{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VODFYAPPSQAKWYTWD6BA3QZOQR","short_pith_number":"pith:VODFYAPP","canonical_record":{"source":{"id":"1506.07279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-24T08:13:03Z","cross_cats_sorted":[],"title_canon_sha256":"1cf95a7d387e81e4478b2829114bea5f0638197998e720ef8cd9e4f0184f1e20","abstract_canon_sha256":"94f943bd3f79f1d69a98eb4fb98a19aec7b6228a1b1d57cdfe03317e698d20c2"},"schema_version":"1.0"},"canonical_sha256":"ab865c01ef9400ab62761f820dc32e8477ae473981a646b7aa871146dc231190","source":{"kind":"arxiv","id":"1506.07279","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07279","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07279v1","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07279","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"pith_short_12","alias_value":"VODFYAPPSQAK","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VODFYAPPSQAKWYTW","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VODFYAPP","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VODFYAPPSQAKWYTWD6BA3QZOQR","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-24T08:13:03Z","cross_cats_sorted":[],"title_canon_sha256":"1cf95a7d387e81e4478b2829114bea5f0638197998e720ef8cd9e4f0184f1e20","abstract_canon_sha256":"94f943bd3f79f1d69a98eb4fb98a19aec7b6228a1b1d57cdfe03317e698d20c2"},"schema_version":"1.0"},"canonical_sha256":"ab865c01ef9400ab62761f820dc32e8477ae473981a646b7aa871146dc231190","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:54.399572Z","signature_b64":"0QWS7eWchJCRweNT8X4J9993PqUH5sTG4ILmrPOEsdF9o1DFUFHGgg0VWi8DzBaeJBxTrT3csniFxfVwjMjDAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab865c01ef9400ab62761f820dc32e8477ae473981a646b7aa871146dc231190","last_reissued_at":"2026-05-18T01:39:54.399123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:54.399123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07279","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":"2026-05-18T01:39:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LlRKrJxb0FDI4UWrcbQub7KBgHdlTyq7A6rMVSKuXo7+LR8RXfRf96xuoBm1KGteGBjmjkLEnf/pn3aqY2wHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:14:00.948888Z"},"content_sha256":"7176ea0b1aaffa5d99646a850ce815018a8a28582129eeadfcb6bd779a710cae","schema_version":"1.0","event_id":"sha256:7176ea0b1aaffa5d99646a850ce815018a8a28582129eeadfcb6bd779a710cae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VODFYAPPSQAKWYTWD6BA3QZOQR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dmitry Turaev, Katsutoshi Shinohara, Masayuki Asaoka","submitted_at":"2015-06-24T08:13:03Z","abstract_excerpt":"We consider semigroup actions on the unit interval generated by strictly increasing $C^r$-maps. We assume that one of the generators has a pair of fixed points, one attracting and one repelling, and a heteroclinic orbit that connects the repeller and attractor, and the other generators form a robust blender, which can bring the points from a small neighborhood of the attractor to an arbitrarily small neighborhood of the repeller. This is a model setting for partially hyperbolic systems with one central direction.\n  We show that, under additional conditions on the non-linearity and the Schwarzi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07279","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":"2026-05-18T01:39:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mgSF5zis5i1gKOQCKdh52IpmONNmezSUL17JxAbeFr41fs4qSUNUnjK8pM1RNm50gRY8cow6wfJt/9JtmmDOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:14:00.949429Z"},"content_sha256":"2efeef42a99a768f97d9dfa43a1b4462b5571a315f0fe5a142c9a9b775b63684","schema_version":"1.0","event_id":"sha256:2efeef42a99a768f97d9dfa43a1b4462b5571a315f0fe5a142c9a9b775b63684"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VODFYAPPSQAKWYTWD6BA3QZOQR/bundle.json","state_url":"https://pith.science/pith/VODFYAPPSQAKWYTWD6BA3QZOQR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VODFYAPPSQAKWYTWD6BA3QZOQR/