{ "vercy": "1.0-draft", "publication": { "status": "research-draft", "adjudicationStatus": "unreviewed", "publishableCanonical": false, "generatedAt": "2026-09-07T13:33:05Z", "providers": [ "Codex", "Grok" ], "missingProviders": [], "pass": 2, "cost": { "grok": { "usd": 0.0096679, "turns": 1, "seconds": 139.8, "error": null }, "codex": { "seconds": 68.1, "error": "Reading additional input from stdin...\nOpenAI Codex v0.153.3\n--------\nworkdir: R:\\02_PROJECTS\\02_Meta_Models_Platforms\\Ver.cy\\current\\thing-registry-backlog\nmodel: gpt-6-astra\nprovider: openai\napproval: never\nsandbox: read-only\nreasoning effort: none\nreasoning summaries: none\nsession id: 01a07c0e-967c-7ea1-a112-eee7252eaab2\n--------\nuser\nYou are drafting a Vercy meta-model for one registered thing. Answer as JSON only, no prose around it.\n\nThing: sudoku\nRegistry id: vr.tr.sudoku\nPlane / domain: INF / INF.KNW\nRegistry definition: (none recorded)\nNames folded into this entry: (none)\n\nA Vercy mod" } }, "enrichment": { "pass": 3, "engine": "claude", "producedAt": "2026-10-06T11:00:00Z", "ingestedAt": "2026-10-06T08:02:47+00:00", "fields": [ "agent_conduct", "ethics", "owners" ] }, "revisions": [ { "at": "2026-10-07T11:33:11+00:00", "engine": "codex", "fields": [ "definition" ], "answering_review": "c52585a7aae40fd9c9cd800afcd1a4a6858659a13ec1e53d3407b44379c9aaa0" } ], "gate": { "passed": true, "version": "1.0", "at": "2026-10-07T12:16:33+00:00", "evidence": [ "completeness 1.00", "sense: Wikidata description", "5 live sources", "review by codex: pass" ] } }, "metaModel": { "id": "THING-Q44914", "registryId": "vr.tr.sudoku", "name": "sudoku", "version": "0.1.0-research.1", "entryKind": "thing", "family": "Thing Registry", "domain": [ "INF.KNW" ], "status": "research-draft" }, "canonicalUrl": "https://ver.cy/models/thing/q44914/", "model": { "registry_id": "vr.tr.sudoku", "name": "sudoku", "purpose": "Enable an AI agent to recognise a sudoku puzzle, assess its rules and current solving state, and choose justified solving, checking or editing actions.", "definition": "Sudoku is a logic-based number-placement puzzle in which a partially filled grid is completed according to declared row, column, region and variant-specific constraints, normally with exactly one intended solution; standard sudoku uses a 9-by-9 grid with the symbols 1-9 appearing once in each row, column and 3-by-3 block, while variants can change grid size, region geometry or constraints.", "scope_statement": "This model owns a sudoku puzzle as a symbol-placement constraint problem, including its declared variant, grid, givens, solution conditions and recorded solving state.", "in_scope": [ "Grid topology, symbol alphabet and declared sudoku rules", "Given symbols and their distinction from editable entries", "Row, column, region and variant-specific constraints", "Candidate symbols, deductions and unresolved placements", "Consistency, solvability, solution multiplicity and completion", "Permitted hints, solving moves and puzzle-authoring changes" ], "out_of_scope": [ "A solver's identity, skill profile or learning history", "Tournament administration, rankings and prize rules", "The software interface, storage format or printed page carrying the puzzle", "General constraint-solving algorithms independently of their application to this puzzle", "Collections, publication licensing and commercial distribution", "Other puzzle families whose rules do not establish a sudoku structure" ], "distinguishing_features": [ "For a standard 9×9 instance, test whether every row, column and 3×3 region must contain each of the nine symbols exactly once.", "Test whether symbols act as distinct labels rather than quantities; standard sudoku does not depend on arithmetic relationships between their numeric values.", "Test for region constraints in addition to row and column uniqueness; row and column uniqueness alone describes a Latin-square constraint system.", "Distinguish an initial puzzle from a solution grid by recording which entries are fixed clues and which are supplied during solving.", "For a claimed variant, identify its sudoku constraints and explicit additions or replacements instead of assuming standard box geometry or rules." ], "characteristics": [ { "name": "Declared ruleset", "kind": "category", "unit_or_values": "Standard 9×9 sudoku; explicitly specified variant; unspecified", "why_it_matters": "Determines which placements and completion checks are applicable." }, { "name": "Grid topology", "kind": "relation", "unit_or_values": "Cells mapped