{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JSRD2UZIXBNOHNYDIGOLLIE57J","short_pith_number":"pith:JSRD2UZI","canonical_record":{"source":{"id":"1212.4440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-18T17:38:52Z","cross_cats_sorted":[],"title_canon_sha256":"1dd6e16562633e8ecb1a78fe89ac49c82f57319d03b9a1e8d35ef29e043f95b8","abstract_canon_sha256":"75969155c1bfab604f453b67bb43333eddf7dae61cc7da47200121b36d9b0525"},"schema_version":"1.0"},"canonical_sha256":"4ca23d5328b85ae3b703419cb5a09dfa51310feb7833201ab1fe17be6de82307","source":{"kind":"arxiv","id":"1212.4440","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4440","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4440v1","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4440","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"JSRD2UZIXBNO","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JSRD2UZIXBNOHNYD","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JSRD2UZI","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JSRD2UZIXBNOHNYDIGOLLIE57J","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-18T17:38:52Z","cross_cats_sorted":[],"title_canon_sha256":"1dd6e16562633e8ecb1a78fe89ac49c82f57319d03b9a1e8d35ef29e043f95b8","abstract_canon_sha256":"75969155c1bfab604f453b67bb43333eddf7dae61cc7da47200121b36d9b0525"},"schema_version":"1.0"},"canonical_sha256":"4ca23d5328b85ae3b703419cb5a09dfa51310feb7833201ab1fe17be6de82307","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:12.989784Z","signature_b64":"2zpoCR+yv4ISWUry5KebMKyxVAdwsLGYKH5FqIHirF0WoWVbCd9u7dX25SK9zeZBahbUosQpn+2lIZMMabx2Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ca23d5328b85ae3b703419cb5a09dfa51310feb7833201ab1fe17be6de82307","last_reissued_at":"2026-05-18T03:38:12.989201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:12.989201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4440","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":"2026-05-18T03:38:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UbRRuIY2t1Ts/3vMYcSwBQFLFnxL+GS339Bhp9lrb+rFHl75QVG9enYabol4NPYkExZ2D2gR0M2Z59vL1S6DCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:33:45.273567Z"},"content_sha256":"ba37d00b9631fd8cbba445f989f6918f63fdf8db7d8560a0553be9ee1b370ab0","schema_version":"1.0","event_id":"sha256:ba37d00b9631fd8cbba445f989f6918f63fdf8db7d8560a0553be9ee1b370ab0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JSRD2UZIXBNOHNYDIGOLLIE57J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random interval homeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Llu\\'is Alsed\\`a, Micha{\\l} Misiurewicz","submitted_at":"2012-12-18T17:38:52Z","abstract_excerpt":"We investigate homeomorphisms of a compact interval, applied randomly. We consider this system as a skew product with the two-sided Bernoulli shift in the base. If on the open interval there is a metric in which almost all maps are contractions, then (with mild additional assumptions) there exists a global pullback attractor, which is a graph of a function from the base to the fiber. It is also a forward attractor. However, the value of this function depends only on the past, so when we take the one-sided shift in the base, it disappears. We illustrate those phenomena on an example, where ther"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4440","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":"2026-05-18T03:38:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMiNPM9jOXieczy/zH605KdEqlnK1gDm0rIcIpOrl3qcJ2icPyp1PyzohI5O5AF7C40qvC+pEN7PMohSRcqNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:33:45.273994Z"},"content_sha256":"a65f5d4cd7605655557747c21633a4499ca17b3d0a7f4fdae289207daa8fbb42","schema_version":"1.0","event_id":"sha256:a65f5d4cd7605655557747c21633a4499ca17b3d0a7f4fdae289207daa8fbb42"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JSRD2UZIXBNOHNYDIGOLLIE57J/bundle.json","state_url":"https://pith.science/pith/JSRD2UZIXBNOHNYDIGOLLIE57J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JSRD2UZIXBNOHNYDIGOLLIE57J/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":"2026-06-01T21:33:45Z","links":{"resolver":"https://pith.science/pith/JSRD2UZIXBNOHNYDIGOLLIE57J","bundle":"https://pith.science/pith/JSRD2UZIXBNOHNYDIGOLLIE57J/bundle.json","state":"https://pith.science/pith/JSRD2UZIXBNOHNYDIGOLLIE57J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JSRD2UZIXBNOHNYDIGOLLIE57J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JSRD2UZIXBNOHNYDIGOLLIE57J","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":"75969155c1bfab604f453b67bb43333eddf7dae61cc7da47200121b36d9b0525","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-18T17:38:52Z","title_canon_sha256":"1dd6e16562633e8ecb1a78fe89ac49c82f57319d03b9a1e8d35ef29e043f95b8"},"schema_version":"1.0","source":{"id":"1212.4440","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4440","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4440v1","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4440","created_at":"2026-05-18T03:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"JSRD2UZIXBNO","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JSRD2UZIXBNOHNYD","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JSRD2UZI","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:a65f5d4cd7605655557747c21633a4499ca17b3d0a7f4fdae289207daa8fbb42","target":"graph","created_at":"2026-05-18T03:38:12Z","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 investigate homeomorphisms of a compact interval, applied randomly. We consider this system as a skew product with the two-sided Bernoulli shift in the base. If on the open interval there is a metric in which almost all maps are contractions, then (with mild additional assumptions) there exists a global pullback attractor, which is a graph of a function from the base to the fiber. It is also a forward attractor. However, the value of this function depends only on the past, so when we take the one-sided shift in the base, it disappears. We illustrate those phenomena on an example, where ther","authors_text":"Llu\\'is Alsed\\`a, Micha{\\l} Misiurewicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-18T17:38:52Z","title":"Random interval homeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4440","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:ba37d00b9631fd8cbba445f989f6918f63fdf8db7d8560a0553be9ee1b370ab0","target":"record","created_at":"2026-05-18T03:38:12Z","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":"75969155c1bfab604f453b67bb43333eddf7dae61cc7da47200121b36d9b0525","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-18T17:38:52Z","title_canon_sha256":"1dd6e16562633e8ecb1a78fe89ac49c82f57319d03b9a1e8d35ef29e043f95b8"},"schema_version":"1.0","source":{"id":"1212.4440","kind":"arxiv","version":1}},"canonical_sha256":"4ca23d5328b85ae3b703419cb5a09dfa51310feb7833201ab1fe17be6de82307","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ca23d5328b85ae3b703419cb5a09dfa51310feb7833201ab1fe17be6de82307","first_computed_at":"2026-05-18T03:38:12.989201Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:12.989201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2zpoCR+yv4ISWUry5KebMKyxVAdwsLGYKH5FqIHirF0WoWVbCd9u7dX25SK9zeZBahbUosQpn+2lIZMMabx2Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:12.989784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4440","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba37d00b9631fd8cbba445f989f6918f63fdf8db7d8560a0553be9ee1b370ab0","sha256:a65f5d4cd7605655557747c21633a4499ca17b3d0a7f4fdae289207daa8fbb42"],"state_sha256":"e5dddfbce5e7e75c6515f500b81bb9cd87c06434c2eb32858201afcf7fe942d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L72mHyxIKhqSheWHwRLxA5cklPCjU4N7j0bmgp6A9dIQiQ7mmFE4YgexmVeyXqQVw/gWjhft8T+0KB1UVT+EAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:33:45.275872Z","bundle_sha256":"9efc2098f276c44f9ec43c9005a278bec9fed3dd0690d3322bddd9a9e7cab1e5"}}