S'"}]},
        {"name":"6c.O.1","group":"OLP 6c","algs":[{"alg":"{B,BR} R' U' R D' R U' R' D R' U' R"}]},
        {"name":"6c.O.2","group":"OLP 6c","algs":[{"alg":"{R,BR} U Rw' U' R U Rw R2' U' R"}]},
        {"name":"6c.O.3","group":"OLP 6c","algs":[{"alg":"{L,U} U' Rw U R' U' Rw' R' U R'"}]},
        {"name":"6c.O.4","group":"OLP 6c","algs":[{"alg":"[U] {B,BL} R D R' U R D' R U' R"}]},
        {"name":"6c.O.5","group":"OLP 6c","algs":[{"alg":"[U] {B,BL} R D R' U R D R U' R' D R2"}]},
        {"name":"6c.O.6","group":"OLP 6c","algs":[{"alg":"[U] L BLw' U' S U BLw L'"},{"alg":"[U] R U R' L R L' U' R B' R B"},{"alg":"{L,U} U' D R' U R D' {L,D} R' U R U'","note":"working-slot variant: solves this case with the unsolved triangles parked on different faces — machine-verified against its own state, not the pictured one"}]},
        {"name":"6c.O.7","group":"OLP 6c","algs":[{"alg":"[U'] {B,U} R' D' R U' R' D R2 U R'"}]},
        {"name":"6c.O.8","group":"OLP 6c","algs":[{"alg":"[U'] {U,BL} L BLw' U S' U' BLw L'"},{"alg":"[U'] {U,BL} R' U' R B' R' B U R' L R' L'"},{"alg":"{R,BR} U D' R U' R' D {BR,F} R B' R' B","note":"as printed this ends one AUF short of the case — append U' (machine-verified)"}]},
        {"name":"6c.O.9","group":"OLP 6c","algs":[{"alg":"[U'] {B,U} R' D' R U' R' D' R' U R D' R"}]},
        {"name":"7.E.1","group":"OLP 7","algs":[{"alg":"S U S U S' U' H"}]},
        {"name":"7.E.2","group":"OLP 7","algs":[{"alg":"[U'] S' U' S' U' S U S'"}]},
        {"name":"7.E.3","group":"OLP 7","algs":[{"alg":"[U] S U S U S' U' S"}]},
        {"name":"7.O.1","group":"OLP 7","algs":[{"alg":"H' U S U' S' U' S'"}]},
        {"name":"7.O.2","group":"OLP 7","algs":[{"alg":"[U'] S' U S U' S' U' S'"}]},
        {"name":"7.O.3","group":"OLP 7","algs":[{"alg":"[U] S U' S' U S U S"}]},
        {"name":"8.E.1","group":"OLP 8","algs":[{"alg":"[U'] S' U H U H"}]},
        {"name":"8.E.2","group":"OLP 8","algs":[{"alg":"{U,BL} S' U' S U' S"}]},
        {"name":"8.E.3","group":"OLP 8","algs":[{"alg":"{U,BR} S U S' U S'"}]},
        {"name":"8.O.1","group":"OLP 8","algs":[{"alg":"[U'] {U,BL} S' U S' U H"}]},
        {"name":"8.O.2","group":"OLP 8","algs":[{"alg":"{U,BL} S U' S U' S'"}]},
        {"name":"8.O.3","group":"OLP 8","algs":[{"alg":"{U,BR} S' U S' U S"}]}
      ]
    },
    "LBT": {
      "name": "LBT — Last Bottom Triple (Algorithmic)",
      "notation": "cif",
      "auf": false,
      "notation_note": "zwegner's page dialect is plain Streeter notation (Uw/BLw/BRw wides, Us slices), all machine-verified. The page's Uo/Uo' rotation tokens are respelled here as {X,Y} re-orientation brackets ({U,BR} = Uo, {U,BL} = Uo') — the site's rotation convention; each respelling is machine-verified move-for-move identical to the page's text. 21 algs are written with a leading Uw/Us setup whose restore the page leaves implicit — as printed they end one wide/slice turn short of solved, and each carries a note with the machine-verified closing token (hover the tag). Diagrams show the exact state the first alg solves; the whole last layer is junk at this step, so top-layer content is arbitrary. Trainer scrambles reproduce each alg's exact state, with AUF randomization off (a U pre-turn would change the case).",
      "description": "Algorithmic LBT: the Bencisco method’s last bottom triple (the corner and two triangles of the bottom-left slot, between the F and BL faces) solved in one look no matter where the pieces are. 95 cases plus the already-solved case (the page’s case 21, omitted here), in six sections by corner location, subdivided into groups of four: a case, its mirror, and the same two with the corner flipped. Case numbers match zwegner’s page.",
      "groups": [
        "S1 corner in slot",
        "S2 one solved",
        "S3 one in wrong slot",
        "S4 one in middle",
        "S5 all on top",
        "S6 both in slot"
      ],
      "sources": [
