Schema annotation seeds, not independently validated mathematical statements. A simplex joins the objects, assumptions and conclusion in its slots. References are partial symbol/syntax candidates. This review contains schema annotations and Lean signature text, not textbook passages or full assistant judgment explanations.
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+ "reference_status": "syntactic_candidates"
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+ },
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+ "keywords": [
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+ "references": [],
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+ },
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+ "quantifier_status": "unreviewed",
+ "references": [],
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+ "references": [],
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+ }
+}Insufficient projected roles; no object roles were invented.
{
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+ "keywords": [
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+ "classified_by": "default",
+ "origin": "deterministic_signature_projection",
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+ "reference_status": "syntactic_candidates"
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+ },
+ "goal": {
+ "name": "goal",
+ "kind": "goal",
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+ "exists_count": 2,
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+ "is_iff": false,
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+ "a",
+ "b"
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+ }
+ }
+}{
+ "name": "schema:p0-f12735802ba0:0b7db1a8100c33a50a08981f:source:v1",
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+ "reference_completeness": "partial"
+ },
+ "roles": {
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+ "kind": "object",
+ "context": "group",
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+ "references": [],
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+ }
+ },
+ "object2": {
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+ "kind": "object",
+ "context": "group size",
+ "attrs": {
+ "symbols": [
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+ ],
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+ "size"
+ ],
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+ "keywords": [
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+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "fact1": {
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+ "context": "finite",
+ "attrs": {
+ "symbols": [
+ "G"
+ ],
+ "keywords": [
+ "finite"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [
+ "object1"
+ ],
+ "reference_status": "explicit_symbol_candidates",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "goal1": {
+ "name": "goal1",
+ "kind": "goal",
+ "context": "nth power equals identity",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "nth",
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+ "introduced": "given",
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+ "references": [],
+ "reference_status": "unknown",
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+ }
+ }
+ }
+}{
+ "name": "schema:p0-f12735802ba0:0b7db1a8100c33a50a08981f:lean:v1",
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+ "attrs": {
+ "side": "lean",
+ "reference_completeness": "syntactic_only"
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+ "roles": {
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+ "kind": "object",
+ "type": "Type*",
+ "attrs": {
+ "binder_kind": "explicit",
+ "classified_by": "sort",
+ "origin": "deterministic_signature_projection",
+ "instances": [
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+ "Fintype G"
+ ],
+ "references": [],
+ "reference_status": "syntactic_candidates"
+ }
+ },
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+ "name": "g",
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+ "classified_by": "default",
+ "origin": "deterministic_signature_projection",
+ "references": [
+ "G"
+ ],
+ "reference_status": "syntactic_candidates"
+ }
+ },
+ "goal": {
+ "name": "goal",
+ "kind": "goal",
+ "type": "g ^ Fintype.card G = 1",
+ "attrs": {
+ "exists_count": 0,
+ "forall_count": 0,
+ "is_iff": false,
+ "references": [
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+ "g"
+ ],
+ "reference_status": "syntactic_candidates",
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+ }
+ }
+ }
+}{
+ "name": "schema:p0-f12735802ba0:e3d40d93cda13ec59c35d9a5:source:v1",
+ "kind": "simplex",
+ "attrs": {
+ "side": "source",
+ "goal_has_exists": true,
+ "reference_completeness": "partial"
+ },
+ "roles": {
+ "object1": {
+ "name": "object1",
+ "kind": "object",
+ "context": "RSA method",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "rsa",
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+ "introduced": "given",
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+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "object2": {
+ "name": "object2",
+ "kind": "object",
+ "context": "messages",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "messages"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "goal1": {
+ "name": "goal1",
+ "kind": "goal",
+ "context": "design secure authenticated message exchange",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
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+ "secure",
+ "authenticated",
+ "message",
+ "exchange"
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+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ }
+ }
+}Insufficient projected roles; no object roles were invented.
