{"format":3,"method":"deterministic","version":"153b95314adb","generated_at":"2026-10-28T13:51:41.433411Z","reason":null,"reason_detail":null,"provenance":"verificada_contra_la_fuente","claims":[{"id":"S1","kind":"enunciado","fact_id":"A5","value":null,"said_as":"Two individuals, a and b. Group them every way: nothing, a, b, both. Then group those groups. Repeated, that step turns a graph of pairs into groups of groups.","text":"Example from the source: if V = {a, b}, then P(V) = {∅, a, b, {a, b}}.","period":null,"said_in":[{"scene":0,"second":null},{"scene":4,"second":null}],"owner_scene":0,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S2","kind":"enunciado","fact_id":"A6","value":null,"said_as":"Two individuals, a and b. Group them every way: nothing, a, b, both. Then group those groups. Repeated, that step turns a graph of pairs into groups of groups.","text":"The n-power set is defined recursively: P¹(V) ≡ P(V); P²(V) = P(P(V)); and in general P^(n+1)(V) = P(P^n(V)), for integer n ≥ 1.","period":null,"said_in":[{"scene":0,"second":null},{"scene":6,"second":null}],"owner_scene":0,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S3","kind":"enunciado","fact_id":"A27","value":null,"said_as":"Two individuals, a and b. Group them every way: nothing, a, b, both. Then group those groups. Repeated, that step turns a graph of pairs into groups of groups.","text":"The n-SuperHyperGraph uses n-SuperVertices (groups of groups of groups, etc.) and n-SuperHyperEdges (edges connecting groups of groups of groups, etc.) to describe complex reality.","period":null,"said_in":[{"scene":0,"second":null},{"scene":7,"second":null}],"owner_scene":0,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Introduction to the n-SuperHyperGraph - the most general form of graph today","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph.pdf","doi":"10.5281/zenodo.6096894","as_of":null}},{"id":"S4","kind":"enunciado","fact_id":"N2","value":null,"said_as":"Two individuals, a and b. Group them every way: nothing, a, b, both. Then group those groups. Repeated, that step turns a graph of pairs into groups of groups.","text":"To illustrate the power-set explosion, the 2020 article takes the two-element set V = {a, b} and computes P(V) = {∅, a, b, {a,b}} — four elements. It then computes P²(V) = P(P(V)) in full, listing every subset of those four elements, arriving at a set whose members include singletons, pairs, triples, and the full set — groups of groups built from just two individuals.","period":null,"said_in":[{"scene":0,"second":null},{"scene":6,"second":null}],"owner_scene":0,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":"2020"}},{"id":"S5","kind":"enunciado","fact_id":"A21","value":null,"said_as":"Florentin Smarandache, University of New Mexico, Gallup, calls the n-SuperHyperGraph “the most general form of graph today, designed in order to catch our complex real world”.","text":"The n-SuperHyperGraph is described by the 2022 article as 'the most general form of graph today, designed in order to catch our complex real world.'","period":null,"said_in":[{"scene":1,"second":null},{"scene":15,"second":null}],"owner_scene":1,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Introduction to the n-SuperHyperGraph - the most general form of graph today","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph.pdf","doi":"10.5281/zenodo.6096894","as_of":null}},{"id":"S6","kind":"enunciado","fact_id":"N6","value":null,"said_as":"Florentin Smarandache, University of New Mexico, Gallup, calls the n-SuperHyperGraph “the most general form of graph today, designed in order to catch our complex real world”.","text":"The 2022 short note — two and a half journal pages — opens by recalling the 2019 and 2020 concepts and closes with the sentence: 'The n-SuperHyperGraph is the most general form of graph today, designed in order to catch our complex real world.' It adds to the catalogue the Neutrosophic Directed Graph (partially directed, partially undirected, partially indeterminate in direction) and the Loop, and formally defines the n-SuperVertex and n-SuperHyperEdge for arbitrary