        "zwegner, 'Algorithmic LBT' — https://zwegner.github.io/cubing/fto/lbt-algs.html (snapshot: data/sources/lbt-zwegner.html, fetched 2026-07-13)",
        "360cubed — the four keyhole cases (LBT 1, 2, 5, 6)",
        "Ben Streeter — the 'trapped triangles' cases (LBT 33, 34, 37, 38) and the traditional flipping-alg cases"
      ],
      "cases": [
        {"name":"LBT 1","group":"S1 corner in slot","recognition":"Corner in slot — one solved, one on top. Keyhole from top.","algs":[{"alg":"BL R' L' R L BL'"}]},
        {"name":"LBT 2","group":"S1 corner in slot","recognition":"Corner in slot — one solved, one on top. Keyhole from top.","algs":[{"alg":"{U,BL} BR' L R L' R' BR"},{"alg":"L BL' R' L R L' BL L'"}]},
        {"name":"LBT 3","group":"S1 corner in slot","recognition":"Corner in slot — one solved, one on top. Join corner with tri on top, 2-flip, return.","algs":[{"alg":"F R' L R L' R B' R' B F'"}]},
        {"name":"LBT 4","group":"S1 corner in slot","recognition":"Corner in slot — one solved, one on top. Join corner with tri on top, 2-flip, return.","algs":[{"alg":"BL' R B' R' B R' L R L' BL"}]},
        {"name":"LBT 5","group":"S1 corner in slot","recognition":"Corner in slot — one solved, one in middle. Keyhole from middle.","algs":[{"alg":"Uw' BL L' R' L R BL'","note":"the leading Uw' is a setup move the page leaves unrestored — as printed this ends one Uw short of solved; append Uw (machine-verified)","closing":"Uw"},{"alg":"BL L' R B' R' B L BL'"},{"alg":"Uw L R' L' BL L' R L BL'","note":"the leading Uw is a setup move the page leaves unrestored — as printed this ends one Uw' short of solved; append Uw' (machine-verified)","closing":"Uw'"}]},
        {"name":"LBT 6","group":"S1 corner in slot","recognition":"Corner in slot — one solved, one in middle. Keyhole from middle.","algs":[{"alg":"{U,BL} Uw BR' R L R' L' BR","note":"the leading Uw is a setup move the page leaves unrestored — as printed this ends one Uw' short of solved; append Uw' (machine-verified)","closing":"Uw'"},{"alg":"L BL' B' R B R' BL L'"},{"alg":"Uw L BL' R B' R' B BL L'","note":"the leading Uw is a setup move the page leaves unrestored — as printed this ends one Uw' short of solved; append Uw' (machine-verified)","closing":"Uw'"},{"alg":"Uw' R' L BL' L R L' BL L'","note":"the leading Uw' is a setup move the page leaves unrestored — as printed this ends one Uw short of solved; append Uw (machine-verified)","closing":"Uw"},{"alg":"Uw' L' U R' L' R L U' L","note":"the leading Uw' is a setup move the page leaves unrestored — as printed this ends one Uw short of solved; append Uw (machine-verified)","closing":"Uw"}]},
        {"name":"LBT 7","group":"S1 corner in slot","recognition":"Corner in slot — one solved, one in middle. Both algs are the same, just notated differently for different execution styles. First alg is a bit easier but worse for lookahead.","algs":[{"alg":"BLw' U' R B' R' B U B' BLw L"},{"alg":"R' F' R L' R' L F L' R L"}]},
        {"name":"LBT 8","group":"S1 corner in slot","recognition":"Corner in slot — one solved, one in middle. Ditto notes from case 7.","algs":[{"alg":"{U,BL} BRw U L' B L B' U' B BRw' R'"},{"alg":"{U,BL} L F L' R L R' F' R L' R'"}]},
        {"name":"LBT 9","group":"S1 corner in slot","recognition":"Corner in slot — one on top, one in middle.","algs":[{"alg":"L R' L R U' B' R B R' U L"}]},
        {"name":"LBT 10","group":"S1 corner in slot","recognition":"Corner in slot — one on top, one in middle.","algs":[{"alg":"U R' L' R U R' L R L' U' L"}]},
        {"name":"LBT 11","group":"S1 corner in slot","recognition":"Corner in slot — one on top, one in middle.","algs":[{"alg":"Us L U R' L' R L U' L R' L R","note":"the leading Us is a setup move the page leaves unrestored — as printed this ends one Us' short of solved; append Us' (machine-verified)","closing":"Us'"}]},
        {"name":"LBT 12","group":"S1 corner in slot","recognition":"Corner in slot — one on top, one in middle.","algs":[{"alg":"R' L' R L' U R B' R' B U' L'"}]},
