{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6YOUHUYPHVJSA2XUIMVEH3EKSH","short_pith_number":"pith:6YOUHUYP","canonical_record":{"source":{"id":"1104.2054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-11T20:17:57Z","cross_cats_sorted":[],"title_canon_sha256":"3aec60bedfd96e3fb2df536e0457622fa58b87a4c9b7b1edf66f08e8a3d2f566","abstract_canon_sha256":"a544505fa29fc4a545708ddeaf704801ec8fe3bc56f6214f27f9198b044e0683"},"schema_version":"1.0"},"canonical_sha256":"f61d43d30f3d53206af4432a43ec8a91e8fa027335d1ceac8ec5aa747578192b","source":{"kind":"arxiv","id":"1104.2054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2054","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2054v1","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2054","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"6YOUHUYPHVJS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6YOUHUYPHVJSA2XU","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6YOUHUYP","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6YOUHUYPHVJSA2XUIMVEH3EKSH","target":"record","payload":{"canonical_record":{"source":{"id":"1104.2054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-11T20:17:57Z","cross_cats_sorted":[],"title_canon_sha256":"3aec60bedfd96e3fb2df536e0457622fa58b87a4c9b7b1edf66f08e8a3d2f566","abstract_canon_sha256":"a544505fa29fc4a545708ddeaf704801ec8fe3bc56f6214f27f9198b044e0683"},"schema_version":"1.0"},"canonical_sha256":"f61d43d30f3d53206af4432a43ec8a91e8fa027335d1ceac8ec5aa747578192b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:35.956583Z","signature_b64":"vcq8WF4Md3VP9cm5rQ1OmDoZoijwWy3iIDHmiZthvxemYbz9MUiawOgCtUa3JgF+9pOGL2fjeMg96X99JUvYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f61d43d30f3d53206af4432a43ec8a91e8fa027335d1ceac8ec5aa747578192b","last_reissued_at":"2026-05-18T04:24:35.955987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:35.955987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.2054","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":"2026-05-18T04:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E4HdmbnO3PbnVD2McxBiiHNxNfLPyuBhwXaO/PG22Z2FNS6W7y1zpZoPT+61nWDT6AORmFAe8EJHn5p2H04YBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:52:29.224661Z"},"content_sha256":"d546b1f6ed68ea27f7b78fb0a9a65a715cf5b9a05d3097e5ae1a7cae90e8a288","schema_version":"1.0","event_id":"sha256:d546b1f6ed68ea27f7b78fb0a9a65a715cf5b9a05d3097e5ae1a7cae90e8a288"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6YOUHUYPHVJSA2XUIMVEH3EKSH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of non abelian affine homotheties group of C^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adlene Ayadi, Yahya N'Dao","submitted_at":"2011-04-11T20:17:57Z","abstract_excerpt":"In this paper we study the action of non abelian subgroup G generated by affine homotheties on C^n. We prove that there exist a subgroup H of C\\{0}, a G-invariant affine subspace E of C^n and b in E such that the closure of any orbit G(z) is equal to H(z-a)+E, z in C^n. In particular, every orbit in E is dense in it. Moreover, if the complementary U=C^n \\E is non empty, every orbit of U is minimal in it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2054","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":"2026-05-18T04:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g8FOzT0FoOS7w4aKqxzyHMV6sdTf4odmiXZRYRAgg1XwBcELI5btcUOQjyW8ku9snUAOeyxZy2pg1pkjtUlSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:52:29.225005Z"},"content_sha256":"72e87d89ac2271a1b0144cc4c21323fd551f6475429dba4a09b9002a7d190ea8","schema_version":"1.0","event_id":"sha256:72e87d89ac2271a1b0144cc4c21323fd551f6475429dba4a09b9002a7d190ea8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YOUHUYPHVJSA2XUIMVEH3EKSH/bundle.json","state_url":"https://pith.science/pith/6YOUHUYPHVJSA2XUIMVEH3EKSH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YOUHUYPHVJSA2XUIMVEH3EKSH/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":"2026-06-23T14:52:29Z","links":{"resolver":"https://pith.science/pith/6YOUHUYPHVJSA2XUIMVEH3EKSH","bundle":"https://pith.science/pith/6YOUHUYPHVJSA2XUIMVEH3EKSH/bundle.json","state":"https://pith.science/pith/6YOUHUYPHVJSA2XUIMVEH3EKSH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YOUHUYPHVJSA2XUIMVEH3EKSH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6YOUHUYPHVJSA2XUIMVEH3EKSH","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":"a544505fa29fc4a545708ddeaf704801ec8fe3bc56f6214f27f9198b044e0683","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-11T20:17:57Z","title_canon_sha256":"3aec60bedfd96e3fb2df536e0457622fa58b87a4c9b7b1edf66f08e8a3d2f566"},"schema_version":"1.0","source":{"id":"1104.2054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2054","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2054v1","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2054","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"6YOUHUYPHVJS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6YOUHUYPHVJSA2XU","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6YOUHUYP","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:72e87d89ac2271a1b0144cc4c21323fd551f6475429dba4a09b9002a7d190ea8","target":"graph","created_at":"2026-05-18T04:24:35Z","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 paper we study the action of non abelian subgroup G generated by affine homotheties on C^n. We prove that there exist a subgroup H of C\\{0}, a G-invariant affine subspace E of C^n and b in E such that the closure of any orbit G(z) is equal to H(z-a)+E, z in C^n. In particular, every orbit in E is dense in it. Moreover, if the complementary U=C^n \\E is non empty, every orbit of U is minimal in it.","authors_text":"Adlene Ayadi, Yahya N'Dao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-11T20:17:57Z","title":"Dynamics of non abelian affine homotheties group of C^n"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2054","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:d546b1f6ed68ea27f7b78fb0a9a65a715cf5b9a05d3097e5ae1a7cae90e8a288","target":"record","created_at":"2026-05-18T04:24:35Z","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":"a544505fa29fc4a545708ddeaf704801ec8fe3bc56f6214f27f9198b044e0683","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-04-11T20:17:57Z","title_canon_sha256":"3aec60bedfd96e3fb2df536e0457622fa58b87a4c9b7b1edf66f08e8a3d2f566"},"schema_version":"1.0","source":{"id":"1104.2054","kind":"arxiv","version":1}},"canonical_sha256":"f61d43d30f3d53206af4432a43ec8a91e8fa027335d1ceac8ec5aa747578192b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f61d43d30f3d53206af4432a43ec8a91e8fa027335d1ceac8ec5aa747578192b","first_computed_at":"2026-05-18T04:24:35.955987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:35.955987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vcq8WF4Md3VP9cm5rQ1OmDoZoijwWy3iIDHmiZthvxemYbz9MUiawOgCtUa3JgF+9pOGL2fjeMg96X99JUvYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:35.956583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d546b1f6ed68ea27f7b78fb0a9a65a715cf5b9a05d3097e5ae1a7cae90e8a288","sha256:72e87d89ac2271a1b0144cc4c21323fd551f6475429dba4a09b9002a7d190ea8"],"state_sha256":"c0a0e4a3e6708419ed8e2691dd84ddb795a3e1bccd8002017453ef714a3afe05"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UG1ALjoJkqeub9ghO2B2iPB6j9lylEyD5qEyP/by2zgduVVH2gWnsRmAk2QwvNkeiTX712wSUKgMWoOHBVMbCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:52:29.226910Z","bundle_sha256":"f690f857db71edd52fa531d0a1a54561a5bc45fadd4bde70577e05819b06ec02"}}