{
+ "name": "schema:p0-f12735802ba0:aaf1250a5104a4f7c1ca0d29:source:v1",
+ "kind": "simplex",
+ "attrs": {
+ "side": "source",
+ "goal_has_exists": false,
+ "reference_completeness": "partial"
+ },
+ "roles": {
+ "object1": {
+ "name": "n",
+ "kind": "object",
+ "context": "modulus",
+ "attrs": {
+ "symbols": [
+ "n"
+ ],
+ "keywords": [
+ "modulus"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "object2": {
+ "name": "a",
+ "kind": "object",
+ "context": "integer",
+ "attrs": {
+ "symbols": [
+ "a"
+ ],
+ "keywords": [
+ "integer"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "object3": {
+ "name": "Φ",
+ "kind": "object",
+ "context": "group of units",
+ "attrs": {
+ "symbols": [
+ "Φ"
+ ],
+ "keywords": [
+ "group",
+ "of",
+ "units"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "fact1": {
+ "name": "a",
+ "kind": "fact",
+ "context": "relatively prime to modulus",
+ "attrs": {
+ "symbols": [
+ "a"
+ ],
+ "keywords": [
+ "relatively",
+ "prime",
+ "to",
+ "modulus"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [
+ "object2"
+ ],
+ "reference_status": "explicit_symbol_candidates",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "goal1": {
+ "name": "goal1",
+ "kind": "goal",
+ "context": "totient power congruent to one",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "totient",
+ "power",
+ "congruent",
+ "to",
+ "one"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ }
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+}Insufficient projected roles; no object roles were invented.
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+ },
+ "goal1": {
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+ "binder_kind": "explicit",
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+ "own": {
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+ "reference_completeness": "partial"
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+ "roles": {
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+ "name": "n",
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+ "context": "modulus",
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+ "keywords": [
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+ "d"
+ ],
+ "keywords": [
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+ "references": [],
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+ }
+ },
+ "object3": {
+ "name": "object3",
+ "kind": "object",
+ "context": "generated cyclic subgroup",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "generated",
+ "cyclic",
+ "subgroup"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "goal1": {
+ "name": "goal1",
+ "kind": "goal",
+ "context": "subgroup equals integer and residue multiples",
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+ "symbols": [],
+ "keywords": [
+ "subgroup",
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+ "kind": "object",
+ "type": "ℕ",
+ "attrs": {
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+ "references": [
+ "n"
+ ],
+ "reference_status": "syntactic_candidates"
+ }
+ },
+ "goal": {
+ "name": "goal",
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+ "type": "\\\\\\n (ZMod n).subgroup.closure ({ZMod.mk d} : Set (ZMod n)) = \\\\\\n {ZMod.mk (k * d % n) | k : ℤ} = \\\\\\n {ZMod.mk (k * d % n) | k : ZMod n}",
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+ "forall_count": 0,
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+}{
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+ "object1": {
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+ "context": "first group",
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+ "symbols": [],
+ "keywords": [
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+ "object2": {
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+ "context": "groups are isomorphic",
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+ "name": "goal1",
+ "kind": "goal",
+ "context": "abelian properties equivalent",
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+ "side": "lean",
+ "reference_completeness": "syntactic_only"
+ },
+ "roles": {
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+ "name": "G",
+ "kind": "object",
+ "type": "Type*",
+ "attrs": {
+ "binder_kind": "explicit",
+ "classified_by": "sort",
+ "origin": "deterministic_signature_projection",
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+ "kind": "object",
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+ "attrs": {
+ "binder_kind": "explicit",
+ "classified_by": "sort",
+ "origin": "deterministic_signature_projection",
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+ ],
+ "references": [],
+ "reference_status": "syntactic_candidates"
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+ },
+ "iso": {
+ "name": "iso",
+ "kind": "fact",
+ "type": "G ≃* H",
+ "attrs": {
+ "binder_kind": "explicit",
+ "classified_by": "relation",
+ "origin": "deterministic_signature_projection",
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+ "reference_status": "syntactic_candidates"
+ }
+ },
+ "goal": {
+ "name": "goal",
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+ "side": "source",
+ "goal_has_exists": true,
+ "reference_completeness": "partial"
+ },
+ "roles": {
+ "object1": {
+ "name": "object1",
+ "kind": "object",
+ "context": "RSA method",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "rsa",
+ "method"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "object2": {
+ "name": "object2",
+ "kind": "object",
+ "context": "message",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "message"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "goal1": {
+ "name": "goal1",
+ "kind": "goal",
+ "context": "design message authentication method",
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+ "symbols": [],
+ "keywords": [
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+ "introduced": "given",
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+ "reference_status": "unknown",
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+ }
+ }
+}Insufficient projected roles; no object roles were invented.