        {"name":"LBT 13","group":"S1 corner in slot","recognition":"Corner in slot — one in wrong slot, one on top. The first alg is the same as 22 but with the R at the end. Both algs are kinda nice, the ones with D moves are easiest to do using wide moves to put the D layer on top, though that's bad for lookahead.","algs":[{"alg":"F' L' R U' R' U L R' F R"},{"alg":"{U,BL} F BL R D R' D' BL' F'"}]},
        {"name":"LBT 14","group":"S1 corner in slot","recognition":"Corner in slot — one in wrong slot, one on top. Same algs but mirrored from case 13, I don't use the same alg for each case.","algs":[{"alg":"F' BR' L' D' L D BR F"},{"alg":"R F U L' R' L R U' F' R'"}]},
        {"name":"LBT 15","group":"S1 corner in slot","recognition":"Corner in slot — one in wrong slot, one on top.","algs":[{"alg":"L' R' L R U' L' R' L R"}]},
        {"name":"LBT 16","group":"S1 corner in slot","recognition":"Corner in slot — one in wrong slot, one on top.","algs":[{"alg":"BL' L R' L' BL L' R L"}]},
        {"name":"LBT 17","group":"S1 corner in slot","recognition":"Corner in slot — one in wrong slot, one in middle.","algs":[{"alg":"R' L' R U L' B L B' U' L"}]},
        {"name":"LBT 18","group":"S1 corner in slot","recognition":"Corner in slot — one in wrong slot, one in middle.","algs":[{"alg":"{U,BL} L R L' U' R B' R' B U R'"}]},
        {"name":"LBT 19","group":"S1 corner in slot","recognition":"Corner in slot — one in wrong slot, one in middle. The D moves are a bit awkward to perform on current hardware, so you can do this alg by rotating to put the R face on top and D face on the right.","algs":[{"alg":"R D R' U R' D' R"}]},
        {"name":"LBT 20","group":"S1 corner in slot","recognition":"Corner in slot — one in wrong slot, one in middle. Ditto notes for case 20, but mirrored.","algs":[{"alg":"{U,BL} L' D' L U' L D L'"}]},
        {"name":"LBT 22","group":"S1 corner in slot","recognition":"Corner in slot — both in slot.","algs":[{"alg":"R F' L' R U' R' U L R' F"}]},
        {"name":"LBT 23","group":"S1 corner in slot","recognition":"Corner in slot — both in slot.","algs":[{"alg":"BL' R B' R' B U B' R B R' U' BL"}]},
        {"name":"LBT 24","group":"S1 corner in slot","recognition":"Corner in slot — both in slot.","algs":[{"alg":"R' L' R L' B L' B'"}]},
        {"name":"LBT 25","group":"S1 corner in slot","recognition":"Corner in slot — both on top.","algs":[{"alg":"L R' L R U' B' U L U' B"}]},
        {"name":"LBT 26","group":"S1 corner in slot","recognition":"Corner in slot — both on top.","algs":[{"alg":"R' L' F' L' R L R' F R L"}]},
        {"name":"LBT 27","group":"S1 corner in slot","recognition":"Corner in slot — both on top.","algs":[{"alg":"R' L' R L' U L' R' L R U' L'"}]},
        {"name":"LBT 28","group":"S1 corner in slot","recognition":"Corner in slot — both on top.","algs":[{"alg":"U' L' R' L F' L R L' R' F R"}]},
        {"name":"LBT 29","group":"S1 corner in slot","recognition":"Corner in slot — both in middle.","algs":[{"alg":"L BL' B' BL L R' L' R BL' B BL L'"}]},
        {"name":"LBT 30","group":"S1 corner in slot","recognition":"Corner in slot — both in middle.","algs":[{"alg":"R' L' R L U' F R B' R' F' B"}]},
        {"name":"LBT 31","group":"S1 corner in slot","recognition":"Corner in slot — both in middle.","algs":[{"alg":"R' F' R' B' R' B R' F L' R L"}]},
        {"name":"LBT 32","group":"S1 corner in slot","recognition":"Corner in slot — both in middle.","algs":[{"alg":"Uw' L U L' B L' B' R' L' R U' L'","note":"the leading Uw' is a setup move the page leaves unrestored — as printed this ends one Uw short of solved; append Uw (machine-verified)","closing":"Uw"}]},
        {"name":"LBT 33","group":"S2 one solved","recognition":"One solved, corner on top — pair on top.","algs":[{"alg":"U' F R' L R L' F'"}]},
        {"name":"LBT 34","group":"S2 one solved","recognition":"One solved, corner on top — pair on top.","algs":[{"alg":"U BL' R B' R' B BL"}]},
