{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:3R7EL2S6RNK3WORHT3332DG3W4","short_pith_number":"pith:3R7EL2S6","schema_version":"1.0","canonical_sha256":"dc7e45ea5e8b55bb3a279ef7bd0cdbb72d1fb2a01189717454c9a19b08e7c496","source":{"kind":"arxiv","id":"2106.01470","version":1},"attestation_state":"computed","paper":{"title":"All-orders asymptotics of tensor model observables from symmetries of restricted partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"hep-th","authors_text":"Joseph Ben Geloun, Sanjaye Ramgoolam","submitted_at":"2021-06-02T21:10:06Z","abstract_excerpt":"The counting of the dimension of the space of $U(N) \\times U(N) \\times U(N)$ polynomial invariants of a complex $3$-index tensor as a function of degree $n$ is known in terms of a sum of squares of Kronecker coefficients. For $n \\le N$, the formula can be expressed in terms of a sum of symmetry factors of partitions of $n$ denoted $Z_3(n)$. We derive the large $n$ all-orders asymptotic formula for $ Z_3(n)$ making contact with high order results previously obtained numerically. The derivation relies on the dominance in the sum, of partitions with many parts of length $1$. The dominance of othe"},"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":"2106.01470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-06-02T21:10:06Z","cross_cats_sorted":["math.CO","math.RT"],"title_canon_sha256":"fc748b7a4659477f87be68c1db987d3d84f3a1eb3368f5195e35593ae1a6337a","abstract_canon_sha256":"b71804cb792b23d6f2fdb42772d97f11e3e9c0e5ee564a4613fffdff5e985716"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:17:59.313345Z","signature_b64":"03UktTihsdBsCuU6plkoddbDsv+MRKImVMhjWkUSMBAVdaeTdUxWi+c32N/ce2de+rNImGKW/aIqw0jsD6HXAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc7e45ea5e8b55bb3a279ef7bd0cdbb72d1fb2a01189717454c9a19b08e7c496","last_reissued_at":"2026-07-05T05:17:59.312968Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:17:59.312968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"All-orders asymptotics of tensor model observables from symmetries of restricted partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RT"],"primary_cat":"hep-th","authors_text":"Joseph Ben Geloun, Sanjaye Ramgoolam","submitted_at":"2021-06-02T21:10:06Z","abstract_excerpt":"The counting of the dimension of the space of $U(N) \\times U(N) \\times U(N)$ polynomial invariants of a complex $3$-index tensor as a function of degree $n$ is known in terms of a sum of squares of Kronecker coefficients. For $n \\le N$, the formula can be expressed in terms of a sum of symmetry factors of partitions of $n$ denoted $Z_3(n)$. We derive the large $n$ all-orders asymptotic formula for $ Z_3(n)$ making contact with high order results previously obtained numerically. The derivation relies on the dominance in the sum, of partitions with many parts of length $1$. The dominance of othe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.01470","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.01470/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2106.01470","created_at":"2026-07-05T05:17:59.313028+00:00"},{"alias_kind":"arxiv_version","alias_value":"2106.01470v1","created_at":"2026-07-05T05:17:59.313028+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.01470","created_at":"2026-07-05T05:17:59.313028+00:00"},{"alias_kind":"pith_short_12","alias_value":"3R7EL2S6RNK3","created_at":"2026-07-05T05:17:59.313028+00:00"},{"alias_kind":"pith_short_16","alias_value":"3R7EL2S6RNK3WORH","created_at":"2026-07-05T05:17:59.313028+00:00"},{"alias_kind":"pith_short_8","alias_value":"3R7EL2S6","created_at":"2026-07-05T05:17:59.313028+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/3R7EL2S6RNK3WORHT3332DG3W4","json":"https://pith.science/pith/3R7EL2S6RNK3WORHT3332DG3W4.json","graph_json":"https://pith.science/api/pith-number/3R7EL2S6RNK3WORHT3332DG3W4/graph.json","events_json":"https://pith.science/api/pith-number/3R7EL2S6RNK3WORHT3332DG3W4/events.json","paper":"https://pith.science/paper/3R7EL2S6"},"agent_actions":{"view_html":"https://pith.science/pith/3R7EL2S6RNK3WORHT3332DG3W4","download_json":"https://pith.science/pith/3R7EL2S6RNK3WORHT3332DG3W4.json","view_paper":"https://pith.science/paper/3R7EL2S6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2106.01470&json=true","fetch_graph":"https://pith.science/api/pith-number/3R7EL2S6RNK3WORHT3332DG3W4/graph.json","fetch_events":"https://pith.science/api/pith-number/3R7EL2S6RNK3WORHT3332DG3W4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3R7EL2S6RNK3WORHT3332DG3W4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3R7EL2S6RNK3WORHT3332DG3W4/action/storage_attestation","attest_author":"https://pith.science/pith/3R7EL2S6RNK3WORHT3332DG3W4/action/author_attestation","sign_citation":"https://pith.science/pith/3R7EL2S6RNK3WORHT3332DG3W4/action/citation_signature","submit_replication":"https://pith.science/pith/3R7EL2S6RNK3WORHT3332DG3W4/action/replication_record"}},"created_at":"2026-07-05T05:17:59.313028+00:00","updated_at":"2026-07-05T05:17:59.313028+00:00"}