{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:6PU2LQ6YFFZ4ELKEW4CIOMUKHS","short_pith_number":"pith:6PU2LQ6Y","canonical_record":{"source":{"id":"1612.09337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-29T22:42:00Z","cross_cats_sorted":[],"title_canon_sha256":"36cd96e61cd6c10889f1a3ba46cd44ea428d7cd239a6ef6bec63dabf6bd74e93","abstract_canon_sha256":"7a966cb5b11cb7b72abf69af7f0d4e0a428e69bc275478fd4fc18dc7fcc98a67"},"schema_version":"1.0"},"canonical_sha256":"f3e9a5c3d82973c22d44b70487328a3c947f2e2c87a70c7855f668fced58d531","source":{"kind":"arxiv","id":"1612.09337","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09337","created_at":"2026-05-18T00:53:39Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09337v2","created_at":"2026-05-18T00:53:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09337","created_at":"2026-05-18T00:53:39Z"},{"alias_kind":"pith_short_12","alias_value":"6PU2LQ6YFFZ4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6PU2LQ6YFFZ4ELKE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6PU2LQ6Y","created_at":"2026-05-18T12:30:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:6PU2LQ6YFFZ4ELKEW4CIOMUKHS","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09337","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-29T22:42:00Z","cross_cats_sorted":[],"title_canon_sha256":"36cd96e61cd6c10889f1a3ba46cd44ea428d7cd239a6ef6bec63dabf6bd74e93","abstract_canon_sha256":"7a966cb5b11cb7b72abf69af7f0d4e0a428e69bc275478fd4fc18dc7fcc98a67"},"schema_version":"1.0"},"canonical_sha256":"f3e9a5c3d82973c22d44b70487328a3c947f2e2c87a70c7855f668fced58d531","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:39.641827Z","signature_b64":"d+hXNd4NlVDIsutXasBHtVgxzRf/ri2ynSNb+8y/g7gZ9Y/jD3DvBpsbn96GBqYDvPc/7ZCXPDxqV5DnDR0aDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3e9a5c3d82973c22d44b70487328a3c947f2e2c87a70c7855f668fced58d531","last_reissued_at":"2026-05-18T00:53:39.641435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:39.641435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09337","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:53:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ORebSl8yveVErUIFJdla5+3G245ViD90rBmypUakyo2ix3L/HpyvUz2ufY5rW5K7uEK18y0uy5qyK3jIkoEmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:27:45.628202Z"},"content_sha256":"8e25323d4f9890c9ca52ef98d79cceb6ff00aa38b97b86878c9b8069932691a8","schema_version":"1.0","event_id":"sha256:8e25323d4f9890c9ca52ef98d79cceb6ff00aa38b97b86878c9b8069932691a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:6PU2LQ6YFFZ4ELKEW4CIOMUKHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transitivity of codimension one non-invertible conservative skew-products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Javier Correa, Martin Andersson","submitted_at":"2016-12-29T22:42:00Z","abstract_excerpt":"In this work we explore the problem of transitivity of volume-preserving skew-products endomorphisms of the n-torus. More specifically, we establish relationships between transitivity and the action induced by the skew-product in the fundamental group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09337","kind":"arxiv","version":2},"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":"2026-05-18T00:53:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mi4F10yKn7CtGgXeJBmIr5JROP4W5Bd8eaifiW5qU9+llakN2+9lDhkh8fFA5560IPqBC7wsyY3aR+BpoeGKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:27:45.628576Z"},"content_sha256":"d3c98a4b290f4d635fbf6649aca56809f9259fcc77e70c93b1362fa7fccfb3ab","schema_version":"1.0","event_id":"sha256:d3c98a4b290f4d635fbf6649aca56809f9259fcc77e70c93b1362fa7fccfb3ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6PU2LQ6YFFZ4ELKEW4CIOMUKHS/bundle.json","state_url":"https://pith.science/pith