to rows, columns, regions and any additional constraint groups", "why_it_matters": "Identifies the cells that constrain each placement." }, { "name": "Symbol alphabet", "kind": "category", "unit_or_values": "Explicit set of permitted symbols; conventionally 1-9 for standard 9×9 sudoku", "why_it_matters": "Prevents display conventions from being mistaken for arithmetic requirements." }, { "name": "Given count", "kind": "measurement", "unit_or_values": "Number of fixed cells", "why_it_matters": "Describes the starting information without treating clue count alone as a difficulty measure." }, { "name": "Entry role", "kind": "category", "unit_or_values": "Given; committed solver entry; tentative assumption; empty", "why_it_matters": "Separates immutable puzzle information from reversible solving work." }, { "name": "Candidate basis", "kind": "category", "unit_or_values": "Immediate constraint filtering; justified deductions; exhaustive solution analysis; unverified notes", "why_it_matters": "Explains what inclusion or exclusion of a candidate actually establishes." }, { "name": "Current-state validity", "kind": "state", "unit_or_values": "Unchecked; no detected direct violation; direct violation detected; proved extendable; proved non-extendable", "why_it_matters": "Distinguishes absence of visible conflicts from existence of a completing solution." }, { "name": "Original-puzzle solution multiplicity", "kind": "state", "unit_or_values": "Unknown; zero; exactly one; at least two, with supporting evidence", "why_it_matters": "Separates solvability and uniqueness from the state of a particular solve attempt." }, { "name": "Difficulty assessment", "kind": "category", "unit_or_values": "Unrated or rating accompanied by solver method, technique vocabulary and rating convention", "why_it_matters": "Makes difficulty claims interpretable rather than universal." } ], "affordances": [ "Validate the grid and givens against the declared sudoku rules.", "Compute or revise candidates while recording their basis.", "Explain a justified placement or elimination at a requested hint level.", "Apply, retract or branch on an editable entry while preserving givens.", "Check completion and determine solution multiplicity with explicit evidence.", "Revise clues or variant constraints in an authoring context and recheck the resulting puzzle." ], "agent_conduct": { "may": [ "Generate, check and solve puzzles, confirming each has a unique solution.", "Explain solving techniques and grade difficulty." ], "must_not": [ "Publish puzzles with no solution or several as if they were valid.", "Copy and republish another publisher's puzzles without permission.", "Present puzzle solving as a proven treatment for memory loss or dementia." ], "requires_human": [ "Republishing puzzle collections commercially." ] }, "ethics": { "considerations": [ "Puzzle setters' work deserves credit even when the format is free to use." ], "affected_parties": [ "Solvers", "Puzzle setters and publishers" ] }, "owners": { "steward": "Nobody owns the format; each setter or publisher holds rights in their own puzzles.", "master_systems": [] }, "what_it_is_for": [ "Sudoku appears in printed puzzle collections, newspapers and digital puzzle applications as a recreational logic activity.", "Solvers complete a partially filled grid by satisfying row, column and block constraints.", "It is also used in teaching and software development to illustrate deduction, search and constraint satisfaction." ], "visual_identification": [ "A standard puzzle has a square grid of nine rows and nine columns.", "Heavier boundaries usually divide the grid into nine blocks of three rows and three columns.", "An unsolved puzzle contains scattered given digits from 1 through 9 among blank cells." ], "failure_modes_and_hazards": [ "Contradictory or insufficient clues can make a puzzle unsolvable or prevent a unique solution.", "Incorrect deductions or recognition errors can propagate through the grid and invalidate subsequent entries.", "Software that overwrites given clues can corrupt the puzzle and produce a misleading completion." ], "facets_not_applicable": { "interfaces": "No generally applicable technical standard, law or official classification governs ordinary sudoku puzzles." } }, "sources": [ { "id": "wikipedia-sudoku", "title": "Sudoku - Wikipedia (Wikimedia Foundation)", "url": "https://en.wikipedia.org/wiki/Sudoku", "what_it_supports": "Specialist definition (Latin square plus block constraint), named variants in common use, Number Place / Nikoli / Times