        {"name":"LBT 35","group":"S2 one solved","recognition":"One solved, corner on top — pair on top.","algs":[{"alg":"L' U' R' L R L' U R' L R"}]},
        {"name":"LBT 36","group":"S2 one solved","recognition":"One solved, corner on top — pair on top.","algs":[{"alg":"{U,BL} R U L R' L' R U' L R' L'"}]},
        {"name":"LBT 37","group":"S2 one solved","recognition":"One solved, corner on top — pair in middle.","algs":[{"alg":"R B' R' F R B R' F'"},{"alg":"Uw F R B' R' B F'","note":"the leading Uw is a setup move the page leaves unrestored — as printed this ends one Uw' short of solved; append Uw' (machine-verified)","closing":"Uw'"},{"alg":"Uw' B' R F' R' B R F R'","note":"the leading Uw' is a setup move the page leaves unrestored — as printed this ends one Uw short of solved; append Uw (machine-verified)","closing":"Uw"}]},
        {"name":"LBT 38","group":"S2 one solved","recognition":"One solved, corner on top — pair in middle.","algs":[{"alg":"L R' L' BL' L R L' BL"},{"alg":"Uw BL' L R' L' R BL","note":"the leading Uw is a setup move the page leaves unrestored — as printed this ends one Uw' short of solved; append Uw' (machine-verified)","closing":"Uw'"},{"alg":"Uw' BL' B' R B R' BL","note":"the leading Uw' is a setup move the page leaves unrestored — as printed this ends one Uw short of solved; append Uw (machine-verified)","closing":"Uw"}]},
        {"name":"LBT 39","group":"S2 one solved","recognition":"One solved, corner on top — pair in middle.","algs":[{"alg":"Uw F U R B' R' B U' F'","note":"the leading Uw is a setup move the page leaves unrestored — as printed this ends one Uw' short of solved; append Uw' (machine-verified)","closing":"Uw'"}]},
        {"name":"LBT 40","group":"S2 one solved","recognition":"One solved, corner on top — pair in middle.","algs":[{"alg":"Uw' BL' U B' R B R' U' BL","note":"the leading Uw' is a setup move the page leaves unrestored — as printed this ends one Uw short of solved; append Uw (machine-verified)","closing":"Uw"}]},
        {"name":"LBT 41","group":"S2 one solved","recognition":"One solved, corner on top — triangle on top above opposite slot.","algs":[{"alg":"U F U' L R' L' R U F'"}]},
        {"name":"LBT 42","group":"S2 one solved","recognition":"One solved, corner on top — triangle on top above opposite slot.","algs":[{"alg":"U BL' U R B' R' B U' BL"}]},
        {"name":"LBT 43","group":"S2 one solved","recognition":"One solved, corner on top — triangle on top above opposite slot.","algs":[{"alg":"{U,BL} U' R' U' R L R' L' U R"}]},
        {"name":"LBT 44","group":"S2 one solved","recognition":"One solved, corner on top — triangle on top above opposite slot.","algs":[{"alg":"U L U L' R' L R U' L'"}]},
        {"name":"LBT 45","group":"S2 one solved","recognition":"One solved, corner on top — triangle on top in back.","algs":[{"alg":"{U,BL} U BR U L R' L' R U' BR'"}]},
        {"name":"LBT 46","group":"S2 one solved","recognition":"One solved, corner on top — triangle on top in back.","algs":[{"alg":"U' BL' U' R' L R L' U BL"}]},
        {"name":"LBT 47","group":"S2 one solved","recognition":"One solved, corner on top — triangle on top in back.","algs":[{"alg":"{U,BL} U BR U R B' R' B U' BR'"}]},
        {"name":"LBT 48","group":"S2 one solved","recognition":"One solved, corner on top — triangle on top in back.","algs":[{"alg":"U BL' U' R B' R' B U BL"}]},
        {"name":"LBT 49","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — pair on top.","algs":[{"alg":"U' L' U' R' L R L' U L"}]},
        {"name":"LBT 50","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — pair on top.","algs":[{"alg":"{U,BL} U R U L R' L' R U' R'"}]},
        {"name":"LBT 51","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — pair on top.","algs":[{"alg":"U L U B' R B R' U' L'"}]},
        {"name":"LBT 52","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — pair on top.","algs":[{"alg":"U' L' U' R B' R' B U L"}]},