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+ "name": "R",
+ "kind": "object",
+ "context": "ring",
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+ "R"
+ ],
+ "keywords": [
+ "ring"
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+ "object2": {
+ "name": "S",
+ "kind": "object",
+ "context": "ring",
+ "attrs": {
+ "symbols": [
+ "S"
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+ "keywords": [
+ "ring"
+ ],
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+ }
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+ "object3": {
+ "name": "f",
+ "kind": "object",
+ "context": "map",
+ "attrs": {
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+ "f"
+ ],
+ "keywords": [
+ "map"
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+ },
+ "object4": {
+ "name": "a",
+ "kind": "object",
+ "context": "ring element",
+ "attrs": {
+ "symbols": [
+ "a"
+ ],
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+ },
+ "object5": {
+ "name": "b",
+ "kind": "object",
+ "context": "ring element",
+ "attrs": {
+ "symbols": [
+ "b"
+ ],
+ "keywords": [
+ "ring",
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+ "introduced": "given",
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+ }
+ },
+ "goal1": {
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+ "attrs": {
+ "side": "lean",
+ "reference_completeness": "syntactic_only"
+ },
+ "roles": {
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+ "name": "R",
+ "kind": "object",
+ "type": "Type*",
+ "attrs": {
+ "binder_kind": "implicit",
+ "classified_by": "sort",
+ "origin": "deterministic_signature_projection",
+ "instances": [
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+ ],
+ "references": [],
+ "reference_status": "syntactic_candidates"
+ }
+ },
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+ "kind": "object",
+ "type": "Type*",
+ "attrs": {
+ "binder_kind": "implicit",
+ "classified_by": "sort",
+ "origin": "deterministic_signature_projection",
+ "instances": [
+ "Ring S"
+ ],
+ "references": [],
+ "reference_status": "syntactic_candidates"
+ }
+ },
+ "f": {
+ "name": "f",
+ "kind": "object",
+ "type": "R → S",
+ "attrs": {
+ "binder_kind": "explicit",
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+ "origin": "deterministic_signature_projection",
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+ "S"
+ ],
+ "reference_status": "syntactic_candidates"
+ }
+ },
+ "goal": {
+ "name": "goal",
+ "kind": "goal",
+ "type": "Function.IsRingHom f ↔ (∀ a b : R, f (a + b) = f a + f b ∧ f (a * b) = f a * f b)",
+ "attrs": {
+ "exists_count": 0,
+ "forall_count": 1,
+ "is_iff": true,
+ "references": [
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+ "reference_status": "syntactic_candidates",
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+}{
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+ "kind": "simplex",
+ "attrs": {
+ "side": "source",
+ "goal_has_exists": true,
+ "reference_completeness": "partial"
+ },
+ "roles": {
+ "object1": {
+ "name": "object1",
+ "kind": "object",
+ "context": "cyclic group",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
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+ "group"
+ ],
+ "introduced": "given",
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+ "reference_status": "unknown",
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+ }
+ },
+ "object2": {
+ "name": "object2",
+ "kind": "object",
+ "context": "rectangle symmetry group",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "rectangle",
+ "symmetry",
+ "group"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "goal1": {
+ "name": "goal1",
+ "kind": "goal",
+ "context": "nonisomorphic groups of order four",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
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+ "groups",
+ "of",
+ "order",
+ "four"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
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+ }
+ }
+ }
+}Insufficient projected roles; no object roles were invented.
