{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:CEWHDU5WUCZIRD75K56ZDJPVNK","short_pith_number":"pith:CEWHDU5W","canonical_record":{"source":{"id":"1908.07635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-20T22:29:13Z","cross_cats_sorted":[],"title_canon_sha256":"1e31d2d39bbbd6e9851f5a309855419eb6d6bf3cca2e73f72a02d438e54be1cb","abstract_canon_sha256":"68d40b5d0d9f3b7e94141fdba570ef80b574476d727f789c2526efec0dc3856b"},"schema_version":"1.0"},"canonical_sha256":"112c71d3b6a0b2888ffd577d91a5f56a95d9f37d17ffd0977faa0a36a240c13b","source":{"kind":"arxiv","id":"1908.07635","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07635","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07635v1","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07635","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"CEWHDU5WUCZI","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_16","alias_value":"CEWHDU5WUCZIRD75","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_8","alias_value":"CEWHDU5W","created_at":"2026-07-04T23:58:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:CEWHDU5WUCZIRD75K56ZDJPVNK","target":"record","payload":{"canonical_record":{"source":{"id":"1908.07635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-20T22:29:13Z","cross_cats_sorted":[],"title_canon_sha256":"1e31d2d39bbbd6e9851f5a309855419eb6d6bf3cca2e73f72a02d438e54be1cb","abstract_canon_sha256":"68d40b5d0d9f3b7e94141fdba570ef80b574476d727f789c2526efec0dc3856b"},"schema_version":"1.0"},"canonical_sha256":"112c71d3b6a0b2888ffd577d91a5f56a95d9f37d17ffd0977faa0a36a240c13b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:59.842803Z","signature_b64":"I3W9TNoJJArAAIRE+WuyCnJPypWoWiq5n6HWtB0sFcci14m+9XIvx2Bncp0pcg40dIrNAPjUZxedKaLMwiMnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"112c71d3b6a0b2888ffd577d91a5f56a95d9f37d17ffd0977faa0a36a240c13b","last_reissued_at":"2026-07-04T23:58:59.842464Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:59.842464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.07635","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":"2026-07-04T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SJDqVG/o1plzMyzq2ERags8ojT06b+wqfgemswqBnd2fG1b4LG4Ue5wy5i5cGXzC43rKWueDxVePE455OeK7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:01:56.290167Z"},"content_sha256":"0f4db5e3c86ffbaf8d0b5ea689b5135e180f7216914530ac5deb64a35bbc826c","schema_version":"1.0","event_id":"sha256:0f4db5e3c86ffbaf8d0b5ea689b5135e180f7216914530ac5deb64a35bbc826c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:CEWHDU5WUCZIRD75K56ZDJPVNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Over-rotation intervals of bimodal interval maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexander Blokh, Sourav Bhattacharya","submitted_at":"2019-08-20T22:29:13Z","abstract_excerpt":"We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given bimodal map is. We then define a new class of polymodal interval maps called well behaved, and generalize the above results onto well behaved maps."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07635","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/1908.07635/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T23:58:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ElrbgXhJ6SxaGjvos7A5GVBk9e53RDFjU7ogt0pJOKCeaFbFImAqNWkJFgtH7UPhCNQ6mBa9ygi3+OzzH5zhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:01:56.290673Z"},"content_sha256":"79364f02a91695a04a70f59870dd9d3b32e2a595a72e3cd1d16f636281e4d5eb","schema_version":"1.0","event_id":"sha256:79364f02a91695a04a70f59870dd9d3b32e2a595a72e3cd1d16f636281e4d5eb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CEWHDU5WUCZIRD75K56ZDJPVNK/bundle.json","state_url":"https://pith.science/pith/CEWHDU5WUCZIRD75K56ZDJPVNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CEWHDU5WUCZIRD75K56ZDJPVNK/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":"2026-08-16T08:01:56Z","links":{"resolver":"https://pith.science/pith/CEWHDU5WUCZIRD75K56ZDJPVNK","bundle":"https://pith.science/pith/CEWHDU5WUCZIRD75K56ZDJPVNK/bundle.json","state":"https://pith.science/pith/CEWHDU5WUCZIRD75K56ZDJPVNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CEWHDU5WUCZIRD75K56ZDJPVNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CEWHDU5WUCZIRD75K56ZDJPVNK","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":"68d40b5d0d9f3b7e94141fdba570ef80b574476d727f789c2526efec0dc3856b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-20T22:29:13Z","title_canon_sha256":"1e31d2d39bbbd6e9851f5a309855419eb6d6bf3cca2e73f72a02d438e54be1cb"},"schema_version":"1.0","source":{"id":"1908.07635","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.07635","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"arxiv_version","alias_value":"1908.07635v1","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07635","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_12","alias_value":"CEWHDU5WUCZI","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_16","alias_value":"CEWHDU5WUCZIRD75","created_at":"2026-07-04T23:58:59Z"},{"alias_kind":"pith_short_8","alias_value":"CEWHDU5W","created_at":"2026-07-04T23:58:59Z"}],"graph_snapshots":[{"event_id":"sha256:79364f02a91695a04a70f59870dd9d3b32e2a595a72e3cd1d16f636281e4d5eb","target":"graph","created_at":"2026-07-04T23:58:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.07635/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We describe all possible bimodal over-twist patterns. In particular, we give an algorithm allowing one to determine what the left endpoint of the over-rotation interval of a given bimodal map is. We then define a new class of polymodal interval maps called well behaved, and generalize the above results onto well behaved maps.","authors_text":"Alexander Blokh, Sourav Bhattacharya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-20T22:29:13Z","title":"Over-rotation intervals of bimodal interval maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07635","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":"sha256:0f4db5e3c86ffbaf8d0b5ea689b5135e180f7216914530ac5deb64a35bbc826c","target":"record","created_at":"2026-07-04T23:58:59Z","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":"68d40b5d0d9f3b7e94141fdba570ef80b574476d727f789c2526efec0dc3856b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-08-20T22:29:13Z","title_canon_sha256":"1e31d2d39bbbd6e9851f5a309855419eb6d6bf3cca2e73f72a02d438e54be1cb"},"schema_version":"1.0","source":{"id":"1908.07635","kind":"arxiv","version":1}},"canonical_sha256":"112c71d3b6a0b2888ffd577d91a5f56a95d9f37d17ffd0977faa0a36a240c13b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"112c71d3b6a0b2888ffd577d91a5f56a95d9f37d17ffd0977faa0a36a240c13b","first_computed_at":"2026-07-04T23:58:59.842464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:59.842464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"I3W9TNoJJArAAIRE+WuyCnJPypWoWiq5n6HWtB0sFcci14m+9XIvx2Bncp0pcg40dIrNAPjUZxedKaLMwiMnDQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:59.842803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.07635","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f4db5e3c86ffbaf8d0b5ea689b5135e180f7216914530ac5deb64a35bbc826c","sha256:79364f02a91695a04a70f59870dd9d3b32e2a595a72e3cd1d16f636281e4d5eb"],"state_sha256":"7a01352f4279676b8e6f494947d73fd33560329d2317e2f4dad9fb9c471f6d4d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q2KPfiyKfXJsrUe3fAVB8mSvlb7jrVj8UO7vpWDJqrAF2FCCqnJ8bkmdReYu6QdbFhbJVkyR7H2mqPqHJPacCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T08:01:56.294032Z","bundle_sha256":"bbb16f5029ba97a417bdb03ea4dc0179ac3270bb2ea26820a4a601885e844543"}}