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":"2026-05-31T21:14:00Z","links":{"resolver":"https://pith.science/pith/VODFYAPPSQAKWYTWD6BA3QZOQR","bundle":"https://pith.science/pith/VODFYAPPSQAKWYTWD6BA3QZOQR/bundle.json","state":"https://pith.science/pith/VODFYAPPSQAKWYTWD6BA3QZOQR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VODFYAPPSQAKWYTWD6BA3QZOQR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VODFYAPPSQAKWYTWD6BA3QZOQR","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":"94f943bd3f79f1d69a98eb4fb98a19aec7b6228a1b1d57cdfe03317e698d20c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-24T08:13:03Z","title_canon_sha256":"1cf95a7d387e81e4478b2829114bea5f0638197998e720ef8cd9e4f0184f1e20"},"schema_version":"1.0","source":{"id":"1506.07279","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07279","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07279v1","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07279","created_at":"2026-05-18T01:39:54Z"},{"alias_kind":"pith_short_12","alias_value":"VODFYAPPSQAK","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VODFYAPPSQAKWYTW","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VODFYAPP","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:2efeef42a99a768f97d9dfa43a1b4462b5571a315f0fe5a142c9a9b775b63684","target":"graph","created_at":"2026-05-18T01:39:54Z","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":"We consider semigroup actions on the unit interval generated by strictly increasing $C^r$-maps. We assume that one of the generators has a pair of fixed points, one attracting and one repelling, and a heteroclinic orbit that connects the repeller and attractor, and the other generators form a robust blender, which can bring the points from a small neighborhood of the attractor to an arbitrarily small neighborhood of the repeller. This is a model setting for partially hyperbolic systems with one central direction.\n  We show that, under additional conditions on the non-linearity and the Schwarzi","authors_text":"Dmitry Turaev, Katsutoshi Shinohara, Masayuki Asaoka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-24T08:13:03Z","title":"Degenerate behavior in non-hyperbolic semigroup actions on the interval: fast growth of periodic points and universal dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07279","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":"sha256:7176ea0b1aaffa5d99646a850ce815018a8a28582129eeadfcb6bd779a710cae","target":"record","created_at":"2026-05-18T01:39:54Z","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":"94f943bd3f79f1d69a98eb4fb98a19aec7b6228a1b1d57cdfe03317e698d20c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-06-24T08:13:03Z","title_canon_sha256":"1cf95a7d387e81e4478b2829114bea5f0638197998e720ef8cd9e4f0184f1e20"},"schema_version":"1.0","source":{"id":"1506.07279","kind":"arxiv","version":1}},"canonical_sha256":"ab865c01ef9400ab62761f820dc32e8477ae473981a646b7aa871146dc231190","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab865c01ef9400ab62761f820dc32e8477ae473981a646b7aa871146dc231190","first_computed_at":"2026-05-18T01:39:54.399123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:54.399123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0QWS7eWchJCRweNT8X4J9993PqUH5sTG4ILmrPOEsdF9o1DFUFHGgg0VWi8DzBaeJBxTrT3csniFxfVwjMjDAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:54.399572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07279","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7176ea0b1aaffa5d99646a850ce815018a8a28582129eeadfcb6bd779a710cae","sha256:2efeef42a99a768f97d9dfa43a1b4462b5571a315f0fe5a142c9a9b775b63684"],"state_sha256":"30d1c9aad37a57a0aaec09c3d8b17392014723a0472fe4137247d18443851e19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AvahEFtUXvzdsT/9a2kTmMNsKH9NcWhpd8TUmzTU72+DV4nA59NTS7uNq2sqD7fYUo2G2w+lmwWOmybmsO8SBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:14:00.952021Z","bundle_sha256":"bb17e37d8e51ea3c771b38471685464615be5387e8fa69ae4435bc4251da8111"}}