        {"name":"LBT 53","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — pair in middle.","algs":[{"alg":"L' U L R' L' R U' L"}]},
        {"name":"LBT 54","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — pair in middle.","algs":[{"alg":"{U,BL} R U' R' L R L' U R'"}]},
        {"name":"LBT 55","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — pair in middle.","algs":[{"alg":"R' L R U B' R B R' U' L'"}]},
        {"name":"LBT 56","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — pair in middle.","algs":[{"alg":"{U,BL} L R' L' U' B L' B' L U R"},{"alg":"R B' R F L' R L R' F' R B"}]},
        {"name":"LBT 57","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — triangle on top above opposite slot.","algs":[{"alg":"{U,BL} B' R B U R' L R L' U' R'"},{"alg":"L R' L' F R L' R' L F' R"}]},
        {"name":"LBT 58","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — triangle on top above opposite slot.","algs":[{"alg":"R L U' R' L R L' U L' R'"}]},
        {"name":"LBT 59","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — triangle on top above opposite slot.","algs":[{"alg":"{U,BL} U R U R' L R L' U' R'"}]},
        {"name":"LBT 60","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — triangle on top above opposite slot.","algs":[{"alg":"U L U R B' R' B U' L'"}]},
        {"name":"LBT 61","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — triangle on top in back.","algs":[{"alg":"{U,BL} U R' L F R F' R L' U' R'"}]},
        {"name":"LBT 62","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — triangle on top in back.","algs":[{"alg":"U' L R' F' L' F L' R U L"}]},
        {"name":"LBT 63","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — triangle on top in back.","algs":[{"alg":"{U,BL} U R U R L R' L' U' R'"}]},
        {"name":"LBT 64","group":"S3 one in wrong slot","recognition":"One in wrong slot, corner on top — triangle on top in back.","algs":[{"alg":"U' L' U' L' R' L R U L"}]},
        {"name":"LBT 65","group":"S4 one in middle","recognition":"One in middle, corner on top — pair on top.","algs":[{"alg":"Us' R' L' R L","note":"the leading Us' is a setup move the page leaves unrestored — as printed this ends one Us short of solved; append Us (machine-verified)","closing":"Us"},{"alg":"{U,BL} U L' D' L' D L'"}]},
        {"name":"LBT 66","group":"S4 one in middle","recognition":"One in middle, corner on top — pair on top.","algs":[{"alg":"{U,BL} Us L R L' R'","note":"the leading Us is a setup move the page leaves unrestored — as printed this ends one Us' short of solved; append Us' (machine-verified)","closing":"Us'"},{"alg":"Us L R' L R L","note":"the leading Us is a setup move the page leaves unrestored — as printed this ends one Us' short of solved; append Us' (machine-verified)","closing":"Us'"},{"alg":"U' R D R D' R"}]},
        {"name":"LBT 67","group":"S4 one in middle","recognition":"One in middle, corner on top — pair on top.","algs":[{"alg":"Uw L U' B' R B R' U L'","note":"the leading Uw is a setup move the page leaves unrestored — as printed this ends one Uw' short of solved; append Uw' (machine-verified)","closing":"Uw'"}]},
        {"name":"LBT 68","group":"S4 one in middle","recognition":"One in middle, corner on top — pair on top.","algs":[{"alg":"Uw' L' U R B' R' B U' L","note":"the leading Uw' is a setup move the page leaves unrestored — as printed this ends one Uw short of solved; append Uw (machine-verified)","closing":"Uw"}]},
        {"name":"LBT 69","group":"S4 one in middle","recognition":"One in middle, corner on top — pair in middle.","algs":[{"alg":"R B' R' B U R' L' R L"}]},
        {"name":"LBT 70","group":"S4 one in middle","recognition":"One in middle, corner on top — pair in middle.","algs":[{"alg":"{U,BL} L R' L' R U' R L R' L'"}]},
        {"name":"LBT 71","group":"S4 one in middle","recognition":"One in middle, corner on top — pair in middle.","algs":[{"alg":"{U,BL} U L R' L' R U' R' B' R B"},{"alg":"R' L R U' B' R B R' U L'"}]},