n.","period":null,"said_in":[{"scene":1,"second":null},{"scene":11,"second":null}],"owner_scene":1,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Introduction to the n-SuperHyperGraph - the most general form of graph today","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph.pdf","doi":"10.5281/zenodo.6096894","as_of":"2022"}},{"id":"S7","kind":"enunciado","fact_id":"A1","value":null,"said_as":"A classical graph joins dots in pairs. A HyperGraph wraps three or more. Each dot is still one individual, in a world of complex groups.","text":"The classical graph connects vertices pairwise; the hypergraph extends this by adding HyperEdges that connect three or more single vertices.","period":null,"said_in":[{"scene":2,"second":null}],"owner_scene":2,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-)HyperAlgebra","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S8","kind":"enunciado","fact_id":"A2","value":null,"said_as":"A classical graph joins dots in pairs. A HyperGraph wraps three or more. Each dot is still one individual, in a world of complex groups.","text":"In our world we encounter complex and sophisticated groups of individuals and complex and sophisticated connections between them — this is the stated motivation for extending the graph model.","period":null,"said_in":[{"scene":2,"second":null}],"owner_scene":2,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S9","kind":"enunciado","fact_id":"A3","value":null,"said_as":"A team folds into one node: the SuperVertex, a group of vertices put all together. An organization, a club, a city, a country.","text":"A SuperVertex is a group of vertices put all together; it may represent a group (organization, team, club, city, country, etc.) of many individuals.","period":null,"said_in":[{"scene":3,"second":null},{"scene":15,"second":null}],"owner_scene":3,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S10","kind":"enunciado","fact_id":"A4","value":null,"said_as":"These vertices live in the power set, P of V: every subset, the empty set and V itself included. For a and b: empty, a, b, the pair.","text":"A SuperHyperGraph (SHG) is an ordered pair SHG = (G ⊆ P(V), E ⊆ P(V)), where P(V) is the power set of V — all subsets of V, including the empty set and the whole set V.","period":null,"said_in":[{"scene":4,"second":null},{"scene":5,"second":null}],"owner_scene":4,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S11","kind":"enunciado","fact_id":"A7","value":null,"said_as":"The n-SuperHyperGraph draws vertices and edges from that n-power set: groups of groups of groups. With n equal to one: the SuperHyperGraph.","text":"The n-SuperHyperGraph (n-SHG) is an ordered pair n-SHG = (Gn ⊆ Pn(V), En ⊆ Pn(V)), where Pn(V) is the n-power set of the set V, for integer n ≥ 1.","period":null,"said_in":[{"scene":7,"second":null}],"owner_scene":7,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S12","kind":"enunciado","fact_id":"A8","value":null,"said_as":"The n-SuperHyperGraph draws vertices and edges from that n-power set: groups of groups of groups. With n equal to one: the SuperHyperGraph.","text":"When n = 1, the 1-SuperHyperGraph is called simply SuperHyperGraph, because only the first power set of V, P(V), is used.","period":null,"said_in":[{"scene":7,"second":null}],"owner_scene":7,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Introduction to the n-SuperHyperGraph - the most general form of graph today","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph.pdf","doi":"10.5281/zenodo.6096894","as_of":null}},{"id":"S13","kind":"enunciado","fact_id":"A9","value":null,"said_as":"Its vertices: the classical SingleVertex, the SuperVertex, and the IndeterminateVertex, unclear or unknown, an unfilled dot.","text":"Catalogue of SHG-vertex types: SingleVertex (the classical one), SuperVertex (a subset of many vertices), IndeterminateVertex (unclear, unknown), and NullVertex (vertex that has no elements).","period":null,"said_in":[{"scene":8,"second":null},{"scene":9,"second":null},{"scene":15,"second":null}],"owner_scene":8,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S14","kind":"enunciado","fact_id":"A11","value":null,"said_as":"Its vertices: the classical SingleVertex, the SuperVertex, and the IndeterminateVertex, unclear