{
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+ "reference_completeness": "partial"
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+ "roles": {
+ "object1": {
+ "name": "G",
+ "kind": "object",
+ "context": "group",
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+ "kind": "object",
+ "context": "subset",
+ "attrs": {
+ "symbols": [
+ "H"
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+ "keywords": [
+ "subset"
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+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
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+ }
+ },
+ "fact1": {
+ "name": "H",
+ "kind": "fact",
+ "context": "nonempty",
+ "attrs": {
+ "symbols": [
+ "H"
+ ],
+ "keywords": [
+ "nonempty"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [
+ "object2"
+ ],
+ "reference_status": "explicit_symbol_candidates",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "goal1": {
+ "name": "goal1",
+ "kind": "goal",
+ "context": "subgroup iff group under inherited operation",
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+ "symbols": [],
+ "keywords": [
+ "subgroup",
+ "iff",
+ "group",
+ "under",
+ "inherited"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ }
+ }
+}{
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+ "attrs": {
+ "side": "lean",
+ "reference_completeness": "syntactic_only"
+ },
+ "roles": {
+ "G": {
+ "name": "G",
+ "kind": "object",
+ "type": "Type*",
+ "attrs": {
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+ "name": "t",
+ "kind": "object",
+ "type": "ℤ",
+ "attrs": {
+ "binder_kind": "explicit",
+ "classified_by": "default",
+ "origin": "deterministic_signature_projection",
+ "references": [],
+ "reference_status": "syntactic_candidates"
+ }
+ },
+ "h1": {
+ "name": "h1",
+ "kind": "fact",
+ "type": "b ≡ a^r [ZMOD n]",
+ "attrs": {
+ "binder_kind": "explicit",
+ "classified_by": "relation",
+ "origin": "deterministic_signature_projection",
+ "references": [
+ "a",
+ "b",
+ "n",
+ "r"
+ ],
+ "reference_status": "syntactic_candidates"
+ }
+ },
+ "h2": {
+ "name": "h2",
+ "kind": "fact",
+ "type": "r * s = 1 + n * t",
+ "attrs": {
+ "binder_kind": "explicit",
+ "classified_by": "relation",
+ "origin": "deterministic_signature_projection",
+ "references": [
+ "n",
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+ "s",
+ "t"
+ ],
+ "reference_status": "syntactic_candidates"
+ }
+ },
+ "goal": {
+ "name": "goal",
+ "kind": "goal",
+ "type": "b^s ≡ a [ZMOD n]",
+ "attrs": {
+ "exists_count": 0,
+ "forall_count": 0,
+ "is_iff": false,
+ "references": [
+ "a",
+ "b",
+ "n",
+ "s"
+ ],
+ "reference_status": "syntactic_candidates",
+ "origin": "deterministic_signature_projection"
+ }
+ }
+ }
+}{
+ "name": "schema:p0-f12735802ba0:f8d2e206681972927560be2c:source:v1",
+ "kind": "simplex",
+ "attrs": {
+ "side": "source",
+ "goal_has_exists": true,
+ "reference_completeness": "partial"
+ },
+ "roles": {
+ "object1": {
+ "name": "object1",
+ "kind": "object",
+ "context": "nonsquare rhombus",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "nonsquare",
+ "rhombus"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "object2": {
+ "name": "object2",
+ "kind": "object",
+ "context": "geometric symmetries",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "geometric",
+ "symmetries"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ },
+ "goal1": {
+ "name": "goal1",
+ "kind": "goal",
+ "context": "identify symmetry group size and classification",
+ "attrs": {
+ "symbols": [],
+ "keywords": [
+ "identify",
+ "symmetry",
+ "group",
+ "size",
+ "and"
+ ],
+ "introduced": "given",
+ "quantifier_status": "unreviewed",
+ "references": [],
+ "reference_status": "unknown",
+ "origin": "frozen_current_chat_annotation"
+ }
+ }
+ }
+}Insufficient projected roles; no object roles were invented.
{html.escape(content)}')
sections.append(f'Private annotation seeds, not independently validated mathematical statements. ' + '
Schema annotation seeds, not independently validated mathematical statements. ' 'A simplex joins the objects, assumptions and conclusion in its slots. ' - 'References are partial symbol/syntax candidates.
' + ''.join(sections) + '') + 'References are partial symbol/syntax candidates. ' + 'This review contains schema annotations and Lean signature text, not textbook passages ' + 'or full assistant judgment explanations.' + ''.join(sections) + '