{"arxiv_id":"hep-th/9910030","incoming":{"papers":69,"sentences":102,"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":6,"sentences":6,"quotes":[{"arxiv_id":"1504.05946","title":"Contractions from $osp(1|32) \\oplus osp(1|32)$ to the M-theory superalgebra extended by additional fermionic generators","url":"/paper/1504.05946","section":"Introduction","sentence":"Using the relation ([ref]) in ([ref]), we obtain the commutators and anti-commutators relations [ref] [ [Z_a,Z_b] = 1/8 J_ab , [equation] i.e., apart from the exterior product of two one-forms, there is a power of $λ$ that depends on the scaling factors of [ref], and a coefficient (structure constant) that depends on the parameters of the linear combination [ref].","intent_p":0.9,"contests_p":null},{"arxiv_id":"0906.4699","title":"AdS_4 x CP^3 superstring in the light-cone gauge","url":"/paper/0906.4699","section":"The supermembrane on $AdS_4×S^7$ and its reduction to the $D=10$ IIA superstring on $AdS_4×ℂℙ^3$","sentence":"Using that $dH_(4)=0$ the variation of $H_(4)$ reduces to [equation] Substituting ([ref]) into ([ref]) and performing the $γ-$matrix rearrangements using the formulae adduced in [ref] yields the expression for the Wess-Zumino 4-form variation [equation] It has to be canceled by the $κ-$variation of the kinetic term of ([ref]) that is defined by the variation of the induced metric determinant $g^(3)$.","intent_p":0.97,"contests_p":null},{"arxiv_id":"1704.05949","title":"Generalised Calibrations in AdS backgrounds from Exceptional Sasaki-Einstein Structures","url":"/paper/1704.05949","section":"M-theory on AdS5 x M6","sentence":"For the internal part we take as reference [ref] and we write all the gamma matrices as tensor products of Pauli matrices","intent_p":0.9,"contests_p":null},{"arxiv_id":"2412.04390","title":"Index and localization for type B superconformal mechanics on singular spaces","url":"/paper/2412.04390","section":"Review of $N=2 B$ superconformal sigma models","sentence":"In what follows we will use the explicit representation for the Dirac matrices of [ref] , namely ^m = 2 ^3⊗…^3 ⊗^+ ⊗1 …⊗1, ^m̅ = 2 ^3⊗…^3 ⊗^- ⊗1 …⊗1, where the $^±$ entry is in the $m$-th position.","intent_p":0.89,"contests_p":null},{"arxiv_id":"1908.04788","title":"de Sitter Vacua from Ten Dimensions","url":"/paper/1908.04788","section":"Ten-dimensional spinor ansatz","sentence":"The ten-dimensional gamma matrices decompose as [equation] For gamma matrices and spinor manipulations, we use the conventions of [ref] , [equation] Under this decomposition, a ten-dimensional Weyl spinor decomposes as $16_+ ↦(2_+⊗4_+)⊕(2_-⊗4_-)$, where subscripts denote chirality.","intent_p":0.85,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":2,"sentences":2,"quotes":[{"arxiv_id":"1802.06413","title":"New spinor classes on the Graf-Clifford algebra","url":"/paper/1802.06413","section":"Pinors, spinors and Fierz identities","sentence":"The values of $σ(B)$ and $τ(B)$ are given onto fibers in Refs. [ref] , according to the following tables:","intent_p":0.9,"contests_p":null},{"arxiv_id":"2108.05109","title":"Supersymmetry algebras in arbitrary signature and their R-symmetry groups","url":"/paper/2108.05109","section":"Summary Table","sentence":"The invariants were taken from [ref] , which uses the notation $ϵ= - σ$ and $η= -τ$.","intent_p":0.99,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":21,"sentences":26,"quotes":[{"arxiv_id":"2607.11150","title":"Conjugate Boundary Conditions, Kaluza-Klein Fermions, and an Extended Seesaw Model","url":"/paper/2607.11150","section":"Introduction","sentence":"However, at first glance, the conventional Majorana-type seesaw seems to be nontrivial in a five-dimensional theory because of the well-known fact that the conventional Majorana condition cannot be imposed on a single five-dimensional spinor[The symplectic Majorana condition is another way to reproduce a Majorana fermion; see, e.g., Refs. [ref] .","intent_p":0.8,"contests_p":null},{"arxiv_id":"2108.05109","title":"Supersymmetry algebras in arbitrary signature and their R-symmetry groups","url":"/paper/2108.05109","section":"Clifford and spinor representations","sentence":"Our presentation is partially based on [ref] , whose conventions