/6PU2LQ6YFFZ4ELKEW4CIOMUKHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6PU2LQ6YFFZ4ELKEW4CIOMUKHS/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":"2026-06-24T19:27:45Z","links":{"resolver":"https://pith.science/pith/6PU2LQ6YFFZ4ELKEW4CIOMUKHS","bundle":"https://pith.science/pith/6PU2LQ6YFFZ4ELKEW4CIOMUKHS/bundle.json","state":"https://pith.science/pith/6PU2LQ6YFFZ4ELKEW4CIOMUKHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6PU2LQ6YFFZ4ELKEW4CIOMUKHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6PU2LQ6YFFZ4ELKEW4CIOMUKHS","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":"7a966cb5b11cb7b72abf69af7f0d4e0a428e69bc275478fd4fc18dc7fcc98a67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-29T22:42:00Z","title_canon_sha256":"36cd96e61cd6c10889f1a3ba46cd44ea428d7cd239a6ef6bec63dabf6bd74e93"},"schema_version":"1.0","source":{"id":"1612.09337","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09337","created_at":"2026-05-18T00:53:39Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09337v2","created_at":"2026-05-18T00:53:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09337","created_at":"2026-05-18T00:53:39Z"},{"alias_kind":"pith_short_12","alias_value":"6PU2LQ6YFFZ4","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6PU2LQ6YFFZ4ELKE","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6PU2LQ6Y","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:d3c98a4b290f4d635fbf6649aca56809f9259fcc77e70c93b1362fa7fccfb3ab","target":"graph","created_at":"2026-05-18T00:53:39Z","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 work we explore the problem of transitivity of volume-preserving skew-products endomorphisms of the n-torus. More specifically, we establish relationships between transitivity and the action induced by the skew-product in the fundamental group.","authors_text":"Javier Correa, Martin Andersson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-29T22:42:00Z","title":"Transitivity of codimension one non-invertible conservative skew-products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09337","kind":"arxiv","version":2},"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":"sha256:8e25323d4f9890c9ca52ef98d79cceb6ff00aa38b97b86878c9b8069932691a8","target":"record","created_at":"2026-05-18T00:53:39Z","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":"7a966cb5b11cb7b72abf69af7f0d4e0a428e69bc275478fd4fc18dc7fcc98a67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-12-29T22:42:00Z","title_canon_sha256":"36cd96e61cd6c10889f1a3ba46cd44ea428d7cd239a6ef6bec63dabf6bd74e93"},"schema_version":"1.0","source":{"id":"1612.09337","kind":"arxiv","version":2}},"canonical_sha256":"f3e9a5c3d82973c22d44b70487328a3c947f2e2c87a70c7855f668fced58d531","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f3e9a5c3d82973c22d44b70487328a3c947f2e2c87a70c7855f668fced58d531","first_computed_at":"2026-05-18T00:53:39.641435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:39.641435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d+hXNd4NlVDIsutXasBHtVgxzRf/ri2ynSNb+8y/g7gZ9Y/jD3DvBpsbn96GBqYDvPc/7ZCXPDxqV5DnDR0aDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:39.641827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09337","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e25323d4f9890c9ca52ef98d79cceb6ff00aa38b97b86878c9b8069932691a8","sha256:d3c98a4b290f4d635fbf6649aca56809f9259fcc77e70c93b1362fa7fccfb3ab"],"state_sha256":"93e7ae181a6e51ddf2da4fd8f54c4a11a6d5094b94ec5afc59028b3adc0fb106"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"28UKlbK2qlWbsDSIgPfnqa/Kddm7fh5WMmNl5IpZeNsl5Atu1xYXam4bfPutvyJoWUdltq+t2XY4sgSNpWBGAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:27:45.630491Z","bundle_sha256":"8f3c8f9e7a99d85f246955b8e01b90893eadc8e667e565f59bafea07ba3996cf"}}