history, and the standard completed-grid and clue-minimum figures.", "url_status": "live" }, { "id": "wikidata-q13191", "title": "Sudoku (Q13191) - Wikidata (Wikimedia Foundation)", "url": "https://www.wikidata.org/wiki/Q13191", "what_it_supports": "Canonical catalogue identifier for the puzzle type and links to equivalent names.", "url_status": "live" }, { "id": "felgenhauer-jarvis-2005", "title": "Enumerating possible Sudoku grids - Bertram Felgenhauer and Frazer Jarvis (University of Sheffield, 2005)", "url": "http://www.afjarvis.staff.shef.ac.uk/sudoku/sudoku.pdf", "what_it_supports": "The accepted count of completed 9×9 Sudoku grids (6,670,903,752,021,072,936,960) after reduction by the first-band symmetries.", "url_status": "live" }, { "id": "mcguire-tugemann-civario-2014", "title": "There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem - Gary McGuire, Bastian Tugemann and Gilles Civario (Experimental Mathematics / Taylor & Francis, 2014; arXiv:1201.0749)", "url": "https://arxiv.org/abs/1201.0749", "what_it_supports": "Proof that no unique-solution 9×9 Sudoku exists with fewer than 17 given cells, which is the lower bound used for clue-count measurement.", "url_status": "live" }, { "id": "wikidata", "title": "Wikidata item Q44914: sudoku", "url": "https://www.wikidata.org/wiki/Q44914", "url_status": "live", "what_it_supports": "identity and sense of the item", "checked_by": "wikidata-api" } ], "structure": { "bundles": [ { "id": "sudoku-rule-identity", "name": "Sudoku rule identity", "description": "The topology and rule commitments that establish what counts as a solution to this sudoku.", "rationale": "An agent cannot assess placements until it knows the symbol set, constraint groups and variant rules.", "layers": [ { "id": "grid-and-symbols", "name": "Grid and symbols", "description": "The playable cells, their grouping and the symbols they accept.", "findings": [ { "id": "constraint-topology", "name": "Constraint topology", "description": "Record the cell layout, alphabet and membership of each row, column and region without inferring missing geometry from appearance alone.", "questions": [ { "text": "Which cells exist, which symbols are permitted, and which rows, columns and regions contain each cell?", "kind": "definition", "id": "constraint-topology-q01" }, { "text": "Does the supplied layout establish a standard 9×9 grid with nine 3×3 regions, or does it require a different explicit topology?", "kind": "boundary", "id": "constraint-topology-q02" } ] } ] }, { "id": "base-and-variant-rules", "name": "Base and variant rules", "description": "The exact requirements imposed on the topology.", "findings": [ { "id": "declared-rule-contract", "name": "Declared rule contract", "description": "Record the applicable all-different requirements and any additional or replacement constraints, including the interpretation of visual markings.", "questions": [ { "text": "Which groups must contain each permitted symbol exactly once, and which variant constraints also apply?", "kind": "definition", "id": "declared-rule-contract-q01" }, { "text": "What supplied instructions establish the meaning of diagonals, cages, paths or other markings, including any rules about unmarked cells?", "kind": "provenance", "id": "declared-rule-contract-q02" } ] } ] } ] }, { "id": "givens-and-solve-state", "name": "Givens and solve state", "description": "The fixed puzzle information and the mutable entries belonging to a solve attempt.", "rationale": "A contradiction caused by a solver entry must not be confused with a defective original puzzle.", "layers": [ { "id": "initial-clue-baseline", "name": "Initial clue baseline", "description": "The original fixed placements against which solving work is interpreted.", "findings": [ { "id": "fixed-given-map", "name": "Fixed given map", "description": "Identify the value and position of every given, together with any uncertainty in transcription or extraction.", "questions": [ { "text": "Which cell values were supplied as fixed givens rather than entered during solving?", "kind": "definition", "id": "fixed-given-map-q01" }, { "text": "What original puzzle representation supports the given map, and which symbols or positions remain uncertain?", "kind": "provenance", "id": "fixed-given-map-q02" } ] } ] }, { "id": "editable-solving-position", "name": "Editable solving position", "description": "The current entries, assumptions and candidate notes of a particular solve attempt.", "findings": [ { "id": "entries-and-candidate-meaning", "name": "Entries and candidate