or unknown, an unfilled dot.","text":"The IndeterminateVertex is represented in the source figure as a dot that is not filled in (IV9 in the example figure).","period":null,"said_in":[{"scene":8,"second":null}],"owner_scene":8,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S15","kind":"enunciado","fact_id":"N4","value":null,"said_as":"Its vertices: the classical SingleVertex, the SuperVertex, and the IndeterminateVertex, unclear or unknown, an unfilled dot.","text":"In the example figure of the 2020 article (Figure 1, a 2-SuperHyperGraph), three specific elements are called out in the caption: IE7,8 — an IndeterminateEdge between single vertices V7 and V8, drawn as a dotted curve; IV9 — an IndeterminateVertex, drawn as an unfilled dot; and ME5,6 — a MultiEdge, drawn as a double edge between single vertices V5 and V6.","period":null,"said_in":[{"scene":8,"second":null},{"scene":10,"second":null}],"owner_scene":8,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":"2020"}},{"id":"S16","kind":"enunciado","fact_id":"A10","value":null,"said_as":"And the NullVertex, with no elements: an abandoned house whose occupants have all left.","text":"The NullVertex example given by the source: an abandoned house whose all occupants left.","period":null,"said_in":[{"scene":9,"second":null},{"scene":15,"second":null}],"owner_scene":9,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S17","kind":"enunciado","fact_id":"N3","value":null,"said_as":"And the NullVertex, with no elements: an abandoned house whose occupants have all left.","text":"The 2020 article introduces the NullVertex with a domestic image: an abandoned house whose all occupants have left. The house still exists as a node in the graph, but it contains no elements. Alongside it, the NullEdge is illustrated by two people who have no connections between them whatsoever — the edge exists as a named object, but it carries no link.","period":null,"said_in":[{"scene":9,"second":null},{"scene":10,"second":null}],"owner_scene":9,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":"2020"}},{"id":"S18","kind":"enunciado","fact_id":"A12","value":null,"said_as":"Its edges: SingleEdge, HyperEdge, SuperEdge, HyperSuperEdge, MultiEdge, Loop. The IndeterminateEdge, unclear or unknown, a dotted curve. The NullEdge: two people with no connections whatsoever.","text":"Catalogue of SHG-edge types: SingleEdge, HyperEdge (three or more single vertices), SuperEdge (two vertices, at least one SuperVertex), HyperSuperEdge (three or more vertices, at least one SuperVertex), MultiEdge (two or more edges between the same vertices, one per attribute value), IndeterminateEdge (unclear or unknown), NullEdge (no connection), and Loop.","period":null,"said_in":[{"scene":10,"second":null}],"owner_scene":10,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S19","kind":"enunciado","fact_id":"A13","value":null,"said_as":"Its edges: SingleEdge, HyperEdge, SuperEdge, HyperSuperEdge, MultiEdge, Loop. The IndeterminateEdge, unclear or unknown, a dotted curve. The NullEdge: two people with no connections whatsoever.","text":"The NullEdge example given by the source: two people that have no connections between them whatsoever.","period":null,"said_in":[{"scene":10,"second":null}],"owner_scene":10,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S20","kind":"enunciado","fact_id":"A14","value":null,"said_as":"Its edges: SingleEdge, HyperEdge, SuperEdge, HyperSuperEdge, MultiEdge, Loop. The IndeterminateEdge, unclear or unknown, a dotted curve. The NullEdge: two people with no connections whatsoever.","text":"The IndeterminateEdge is represented in the source figure as a dotted connecting curve (IE7,8 between single vertices V7 and V8 in the example figure).","period":null,"said_in":[{"scene":10,"second":null}],"owner_scene":10,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S21","kind":"enunciado","fact_id":"A15","value":null,"said_as":"An arrowhead, a bare line, a dotted stroke: the Neutrosophic Directed Graph, partly directed, partly undirected, partly indeterminate in direction.","text":"The 2022 article adds the Neutrosophic Directed Graph to the edge-type catalogue: partially directed, partially