{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:JPIIMIDIUYOAE7K4TTKA6MLESM","short_pith_number":"pith:JPIIMIDI","canonical_record":{"source":{"id":"1012.4901","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-22T07:35:17Z","cross_cats_sorted":[],"title_canon_sha256":"e377ec6ee68f3a2e228704e0e8a79822b04e1609d06dcde696aa1e53f3b7d6b6","abstract_canon_sha256":"0873659f616b114a23f58472b4c098f04034746e1d33f4b4ff4747eb551d23f9"},"schema_version":"1.0"},"canonical_sha256":"4bd0862068a61c027d5c9cd40f31649311e83ab4a87c26e1299c7bb5ad5805c0","source":{"kind":"arxiv","id":"1012.4901","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4901","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4901v4","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4901","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"JPIIMIDIUYOA","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JPIIMIDIUYOAE7K4","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JPIIMIDI","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:JPIIMIDIUYOAE7K4TTKA6MLESM","target":"record","payload":{"canonical_record":{"source":{"id":"1012.4901","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-22T07:35:17Z","cross_cats_sorted":[],"title_canon_sha256":"e377ec6ee68f3a2e228704e0e8a79822b04e1609d06dcde696aa1e53f3b7d6b6","abstract_canon_sha256":"0873659f616b114a23f58472b4c098f04034746e1d33f4b4ff4747eb551d23f9"},"schema_version":"1.0"},"canonical_sha256":"4bd0862068a61c027d5c9cd40f31649311e83ab4a87c26e1299c7bb5ad5805c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:01.332052Z","signature_b64":"Y6hd+bvIMbnPDMEELF3lcSCtFqdbv5nZXuuaZ8YgyFc18ifoTMT4g79C+PAU5BhuoN6JKolw2P/1JIrydECQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bd0862068a61c027d5c9cd40f31649311e83ab4a87c26e1299c7bb5ad5805c0","last_reissued_at":"2026-05-18T04:26:01.331653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:01.331653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.4901","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JGYyKP0Mzp9Yaz2npeJZOh8LPsxGBqX9L5xTrYpWeTYOvFUsqZK4PGHX057SK2CQVInX1ZpKsPs09FiSYay+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:44:04.148991Z"},"content_sha256":"0903315c2aa17d40fd7de42b5a7ba736e44b2f3b9339e8ef93329d09914e838e","schema_version":"1.0","event_id":"sha256:0903315c2aa17d40fd7de42b5a7ba736e44b2f3b9339e8ef93329d09914e838e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:JPIIMIDIUYOAE7K4TTKA6MLESM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hypercyclic Abelian Affine Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Adlene Ayadi","submitted_at":"2010-12-22T07:35:17Z","abstract_excerpt":"In this paper, we give a characterization of hypercyclic abelian affine group G. If G is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by n affine maps on C^n has a dense orbit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4901","kind":"arxiv","version":4},"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":"2026-05-18T04:26:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zGXj1vMLGag5xPAWeS+u/CFVFUeLMT8z7hDvwuR8/2yymazqCx87FHDDJTK754IhJyTDvJrP5ra3AvSAgpIjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:44:04.149355Z"},"content_sha256":"9d3f2eab23b402facf1bbd3a902a3738c8912d7e3fbacf7cc93bd87db68aaa05","schema_version":"1.0","event_id":"sha256:9d3f2eab23b402facf1bbd3a902a3738c8912d7e3fbacf7cc93bd87db68aaa05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPIIMIDIUYOAE7K4TTKA6MLESM/bundle.json","state_url":"https://pith.science/pith/JPIIMIDIUYOAE7K4TTKA6MLESM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPIIMIDIUYOAE7K4TTKA6MLESM/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":"2026-06-23T16:44:04Z","links":{"resolver":"https://pith.science/pith/JPIIMIDIUYOAE7K4TTKA6MLESM","bundle":"https://pith.science/pith/JPIIMIDIUYOAE7K4TTKA6MLESM/bundle.json","state":"https://pith.science/pith/JPIIMIDIUYOAE7K4TTKA6MLESM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPIIMIDIUYOAE7K4TTKA6MLESM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JPIIMIDIUYOAE7K4TTKA6MLESM","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":"0873659f616b114a23f58472b4c098f04034746e1d33f4b4ff4747eb551d23f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-22T07:35:17Z","title_canon_sha256":"e377ec6ee68f3a2e228704e0e8a79822b04e1609d06dcde696aa1e53f3b7d6b6"},"schema_version":"1.0","source":{"id":"1012.4901","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.4901","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1012.4901v4","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.4901","created_at":"2026-05-18T04:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"JPIIMIDIUYOA","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JPIIMIDIUYOAE7K4","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JPIIMIDI","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:9d3f2eab23b402facf1bbd3a902a3738c8912d7e3fbacf7cc93bd87db68aaa05","target":"graph","created_at":"2026-05-18T04:26:01Z","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 give a characterization of hypercyclic abelian affine group G. If G is finitely generated, this characterization is explicit. We prove in particular that no abelian group generated by n affine maps on C^n has a dense orbit.","authors_text":"Adlene Ayadi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-22T07:35:17Z","title":"Hypercyclic Abelian Affine Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4901","kind":"arxiv","version":4},"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":"sha256:0903315c2aa17d40fd7de42b5a7ba736e44b2f3b9339e8ef93329d09914e838e","target":"record","created_at":"2026-05-18T04:26:01Z","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":"0873659f616b114a23f58472b4c098f04034746e1d33f4b4ff4747eb551d23f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-12-22T07:35:17Z","title_canon_sha256":"e377ec6ee68f3a2e228704e0e8a79822b04e1609d06dcde696aa1e53f3b7d6b6"},"schema_version":"1.0","source":{"id":"1012.4901","kind":"arxiv","version":4}},"canonical_sha256":"4bd0862068a61c027d5c9cd40f31649311e83ab4a87c26e1299c7bb5ad5805c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bd0862068a61c027d5c9cd40f31649311e83ab4a87c26e1299c7bb5ad5805c0","first_computed_at":"2026-05-18T04:26:01.331653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:01.331653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y6hd+bvIMbnPDMEELF3lcSCtFqdbv5nZXuuaZ8YgyFc18ifoTMT4g79C+PAU5BhuoN6JKolw2P/1JIrydECQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:01.332052Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.4901","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0903315c2aa17d40fd7de42b5a7ba736e44b2f3b9339e8ef93329d09914e838e","sha256:9d3f2eab23b402facf1bbd3a902a3738c8912d7e3fbacf7cc93bd87db68aaa05"],"state_sha256":"0aed3bdbdce7b570bdcfd95f1338a4c9f146c81ec24844763fb57e9784310b57"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8an7ZC1PhERqx4FIvA7ocaX8+Har0vc8yfxQELh4gByAvHkb4soGqj8J7VHdhcZhg3zgVKNSpy9jQPgrU3LtCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:44:04.151304Z","bundle_sha256":"7ebd8c6d75a843bba5fc8b58e0390d98d31af186010aea1f8f1c05fae087d910"}}