meaning", "description": "Distinguish committed entries, branch assumptions and candidate notes; record whether notes are complete and how candidates were derived.", "questions": [ { "text": "Which cells are empty, committed or tentative, and which candidate sets are complete rather than partial notes?", "kind": "measurement", "id": "entries-and-candidate-meaning-q01" }, { "text": "Which entries or candidate removals may be reversed without changing the original givens or rules?", "kind": "action", "id": "entries-and-candidate-meaning-q02" } ] } ] } ] }, { "id": "sudoku-validity-and-solutions", "name": "Sudoku validity and solutions", "description": "Evidence about direct conflicts, possible completions and uniqueness.", "rationale": "A filled or conflict-free grid is not sufficient evidence that the puzzle has been correctly solved or uniquely specified.", "layers": [ { "id": "position-consistency", "name": "Position consistency", "description": "Checks on the current entries and their ability to participate in a completion.", "findings": [ { "id": "conflicts-and-dead-ends", "name": "Conflicts and dead ends", "description": "Identify repeated symbols, violated variant constraints and proved impossibility, retaining the entries and reasoning responsible for each diagnosis.", "questions": [ { "text": "Which current entries directly violate a row, column, region or declared variant constraint?", "kind": "measurement", "id": "conflicts-and-dead-ends-q01" }, { "text": "Has a dead end been proved, such as a soundly derived empty candidate set or a required symbol with no possible position, and on which assumptions does that proof depend?", "kind": "measurement", "id": "conflicts-and-dead-ends-q02" } ] } ] }, { "id": "completion-and-multiplicity", "name": "Completion and multiplicity", "description": "Separate assessment of a submitted completion and the original puzzle's solution set.", "findings": [ { "id": "solution-evidence", "name": "Solution evidence", "description": "Record whether a full grid satisfies all rules and givens, and whether the original puzzle has zero, exactly one or multiple solutions.", "questions": [ { "text": "Does the proposed completion fill every playable cell, preserve all givens and satisfy every declared constraint?", "kind": "measurement", "id": "solution-evidence-q01" }, { "text": "What evidence establishes the original puzzle's solution multiplicity, and does it exclude solver-added entries from the premise?", "kind": "provenance", "id": "solution-evidence-q02" } ] } ] } ] }, { "id": "deductions-hints-and-revisions", "name": "Deductions, hints and revisions", "description": "The justified next steps available during solving or puzzle authoring.", "rationale": "An agent needs to distinguish a forced deduction, a search assumption and a change to the puzzle itself.", "layers": [ { "id": "justified-solving-moves", "name": "Justified solving moves", "description": "Placements and candidate eliminations with inspectable reasoning.", "findings": [ { "id": "deduction-support-and-hint-depth", "name": "Deduction support and hint depth", "description": "Connect each proposed move to its supporting cells, candidates and constraints, identifying any dependence on uniqueness or a branch assumption.", "questions": [ { "text": "Which placement or elimination follows, and what cells, constraints and assumptions justify it?", "kind": "action", "id": "deduction-support-and-hint-depth-q01" }, { "text": "Should the next hint identify a unit to inspect, name a technique, explain the deduction or reveal the placement?", "kind": "action", "id": "deduction-support-and-hint-depth-q02" } ] } ] }, { "id": "search-and-puzzle-revision", "name": "Search and puzzle revision", "description": "Controlled branching during solving and changes to clues or rules during authoring.", "findings": [ { "id": "branch-or-revise", "name": "Branch or revise", "description": "Record whether the next operation explores an assumption within the current puzzle or creates a revised puzzle requiring fresh validation.", "questions": [ { "text": "Does the operation assume a candidate for search, or change a given, region or rule and therefore revise the puzzle?", "kind": "boundary", "id": "branch-or-revise-q01" }, { "text": "After the operation, what must be restored or rechecked, including branch-dependent deductions, solvability, uniqueness and any difficulty rating?", "kind": "action", "id": "branch-or-revise-q02" } ] } ] } ] }, { "id": "evidence-and-external-alignment", "name": "Evidence and external