        {"name":"LBT 72","group":"S4 one in middle","recognition":"One in middle, corner on top — pair in middle.","algs":[{"alg":"R' L R U L R' L' R U' L'"}]},
        {"name":"LBT 73","group":"S4 one in middle","recognition":"One in middle, corner on top — triangle on top above opposite slot.","algs":[{"alg":"U L U R' L R L' U' L'"}]},
        {"name":"LBT 74","group":"S4 one in middle","recognition":"One in middle, corner on top — triangle on top above opposite slot.","algs":[{"alg":"{U,BL} U' R' U' L R' L' R U R"}]},
        {"name":"LBT 75","group":"S4 one in middle","recognition":"One in middle, corner on top — triangle on top above opposite slot.","algs":[{"alg":"{U,BL} Uw U R' U' R' L R L' U R","note":"the leading Uw is a setup move the page leaves unrestored — as printed this ends one Uw' short of solved; append Uw' (machine-verified)","closing":"Uw'"}]},
        {"name":"LBT 76","group":"S4 one in middle","recognition":"One in middle, corner on top — triangle on top above opposite slot.","algs":[{"alg":"Uw' U' L U L R' L' R U' L'","note":"the leading Uw' is a setup move the page leaves unrestored — as printed this ends one Uw short of solved; append Uw (machine-verified)","closing":"Uw"}]},
        {"name":"LBT 77","group":"S4 one in middle","recognition":"One in middle, corner on top — triangle on top in back.","algs":[{"alg":"U L R' L' R U' L' R' L R"}]},
        {"name":"LBT 78","group":"S4 one in middle","recognition":"One in middle, corner on top — triangle on top in back.","algs":[{"alg":"U' L R' L' R U R' L' R L"}]},
        {"name":"LBT 79","group":"S4 one in middle","recognition":"One in middle, corner on top — triangle on top in back.","algs":[{"alg":"{U,BL} L R F L' R' L R F' L' R'"}]},
        {"name":"LBT 80","group":"S4 one in middle","recognition":"One in middle, corner on top — triangle on top in back.","algs":[{"alg":"R' L' F' R L R' L' F R L"}]},
        {"name":"LBT 81","group":"S5 all on top","recognition":"All on top — triangles on left.","algs":[{"alg":"{U,BL} R L R' L' U' R L R' L'"},{"alg":"{U,BL} L R' L' R U B' R' B R"},{"alg":"U R' U' R L' R' L U R"}]},
        {"name":"LBT 82","group":"S5 all on top","recognition":"All on top — triangles on left.","algs":[{"alg":"B' R B R' U L' R' L R"}]},
        {"name":"LBT 83","group":"S5 all on top","recognition":"All on top — triangles on left.","algs":[{"alg":"L R' L R U' R B' R' B U L"}]},
        {"name":"LBT 84","group":"S5 all on top","recognition":"All on top — triangles on left.","algs":[{"alg":"R L U L R' L' R U' L' R'"},{"alg":"{U,BL} R' L R F R L' R' L F' L'"}]},
        {"name":"LBT 85","group":"S5 all on top","recognition":"All on top — triangles on right.","algs":[{"alg":"B' R B R' U' R' L' R L"}]},
        {"name":"LBT 86","group":"S5 all on top","recognition":"All on top — triangles on right.","algs":[{"alg":"{U,BL} L U L' R L R' U' L'"}]},
        {"name":"LBT 87","group":"S5 all on top","recognition":"All on top — triangles on right.","algs":[{"alg":"{U,BL} U L' R' U' R' L R L' U R L"}]},
        {"name":"LBT 88","group":"S5 all on top","recognition":"All on top — triangles on right.","algs":[{"alg":"U R L U' B' R B R' U L' R'"}]},
        {"name":"LBT 89","group":"S5 all on top","recognition":"All on top — triangles in back.","algs":[{"alg":"{U,BL} L U F L' R L R' F' U' L'"}]},
        {"name":"LBT 90","group":"S5 all on top","recognition":"All on top — triangles in back.","algs":[{"alg":"L B U' L U B L' BL L' BL' B"}]},
        {"name":"LBT 91","group":"S5 all on top","recognition":"All on top — triangles in back.","algs":[{"alg":"F' BL' F' B L' B' L F BL F"}]},
        {"name":"LBT 92","group":"S5 all on top","recognition":"All on top — triangles in back.","algs":[{"alg":"{U,BL} BR R' L R BR' L' U' R L R' L'"}]},
        {"name":"LBT 93","group":"S6 both in slot","recognition":"Both in slot, corner on top — both in slot, corner on top.","algs":[{"alg":"BL' U' BL R' L R L' BL' U BL"}]},