we follow except for some tweaks where we follow [ref] .","intent_p":0.87,"contests_p":null},{"arxiv_id":"1105.4852","title":"AdS_5 Supersymmetry in N=1 Superspace","url":"/paper/1105.4852","section":"Warped Superspace","sentence":"The AdS$_5$ superalgebra is SU(2,2$|$1), which has the following commutation relations [ref] :","intent_p":0.85,"contests_p":null},{"arxiv_id":"1609.00490","title":"SU(2|2) supersymmetric mechanics","url":"/paper/1609.00490","section":"Superconformal algebra $osp(4^* |4)$ and its $su(2|2)$ subalgebra","sentence":"There are four superconformal $N= 8$, $d=1$ algebras [ref] : $osp(8|2)$, $su(1,1|4)$, $F(4)$, $osp(4^* |4)$.","intent_p":0.82,"contests_p":null},{"arxiv_id":"1802.04733","title":"Supersymmetric objects in gauged supergravities","url":"/paper/1802.04733","section":"Killing Spinors and Supersymmetry of Classical Solutions","sentence":"More precisely a set of Killing spinors is a set of $SUSY$ invariant spinors for which the supersymmetry transformations leaves a particular solution invariant[This section is partially based on [ref] .].","intent_p":0.96,"contests_p":null}]}],"unlabelled_sentences":68},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":{"arxiv_id":"hep-th/9910030","kind":"model","paper_version":7,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T20:20:55+00:00","loaded_at":"2026-10-28T01:03:47.895948+00:00","evidence":"substantial","account":[],"groups":[{"kind":"method_or_tool","label":"Uses its method or tool","papers":4,"entries":[{"p":0.97,"quote":null,"citing":[{"self":false,"year":2009,"title":"AdS_4 x CP^3 superstring in the light-cone gauge","arxiv_id":"0906.4699"}],"verified":true,"paraphrase":"Used the formulae given in this paper to rearrange gamma matrices and obtain the variation of the Wess-Zumino 4-form."},{"p":0.9,"quote":null,"citing":[{"self":false,"year":2017,"title":"Generalised Calibrations in AdS backgrounds from Exceptional Sasaki-Einstein Structures","arxiv_id":"1704.05949"}],"verified":true,"paraphrase":"Took this paper as reference for the internal part and wrote all the gamma matrices as tensor products of Pauli matrices."},{"p":0.89,"quote":null,"citing":[{"self":false,"year":2024,"title":"Index and localization for type B superconformal mechanics on singular spaces","arxiv_id":"2412.04390"}],"verified":true,"paraphrase":"Used the explicit representation for the Dirac matrices of this paper."},{"p":0.97,"quote":null,"citing":[{"self":false,"year":2017,"title":"BPS objects in D=7 supergravity and their M-theory origin","arxiv_id":"1707.06152"}],"verified":true,"paraphrase":"Adopted the explicit representation for the Clifford algebra given in this paper."}],"papers_all":5,"self_papers":0,"self_entries":[]},{"kind":"data_used","label":"Uses its data or values","papers":1,"entries":[{"p":0.99,"quote":null,"citing":[{"self":false,"year":2021,"title":"Supersymmetry algebras in arbitrary signature and their R-symmetry groups","arxiv_id":"2108.05109"}],"verified":true,"paraphrase":"Took the invariants from this paper, which uses the notation epsilon equals minus sigma and eta equals minus tau."}],"papers_all":2,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"data_used":2,"method_or_tool":5},"dropped":{"relied_on":0,"unknown_ids":0,"account_lines":0,"contest_vetoed":0,"below_threshold":0,"contest_drawback":0,"contest_without_basis":0,"contest_not_one_sentence":0,"contest_on_group_citation":0},"papers_read":23,"self_papers":2,"citing_papers":68,"sentences_read":26,"citing_sentences":101,"unambiguous_read":26,"typed_independent":7,"independent_papers":66,"by_kind_independent":{"data_used":2,"method_or_tool":5}},"input_sha256":"b7868be3f967ce339a04e9e7115df93687d75c987b821ec204d28041a5443824","method":"For a paper with five or more citing arXiv papers, Pith selected up to 40 citing sentences its citation classifier typed, read those whose citation markers point at this paper alone, and wrote one paraphrase for each later paper in each group, each resting on one sentence. A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"5 later papers by other authors are listed below: 4 used its method or tool and 1 used its data or values."},"_links":{"html":"https://pith.science/paper/hep-th/9910030"}}