undirected, and partially indeterminate in direction.","period":null,"said_in":[{"scene":11,"second":null}],"owner_scene":11,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Introduction to the n-SuperHyperGraph - the most general form of graph today","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph.pdf","doi":"10.5281/zenodo.6096894","as_of":null}},{"id":"S22","kind":"enunciado","fact_id":"A17","value":null,"said_as":"Every vertex and edge carries many attributes: the Plithogenic n-SuperHyperGraph. Size: short, medium, long. Color: red, yellow. A fuzzy example: short 0.8, medium 0.2, long 0.1; red 0.3, yellow 0.5.","text":"A Plithogenic n-SuperHyperGraph (n-PSHG) is a n-SuperHyperGraph whose each n-SHG-vertex and each n-SHG-edge are characterized by many distinct attribute values (a1, a2, …, ap), p ≥ 1.","period":null,"said_in":[{"scene":12,"second":null}],"owner_scene":12,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S23","kind":"enunciado","fact_id":"A18","value":null,"said_as":"Every vertex and edge carries many attributes: the Plithogenic n-SuperHyperGraph. Size: short, medium, long. Color: red, yellow. A fuzzy example: short 0.8, medium 0.2, long 0.1; red 0.3, yellow 0.5.","text":"Plithogenic example from the source: attributes a1 = size (values: short, medium, long) and a2 = color (values: red, yellow); fuzzy degree example V1(a1{0.8, 0.2, 0.1}, a2{0.3, 0.5}).","period":null,"said_in":[{"scene":12,"second":null}],"owner_scene":12,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S24","kind":"enunciado","fact_id":"N5","value":null,"said_as":"Every vertex and edge carries many attributes: the Plithogenic n-SuperHyperGraph. Size: short, medium, long. Color: red, yellow. A fuzzy example: short 0.8, medium 0.2, long 0.1; red 0.3, yellow 0.5.","text":"The 2020 article takes vertices V1 and V2, each characterized by two attributes — a1 = size (values: short, medium, long) and a2 = color (values: red, yellow) — and shows three levels of edge representation: a SingleEdge treating both attributes together (Figure 2); a MultiEdge with one edge per attribute — top edge for size, bottom edge for color (Figure 3); and a Refined MultiEdge that splits the size edge into three sub-edges and the color edge into two sub-edges (Figure 4). The fuzzy degree example given is V1(a1{0.8, 0.2, 0.1}, a2{0.3, 0.5}).","period":null,"said_in":[{"scene":12,"second":null},{"scene":13,"second":null}],"owner_scene":12,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":"2020"}},{"id":"S25","kind":"enunciado","fact_id":"A16","value":null,"said_as":"One edge becomes a MultiEdge, one per attribute, then a Refined MultiEdge: three sub-edges for size, two for color. Degrees run from crisp to refined neutrosophic.","text":"The MultiEdge ME5,6 in the example figure is a double edge between single vertices V5 and V6; each attribute value generates one edge, so more attribute values produce more edges between the same vertices.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S26","kind":"enunciado","fact_id":"A19","value":null,"said_as":"One edge becomes a MultiEdge, one per attribute, then a Refined MultiEdge: three sub-edges for size, two for color. Degrees run from crisp to refined neutrosophic.","text":"The Refined MultiEdge splits the MultiEdge further: the edge for attribute a1 (size) is split into three sub-edges (for values short, medium, long), and the edge for attribute a2 (color) is split into two sub-edges (for values red, yellow).","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S27","kind":"enunciado","fact_id":"A20","value":null,"said_as":"One edge becomes a MultiEdge, one per attribute, then a Refined MultiEdge: three sub-edges for size, two for color. Degrees run from crisp to refined neutrosophic.","text":"The degrees of appurtenance of a vertex or edge to the Plithogenic n-SHG may be: crisp, fuzzy, intuitionistic fuzzy, picture fuzzy, spherical fuzzy, neutrosophic, or refined neutrosophic.","period":null,"said_in":[{"scene":13,"second":null}],"owner_scene":13,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Introduction to the n-SuperHyperGraph - the most general form of graph