alignment", "description": "What the world already says about this thing, gathered so the model can be checked against it.", "rationale": "A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.", "layers": [ { "id": "reported-evidence", "name": "Reported evidence", "description": "Findings from the breadth pass, kept separate from the structural claims.", "findings": [ { "id": "evidence-kinds", "name": "Kinds and varieties", "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.", "evidence": [ "Classic 9×9 Sudoku (row, column, and 3×3 block uniqueness)", "Mini Sudoku (4×4 Shidoku and 6×6 grids with matching box shapes)", "Large-order Sudoku (16×16 Hexadoku, 25×25, and other n²×n² grids)", "Killer Sudoku (disjoint cages with given sums; digits remain unique inside each cage)", "Diagonal Sudoku / Sudoku X (both main diagonals also contain 1-9)", "Jigsaw / irregular Sudoku (nine connected regions replace the 3×3 blocks)", "Overlapping multi-grid Sudoku (Samurai and similar unions of 9×9 grids)", "Extra-region / Hyper Sudoku (Windoku): additional shaded 3×3 windows that also contain 1-9" ], "questions": [ { "id": "evidence-kinds-q01", "text": "Which of these kinds and varieties hold for the sense of sudoku this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-identifiers", "name": "Identifiers and schemes", "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.", "evidence": [ { "scheme": "Wikidata item", "value_or_pattern": "Q13191", "note": "Primary linked-data item for the puzzle type, not for any single published grid." }, { "scheme": "Library of Congress Subject Heading", "value_or_pattern": "Sudoku", "note": "Catalogue heading used for books and serials of puzzles, not a product SKU." } ], "questions": [ { "id": "evidence-identifiers-q01", "text": "Which of these identifiers and schemes hold for the sense of sudoku this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-standards-and-regulation", "name": "Standards and regulation", "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.", "evidence": [ "World Puzzle Federation issues the competition regulations for the World Sudoku Championship (grid size, permitted variants, scoring, and uniqueness of the intended solution).", "Nikoli Co., Ltd. set the Japanese house conventions (unique solution; often rotationally symmetric givens) and historically held a trademark on the name 数独 in Japan.", "There is no ISO, IEC, or statutory product standard for Sudoku as a puzzle form; newspaper and app instances are editorial products." ], "questions": [ { "id": "evidence-standards-and-regulation-q01", "text": "Which of these standards and regulation hold for the sense of sudoku this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-real-world-use", "name": "Real-world use", "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.", "evidence": [ "Printed as a daily or weekly feature in newspapers and puzzle magazines, with a given grid and a later published solution.", "Sold as graded paperback collections and as timed puzzles in mobile and web apps.", "Used as the set piece of the World Sudoku Championship and national qualifying contests under World Puzzle Federation rules.", "Used in computer science as a canonical exact-cover / dancing-links and constraint-satisfaction example.", "Worked by hand on paper as a recreational logic pastime, often rated by estimated technique depth rather than by clue count alone." ], "questions": [ { "id": "evidence-real-world-use-q01", "text": "Which of these real-world use hold for the sense of sudoku this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-measurements", "name": "Typical measurements", "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.", "evidence": [ { "quantity": "Grid order (side length)", "typical_range": "9 for the classic form; also 4, 6, 16, 25 in published variants", "unit": "cells" }, { "quantity": "Given cells (clues) on a unique 9×9 puzzle", "typical_range": "17-36 in well-posed published puzzles; 17 is the proven minimum", "unit": "cells" }, { "quantity": "Completed 9×9 grids", "typical_range": "6670903752021072936960 (exact count)", "unit": "grids" }, { "quantity": "Essentially different 9×9 grids (up to the Sudoku symmetry group)", "typical_range": "5472730538 (exact count)", "unit": "grids" }, { "quantity": "Wall-clock solve time for a newspaper-grade 9×9", "typical_range": "5-45", "unit": "minutes" } ], "questions": [ { "id": "evidence-measurements-q01", "text": "Which of these typical measurements hold for the sense of sudoku