{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LMPME7YVMQAJLQ52A5Z5QXLTSE","short_pith_number":"pith:LMPME7YV","schema_version":"1.0","canonical_sha256":"5b1ec27f15640095c3ba0773d85d73912e9bcbe6b8981815bc794dbe1cac9de3","source":{"kind":"arxiv","id":"1808.07783","version":1},"attestation_state":"computed","paper":{"title":"From Kronecker to tableau pseudo-characters in tensor models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov, H. Itoyama","submitted_at":"2018-08-23T14:46:35Z","abstract_excerpt":"We present a brief summary of the recent discovery of direct tensorial analogue of characters. We distinguish three degrees of generalization: (1) $c$-number Kronecker characters made with the help of symmetric group characters and inheriting most of the nice properties of conventional Schur functions, except for forming a complete basis for the case of rank $r>2$ tensors: they are orthogonal, are eigenfunctions of appropriate cut-and-join operators and form a complete basis for the operators with non-zero Gaussian averages; (2) genuine matrix-valued tensorial quantities, forming an over-compl"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1808.07783","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-08-23T14:46:35Z","cross_cats_sorted":[],"title_canon_sha256":"3321db43f4e7b0c705c4cc3a709329094a62f5b105d3c7ae4a6992bc46554bc9","abstract_canon_sha256":"5c3d4cea7a07dd7f9fe3fdc79f9c0d3b482ca955e552bf60d52c5492743c3958"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:47.665690Z","signature_b64":"1nVEcEPJbpGe8XFZp3kaw6pYYG9Wu3vvLrvAx/RJHtRgWjzp9BmzAgLnCSAodUNlQFMSpNEcKO9y/OC2kMgPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b1ec27f15640095c3ba0773d85d73912e9bcbe6b8981815bc794dbe1cac9de3","last_reissued_at":"2026-05-17T23:58:47.665267Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:47.665267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From Kronecker to tableau pseudo-characters in tensor models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov, H. Itoyama","submitted_at":"2018-08-23T14:46:35Z","abstract_excerpt":"We present a brief summary of the recent discovery of direct tensorial analogue of characters. We distinguish three degrees of generalization: (1) $c$-number Kronecker characters made with the help of symmetric group characters and inheriting most of the nice properties of conventional Schur functions, except for forming a complete basis for the case of rank $r>2$ tensors: they are orthogonal, are eigenfunctions of appropriate cut-and-join operators and form a complete basis for the operators with non-zero Gaussian averages; (2) genuine matrix-valued tensorial quantities, forming an over-compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.07783","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1808.07783","created_at":"2026-05-17T23:58:47.665344+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.07783v1","created_at":"2026-05-17T23:58:47.665344+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.07783","created_at":"2026-05-17T23:58:47.665344+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMPME7YVMQAJ","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMPME7YVMQAJLQ52","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMPME7YV","created_at":"2026-05-18T12:32:37.024351+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LMPME7YVMQAJLQ52A5Z5QXLTSE","json":"https://pith.science/pith/LMPME7YVMQAJLQ52A5Z5QXLTSE.json","graph_json":"https://pith.science/api/pith-number/LMPME7YVMQAJLQ52A5Z5QXLTSE/graph.json","events_json":"https://pith.science/api/pith-number/LMPME7YVMQAJLQ52A5Z5QXLTSE/events.json","paper":"https://pith.science/paper/LMPME7YV"},"agent_actions":{"view_html":"https://pith.science/pith/LMPME7YVMQAJLQ52A5Z5QXLTSE","download_json":"https://pith.science/pith/LMPME7YVMQAJLQ52A5Z5QXLTSE.json","view_paper":"https://pith.science/paper/LMPME7YV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.07783&json=true","fetch_graph":"https://pith.science/api/pith-number/LMPME7YVMQAJLQ52A5Z5QXLTSE/graph.json","fetch_events":"https://pith.science/api/pith-number/LMPME7YVMQAJLQ52A5Z5QXLTSE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMPME7YVMQAJLQ52A5Z5QXLTSE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMPME7YVMQAJLQ52A5Z5QXLTSE/action/storage_attestation","attest_author":"https://pith.science/pith/LMPME7YVMQAJLQ52A5Z5QXLTSE/action/author_attestation","sign_citation":"https://pith.science/pith/LMPME7YVMQAJLQ52A5Z5QXLTSE/action/citation_signature","submit_replication":"https://pith.science/pith/LMPME7YVMQAJLQ52A5Z5QXLTSE/action/replication_record"}},"created_at":"2026-05-17T23:58:47.665344+00:00","updated_at":"2026-05-17T23:58:47.665344+00:00"}