today","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph.pdf","doi":"10.5281/zenodo.6096894","as_of":null}},{"id":"S28","kind":"enunciado","fact_id":"A23","value":null,"said_as":"The same 2020 article extends HyperAlgebra into a triad. An operation well-defined for every n-tuple: n-ary HyperAlgebra. For some, indeterminate or outer-defined for others: NeutroHyperAlgebra. Outer-defined for all: AntiHyperAlgebra.","text":"The 2020 article extends classical HyperAlgebra to n-ary HyperAlgebra: a set S endowed with an n-ary HyperOperation *n mapping n-tuples of S into P(S), well-defined for all n-tuples.","period":null,"said_in":[{"scene":14,"second":null}],"owner_scene":14,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S29","kind":"enunciado","fact_id":"A24","value":null,"said_as":"The same 2020 article extends HyperAlgebra into a triad. An operation well-defined for every n-tuple: n-ary HyperAlgebra. For some, indeterminate or outer-defined for others: NeutroHyperAlgebra. Outer-defined for all: AntiHyperAlgebra.","text":"The neutrosophic triplet introduced in the 2020 article: (n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra). The NeutroHyperAlgebra has an operation well-defined for some n-tuples and indeterminate or outer-defined for others. The AntiHyperAlgebra has an operation outer-defined for all n-tuples.","period":null,"said_in":[{"scene":14,"second":null}],"owner_scene":14,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":null}},{"id":"S30","kind":"enunciado","fact_id":"A22","value":null,"said_as":"2019, the SuperVertex. 2020, recalled and improved. 2022, the claim of maximal generality. Read this way, a network holds its teams, its unknowns and its empty houses in one graph.","text":"History given by the sources: the SuperVertex was introduced in 2019, then the SuperHyperGraph was constructed on P(V), and further extended to the n-SuperHyperGraph built on P^n(V), in order to overcome the complex groups of individuals and the sophisticated connections between them.","period":null,"said_in":[{"scene":15,"second":null}],"owner_scene":15,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Introduction to the n-SuperHyperGraph - the most general form of graph today","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph.pdf","doi":"10.5281/zenodo.6096894","as_of":null}},{"id":"S31","kind":"enunciado","fact_id":"N1","value":null,"said_as":"2019, the SuperVertex. 2020, recalled and improved. 2022, the claim of maximal generality. Read this way, a network holds its teams, its unknowns and its empty houses in one graph.","text":"In 2019, working on Nidus Idearum Vol. 7, Smarandache writes down for the first time the SuperVertex — a group of vertices put all together — and from it builds the SuperHyperGraph on P(V) and then the n-SuperHyperGraph on P^n(V). The two ideas appear on pages 107-113 of that volume, alongside the neutrosophic triplet for n-ary HyperAlgebra on pages 104-106.","period":null,"said_in":[{"scene":15,"second":null}],"owner_scene":15,"backing":"respaldada_en_su_escena","on_screen":null,"citation":{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","as_of":"2019"}}],"sources":[{"title":"Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-)HyperAlgebra","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph-n-HyperAlgebra.pdf","doi":"10.5281/zenodo.3783103","authors":[],"role":"principal","read":true,"claims":["S1","S2","S4","S7","S8","S9","S10","S11","S13","S14","S15","S16","S17","S18","S19","S20","S22","S23","S24","S25","S26","S28","S29","S31"]},{"title":"Introduction to the n-SuperHyperGraph - the most general form of graph today","url":"https://fs.unm.edu/NSS/n-SuperHyperGraph.pdf","doi":"10.5281/zenodo.6096894","authors":["Florentin Smarandache"],"role":"declarada","read":true,"claims":["S3","S5","S6","S12","S21","S27","S30"]}],"summary":{"codex":"present","figures_total":0,"backed_in_scene":0,"derived":0,"unbacked":0,"context_only":0,"figures_on_screen":{"drawn":0,"approx":0,"withheld":0,"notShown":0},"plotted_values_approx":0,"plotted_values_withheld":0,"figures_outside_the_cut":0},"doi":null,"certifications":[],"claimsDigest":"e8bf8c10cab15577f82042ec5985cd9c421a2cbd351f885b97262b088f76f3fc"}