this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-failure-modes-and-hazards", "name": "Failure modes and hazards", "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.", "evidence": [ "Underconstrained givens yield two or more completions, so the puzzle is ill-posed by the uniqueness convention.", "Overconstrained or misprinted givens yield no completion.", "A puzzle billed as 'logic-only' may still require trial-and-error (bifurcation) beyond the techniques implied by its grade.", "In Japan, generic use of the trademarked name 数独 has produced naming and branding disputes; elsewhere the word is treated as generic.", "Compulsive play can displace time; there is no established physical injury mechanism beyond ordinary visual fatigue." ], "questions": [ { "id": "evidence-failure-modes-and-hazards-q01", "text": "Which of these failure modes and hazards hold for the sense of sudoku this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-regional-variation", "name": "Regional variation", "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.", "evidence": [ "United States origin as 'Number Place' in Dell Magazines (Howard Garns, 1979); that name still appears in some American puzzle books.", "Japan: Nikoli named and popularised it as 数独 (sūdoku, 'single number') from 1984, with a house style that favours symmetric givens and a unique solution.", "United Kingdom: The Times launched a daily 'Su Doku' in 2004 (Wayne Gould's computer-generated grids), which seeded the worldwide newspaper boom; early British hyphenation has largely disappeared.", "Most European and Latin American papers now use the unhyphenated loanword 'sudoku' rather than a calque.", "Championship practice (which variants are live, how difficulty is scored) follows World Puzzle Federation rules and can differ from Nikoli magazine style and from app generators." ], "questions": [ { "id": "evidence-regional-variation-q01", "text": "Which of these regional variation hold for the sense of sudoku this model covers, and on what evidence?", "kind": "provenance" } ] }, { "id": "evidence-neighbours", "name": "Neighbouring kinds and how to tell them apart", "description": "Reported by the breadth pass; each item needs checking against its source before it becomes normative.", "evidence": [ { "name": "Latin square", "difference": "A Latin square of order 9 already has unique symbols in every row and column; Sudoku adds the nine 3×3 block constraints (and is presented as a partial grid to complete)." }, { "name": "Magic square", "difference": "A magic square is defined by equal line sums, not by partitioning {1…9} through rows, columns and blocks; a 3×3 magic square uses 1-9 but is not a Sudoku and does not scale to the 9×9 puzzle." }, { "name": "KenKen / Calcudoku", "difference": "KenKen is a Latin square whose regions are arithmetic cages with an operation and a target; it does not use Sudoku's 3×3 blocks unless a hybrid explicitly adds them." }, { "name": "Kakuro", "difference": "Kakuro is a crossword-shaped grid of digit runs with given sums; it is not a square of 1-9 with block uniqueness." }, { "name": "Futoshiki", "difference": "Futoshiki is an order-n Latin square plus inequality signs between adjacent cells, with no 3×3 block constraint." }, { "name": "Crossword", "difference": "A crossword places letters under lexical and crossing constraints; Sudoku places a closed digit alphabet under uniqueness constraints and has no vocabulary." } ], "questions": [ { "id": "evidence-neighbours-q01", "text": "Which of these neighbouring kinds and how to tell them apart hold for the sense of sudoku this model covers, and on what evidence?", "kind": "provenance" } ] } ] } ] } ] }, "openQuestions": [ "Does this registry entry cover sudoku variants, overlapping grids and non-9×9 sizes, or should some link to separate registered concepts?", "Should uniqueness be a required publication condition for an intended sudoku puzzle, or a quality state that permits ambiguous and unsatisfiable instances to remain represented?", "Which technique vocabulary and solver assumptions should govern difficulty assessments, including whether uniqueness-dependent deductions are permitted?", "What evidence standard should establish unsatisfiability or uniqueness: reproducible exhaustive search, an inspectable proof, or another accepted verification method?", "Which changes of symbols, orientation or clue placement preserve puzzle identity for catalogue purposes, and which create a distinct puzzle?" ], "statistics": { "bundles": 5, "layers": 9, "findings": 16, "questions": 24 } }