        {"name":"LBT 94","group":"S6 both in slot","recognition":"Both in slot, corner on top — both in slot, corner on top.","algs":[{"alg":"L' U' R B' R L' R L B U L"}]},
        {"name":"LBT 95","group":"S6 both in slot","recognition":"Both in slot, corner on top — both in slot, corner on top.","algs":[{"alg":"BL' U BL R' L R L' BL' U' BL"},{"alg":"BL' U' BL R B' R' B BL' U BL"}]},
        {"name":"LBT 96","group":"S6 both in slot","recognition":"Both in slot, corner on top — both in slot, corner on top.","algs":[{"alg":"U L U L' R B' R' B' L B' U' L'"}]}
      ]
    },
    "1LP": {
      "name": "1LP — One-Look Pair Formation",
      "notation": "cif",
      "notation_note": "The sheet’s dialect, all machine-verified: S/H are the sledge (R’ L R L’) and hedge (R B’ R’ B) triggers, and (U)/(U’) are AUF turns written in parentheses (executed as the plain move). The sheet’s [Uo]/[Uo’] whole-puzzle rotation marks are respelled here as {X,Y} re-orientation brackets ({U,BR} = Uo, {U,BL} = Uo’) — the site’s rotation convention; each respelling is machine-verified move-for-move identical. A leading rotation gives the solution for a rotated view of the same case, a trailing one annotates the ending orientation (rotations never change the state). Diagrams show the exact state each case’s first sequence resolves. Every sequence is machine-verified as a correct flip sequence: from any state matching its case’s yellow/blue appearance it leaves all three pairs structurally formed, landing in the TCP stage. The parity column and comments are the sheet’s own prose.",
      "description": "One-look pair formation for the Bencisco last layer: form the three corner-triangle pairs in a single look, then finish with one of the 18 TCP algorithms (or 2-look). Pair formation is NEUTRAL (colors are ignored while pairing), rotationless, and ergonomic. Case 6c on the sheet is the already-paired state (omitted here). Solutions are given per AUF and per puzzle orientation; parity notes say whether a sequence preserves the permutation parity.",
      "groups": [
        "Parity stays",
        "Parity flips"
      ],
      "sources": [
        "Sheet: Ben Streeter, Jim Steenvoorden, Casper Hegt, 'One Look Pair Formation (1LP) Cases and Solutions', V3 — supplied as 1LP_Rotationless_V3.pdf (transcription: data/sources/1lp-rotationless-v3.json)"
      ],
      "cases": [
        {"name":"1LP 1","group":"Parity stays","recognition":"This OLP has only 11 possible permutations. I recommend learning algorithms for them; they are short and easy to recognize.","moves_note":"sheet parity column: stays — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"H"}]},
        {"name":"1LP 2","group":"Parity flips","recognition":"There are good solutions here for each AUF, which you can also use to force a 4-move TCP in some circumstances.","moves_note":"sheet parity column: flips — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"H U' H U {U,BR}"},{"alg":"(U) S' U' S' U"},{"alg":"(U') S U S U'"}]},
        {"name":"1LP 3","group":"Parity stays","recognition":"You can force a 4-move TCP in this case most of the time, which helps avoid the H' solution.","moves_note":"sheet parity column: stays — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"(U') H' U'"},{"alg":"{U,BR} (U) S U","note":"solution for a rotated view of the case — the leading {U,BR} executes as a whole-puzzle rotation (state-neutral re-grip)"},{"alg":"{U,BL} (U) S' U {U,BR}","note":"solution for a rotated view of the case — the leading {U,BL} executes as a whole-puzzle rotation (state-neutral re-grip)"}]},
        {"name":"1LP 4a","group":"Parity flips","recognition":"This case has only one unique solution for pair formation. Rotating to avoid H' is recommended.","moves_note":"sheet parity column: flips — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"(U) S U {U,BR}"},{"alg":"{U,BR} (U) S' U {U,BL}","note":"solution for a rotated view of the case — the leading {U,BR} executes as a whole-puzzle rotation (state-neutral re-grip)"},{"alg":"{U,BL} (U) H' U {U,BL}","note":"same physical solution as line 1, respelled from the rotated grip its leading {U,BL} rotation executes — state-identical, machine-verified"}]},
