{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:N5JUHCLERO4WPGMO2MK6ZDHYUG","short_pith_number":"pith:N5JUHCLE","canonical_record":{"source":{"id":"1609.01039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-05T07:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"0ea5a6b8f32f65c8db32842e8a1db395a279adfcf3609d30932bb07ab410bb4e","abstract_canon_sha256":"a64b2dec2edfcb0a49dfa34d45bc7d2dce0e2f3404db40c48d3996eca95b89de"},"schema_version":"1.0"},"canonical_sha256":"6f534389648bb967998ed315ec8cf8a180f26c7e2e20db0f8da9cc9c656a6a03","source":{"kind":"arxiv","id":"1609.01039","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01039","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01039v1","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01039","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"N5JUHCLERO4W","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N5JUHCLERO4WPGMO","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N5JUHCLE","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:N5JUHCLERO4WPGMO2MK6ZDHYUG","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-05T07:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"0ea5a6b8f32f65c8db32842e8a1db395a279adfcf3609d30932bb07ab410bb4e","abstract_canon_sha256":"a64b2dec2edfcb0a49dfa34d45bc7d2dce0e2f3404db40c48d3996eca95b89de"},"schema_version":"1.0"},"canonical_sha256":"6f534389648bb967998ed315ec8cf8a180f26c7e2e20db0f8da9cc9c656a6a03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:19.227837Z","signature_b64":"M1S0WTbpkNykSWe4vGiEPnwEGiF3gfW30Wdxhv9WKK3zpE7XkyyxuDQ2J7OUb6Sp5F1JZuIjcYYfpt0aS+aICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f534389648bb967998ed315ec8cf8a180f26c7e2e20db0f8da9cc9c656a6a03","last_reissued_at":"2026-05-18T01:06:19.227389Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:19.227389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01039","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L2nZhjxVy7yMFZVDrVHSfCBsKYdvOYNX0nqkh35ot+c6hw3nJfPeT5FHt2Z1MpEKu0rGgVWxEmHGR3x6+q1LCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:52:20.698756Z"},"content_sha256":"64868687d0fc5e9123dc1cc861488df4bbdf83124f815a3fc4138de9ffd48a8b","schema_version":"1.0","event_id":"sha256:64868687d0fc5e9123dc1cc861488df4bbdf83124f815a3fc4138de9ffd48a8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:N5JUHCLERO4WPGMO2MK6ZDHYUG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some properties of associated spaces with sub-Hankel determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hideyuki Ishi, Takeyoshi Kogiso","submitted_at":"2016-09-05T07:11:45Z","abstract_excerpt":"In this note, we show that the space associated with sub-Hankel determinant is a non-reductive, regular prehomogeneous vector space, and we give the multiplicative Legendre transforms of sub-Hankel determinants. Moreover we observe certain relations between $b$-functions of polarization of PVpolynomials and $b$-functions of sub-Hankel determinants, and give some formulas about sub-Hankel determinants whose components are orthogonal ponlynomials."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01039","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DcNR+Gs520e2ffAUFdLfBPb8yYkPT+uTt+lRTNZabsqUChSDRWSXeT4wPGJ4lWc5LN4KopO3gX0w/jexNpnzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T14:52:20.699471Z"},"content_sha256":"4381d221c96c7a5753340b54eeaca734c476e1650fb3e3d99bbed5ef9bedeb94","schema_version":"1.0","event_id":"sha256:4381d221c96c7a5753340b54eeaca734c476e1650fb3e3d99bbed5ef9bedeb94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N5JUHCLERO4WPGMO2MK6ZDHYUG/bundle.json","state_url":"https://pith.science/pith/N5JUHCLERO4WPGMO2MK6ZDHYUG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N5JUHCLERO4WPGMO2MK6ZDHYUG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-06T14:52:20Z","links":{"resolver":"https://pith.science/pith/N5JUHCLERO4WPGMO2MK6ZDHYUG","bundle":"https://pith.science/pith/N5JUHCLERO4WPGMO2MK6ZDHYUG/bundle.json","state":"https://pith.science/pith/N5JUHCLERO4WPGMO2MK6ZDHYUG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N5JUHCLERO4WPGMO2MK6ZDHYUG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N5JUHCLERO4WPGMO2MK6ZDHYUG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a64b2dec2edfcb0a49dfa34d45bc7d2dce0e2f3404db40c48d3996eca95b89de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-05T07:11:45Z","title_canon_sha256":"0ea5a6b8f32f65c8db32842e8a1db395a279adfcf3609d30932bb07ab410bb4e"},"schema_version":"1.0","source":{"id":"1609.01039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01039","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01039v1","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01039","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"N5JUHCLERO4W","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N5JUHCLERO4WPGMO","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N5JUHCLE","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:4381d221c96c7a5753340b54eeaca734c476e1650fb3e3d99bbed5ef9bedeb94","target":"graph","created_at":"2026-05-18T01:06:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this note, we show that the space associated with sub-Hankel determinant is a non-reductive, regular prehomogeneous vector space, and we give the multiplicative Legendre transforms of sub-Hankel determinants. Moreover we observe certain relations between $b$-functions of polarization of PVpolynomials and $b$-functions of sub-Hankel determinants, and give some formulas about sub-Hankel determinants whose components are orthogonal ponlynomials.","authors_text":"Hideyuki Ishi, Takeyoshi Kogiso","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-05T07:11:45Z","title":"Some properties of associated spaces with sub-Hankel determinants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01039","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:64868687d0fc5e9123dc1cc861488df4bbdf83124f815a3fc4138de9ffd48a8b","target":"record","created_at":"2026-05-18T01:06:19Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a64b2dec2edfcb0a49dfa34d45bc7d2dce0e2f3404db40c48d3996eca95b89de","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-09-05T07:11:45Z","title_canon_sha256":"0ea5a6b8f32f65c8db32842e8a1db395a279adfcf3609d30932bb07ab410bb4e"},"schema_version":"1.0","source":{"id":"1609.01039","kind":"arxiv","version":1}},"canonical_sha256":"6f534389648bb967998ed315ec8cf8a180f26c7e2e20db0f8da9cc9c656a6a03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f534389648bb967998ed315ec8cf8a180f26c7e2e20db0f8da9cc9c656a6a03","first_computed_at":"2026-05-18T01:06:19.227389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:19.227389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M1S0WTbpkNykSWe4vGiEPnwEGiF3gfW30Wdxhv9WKK3zpE7XkyyxuDQ2J7OUb6Sp5F1JZuIjcYYfpt0aS+aICA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:19.227837Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64868687d0fc5e9123dc1cc861488df4bbdf83124f815a3fc4138de9ffd48a8b","sha256:4381d221c96c7a5753340b54eeaca734c476e1650fb3e3d99bbed5ef9bedeb94"],"state_sha256":"bddf2452b705c3fc968994c9f4960c098ac7329f8edc88d0d6473a90f183962a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EyH/aOYx3H2a7xFmBKR7KkKN4zY6YBYqpLLZYMG2O/Z0HhK7W23NoGt6Qg4rmLrDbySVcj3FdFbqS3zg50lJDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T14:52:20.703594Z","bundle_sha256":"bd38dc44509cc543b422586634e2b0e60e2a66ca3afad62d5ca1d88f8dcfe8fc"}}