        {"name":"1LP 4b","group":"Parity flips","recognition":"The mirror image of the previous 4a case.","moves_note":"sheet parity column: flips — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"(U') S' U' {U,BL}"},{"alg":"{U,BR} (U') H' U' {U,BL}","note":"solution for a rotated view of the case — the leading {U,BR} executes as a whole-puzzle rotation (state-neutral re-grip)"},{"alg":"{U,BL} (U') S U' {U,BR}","note":"same physical solution as line 2, respelled from the rotated grip its leading {U,BL} rotation executes — state-identical, machine-verified"}]},
        {"name":"1LP 4c","group":"Parity stays","recognition":"Both U and U' AUFs work here; they have been chosen to keep the original permutation state.","moves_note":"sheet parity column: stays — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"(U) S' U S U' {U,BR}"},{"alg":"{U,BR} (U') S' U' S U {U,BR}","note":"solution for a rotated view of the case — the leading {U,BR} executes as a whole-puzzle rotation (state-neutral re-grip)"},{"alg":"{U,BL} (U) S U S' U' {U,BL}","note":"same physical solution as line 1, respelled from the rotated grip its leading {U,BL} rotation executes — state-identical, machine-verified"}]},
        {"name":"1LP 5","group":"Parity flips","recognition":"There are many possible solutions here for each AUF, but the ones listed are considered the best for avoiding regrips.","moves_note":"sheet parity column: flips — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"S' U' S U {U,BL}"},{"alg":"{U,BR} (U) S' U' S' U {U,BL}","note":"solution for a rotated view of the case — the leading {U,BR} executes as a whole-puzzle rotation (state-neutral re-grip)"},{"alg":"{U,BL} (U') S U S U' {U,BR}","note":"solution for a rotated view of the case — the leading {U,BL} executes as a whole-puzzle rotation (state-neutral re-grip)"}]},
        {"name":"1LP 6a","group":"Parity flips","recognition":"This case also has only one unique PF solution. Rotating to avoid H' is recommended.","moves_note":"sheet parity column: flips — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"(U') S U {U,BL}"},{"alg":"{U,BR} (U') S' U","note":"solution for a rotated view of the case — the leading {U,BR} executes as a whole-puzzle rotation (state-neutral re-grip)"},{"alg":"{U,BL} (U') H' U","note":"same physical solution as line 1, respelled from the rotated grip its leading {U,BL} rotation executes — state-identical, machine-verified"}]},
        {"name":"1LP 6b","group":"Parity flips","recognition":"The mirror image of the previous 6a case.","moves_note":"sheet parity column: flips — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"(U) S' U' {U,BR}"},{"alg":"{U,BR} (U) H' U' {U,BR}","note":"solution for a rotated view of the case — the leading {U,BR} executes as a whole-puzzle rotation (state-neutral re-grip)"},{"alg":"{U,BL} (U) S U'","note":"same physical solution as line 2, respelled from the rotated grip its leading {U,BL} rotation executes — state-identical, machine-verified"}]},
        {"name":"1LP 7","group":"Parity stays","recognition":"This is three flips away from a completed PF. However you can go straight into the solution without any AUF which is nice.","moves_note":"sheet parity column: stays — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"S' U' S' U' S U {U,BR}"}]},
        {"name":"1LP 8","group":"Parity flips","recognition":"Both the even/odd cases can be forced into a 4-move TCP, but the even permutation is the only case really worth learning.","moves_note":"sheet parity column: flips — the author’s own permutation bookkeeping, carried verbatim","algs":[{"alg":"H U H U"},{"alg":"(U) S' U S' U {U,BL}"},{"alg":"(U') S U' S U' {U,BR}"}]}
      ]
    }
  }
}