{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:4W6M7N265LO5L4BRETPDHPYVBM","short_pith_number":"pith:4W6M7N26","canonical_record":{"source":{"id":"1609.01631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-06T16:04:23Z","cross_cats_sorted":[],"title_canon_sha256":"5abfa6dc6d699f4f60cf6c0bf7c2fd5c87852f2324f40d44b0ce500f3ad95db4","abstract_canon_sha256":"a6f8eb3e510c668ad17f5a581835b32f0fcc71acbb251d4a729aae14ab3694cb"},"schema_version":"1.0"},"canonical_sha256":"e5bccfb75eeaddd5f03124de33bf150b1fd81a63087c38afbb743924c6bca017","source":{"kind":"arxiv","id":"1609.01631","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01631","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01631v2","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01631","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"4W6M7N265LO5","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4W6M7N265LO5L4BR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4W6M7N26","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:4W6M7N265LO5L4BRETPDHPYVBM","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-06T16:04:23Z","cross_cats_sorted":[],"title_canon_sha256":"5abfa6dc6d699f4f60cf6c0bf7c2fd5c87852f2324f40d44b0ce500f3ad95db4","abstract_canon_sha256":"a6f8eb3e510c668ad17f5a581835b32f0fcc71acbb251d4a729aae14ab3694cb"},"schema_version":"1.0"},"canonical_sha256":"e5bccfb75eeaddd5f03124de33bf150b1fd81a63087c38afbb743924c6bca017","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:59.888398Z","signature_b64":"oVcdUokGjndCfvoajjKGunMniMiO479FaHw8EELk/BFpZLszhY5JvmJB7Xhd7MUTbCB+a84emqm5OPeQM/EjDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5bccfb75eeaddd5f03124de33bf150b1fd81a63087c38afbb743924c6bca017","last_reissued_at":"2026-05-18T00:51:59.887893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:59.887893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01631","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":"2026-05-18T00:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dmolkCXIrqzBCL0gcisVWR8qApfHGIJVSEs9xBW4dmyvTPyy94LAnKk5XA8llO/2gnyu6jdupg8De8Cs89/hDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:09:01.669145Z"},"content_sha256":"0bd167e328a73955315c62ecb9d89f37e531f4b4d7fad61a1935d4652a5437f1","schema_version":"1.0","event_id":"sha256:0bd167e328a73955315c62ecb9d89f37e531f4b4d7fad61a1935d4652a5437f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:4W6M7N265LO5L4BRETPDHPYVBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mixing completely scrambled system exists","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jan P. Boro\\'nski, Ji\\v{r}\\'i Kupka, Piotr Oprocha","submitted_at":"2016-09-06T16:04:23Z","abstract_excerpt":"We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that for any integer $n\\geq 1$ there is a continuum of topological dimension $n$ supporting a transitive completely scrambled homeomorphism, and $n$-dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15 year old open problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01631","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":"2026-05-18T00:51:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tN3kla7LKS0yeQqDecMaOS3A8odxHZemGSJD6GWP7fl+U5giIBlN4dDYh5UuveHgh7jmP9Xdzj1rGdFn5CgiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T08:09:01.669510Z"},"content_sha256":"e043ba2e2e92ea63678c8e1583293b0ae3d63dd4a651f18ad2b1efbb9f24eeb5","schema_version":"1.0","event_id":"sha256:e043ba2e2e92ea63678c8e1583293b0ae3d63dd4a651f18ad2b1efbb9f24eeb5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4W6M7N265LO5L4BRETPDHPYVBM/bundle.json","state_url":"https://pith.science/pith/4W6M7N265LO5L4BRETPDHPYVBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4W6M7N265LO5L4BRETPDHPYVBM/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":"2026-06-06T08:09:01Z","links":{"resolver":"https://pith.science/pith/4W6M7N265LO5L4BRETPDHPYVBM","bundle":"https://pith.science/pith/4W6M7N265LO5L4BRETPDHPYVBM/bundle.json","state":"https://pith.science/pith/4W6M7N265LO5L4BRETPDHPYVBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4W6M7N265LO5L4BRETPDHPYVBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:4W6M7N265LO5L4BRETPDHPYVBM","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":"a6f8eb3e510c668ad17f5a581835b32f0fcc71acbb251d4a729aae14ab3694cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-06T16:04:23Z","title_canon_sha256":"5abfa6dc6d699f4f60cf6c0bf7c2fd5c87852f2324f40d44b0ce500f3ad95db4"},"schema_version":"1.0","source":{"id":"1609.01631","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01631","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01631v2","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01631","created_at":"2026-05-18T00:51:59Z"},{"alias_kind":"pith_short_12","alias_value":"4W6M7N265LO5","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"4W6M7N265LO5L4BR","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"4W6M7N26","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:e043ba2e2e92ea63678c8e1583293b0ae3d63dd4a651f18ad2b1efbb9f24eeb5","target":"graph","created_at":"2026-05-18T00:51:59Z","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"},"paper":{"abstract_excerpt":"We prove that there exists a topologically mixing homeomorphism which is completely scrambled. We also prove that for any integer $n\\geq 1$ there is a continuum of topological dimension $n$ supporting a transitive completely scrambled homeomorphism, and $n$-dimensional compactum supporting a weakly mixing completely scrambled homeomorphism. This solves a 15 year old open problem.","authors_text":"Jan P. Boro\\'nski, Ji\\v{r}\\'i Kupka, Piotr Oprocha","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-06T16:04:23Z","title":"Mixing completely scrambled system exists"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01631","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":"sha256:0bd167e328a73955315c62ecb9d89f37e531f4b4d7fad61a1935d4652a5437f1","target":"record","created_at":"2026-05-18T00:51:59Z","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":"a6f8eb3e510c668ad17f5a581835b32f0fcc71acbb251d4a729aae14ab3694cb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-09-06T16:04:23Z","title_canon_sha256":"5abfa6dc6d699f4f60cf6c0bf7c2fd5c87852f2324f40d44b0ce500f3ad95db4"},"schema_version":"1.0","source":{"id":"1609.01631","kind":"arxiv","version":2}},"canonical_sha256":"e5bccfb75eeaddd5f03124de33bf150b1fd81a63087c38afbb743924c6bca017","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5bccfb75eeaddd5f03124de33bf150b1fd81a63087c38afbb743924c6bca017","first_computed_at":"2026-05-18T00:51:59.887893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:59.887893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oVcdUokGjndCfvoajjKGunMniMiO479FaHw8EELk/BFpZLszhY5JvmJB7Xhd7MUTbCB+a84emqm5OPeQM/EjDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:59.888398Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01631","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bd167e328a73955315c62ecb9d89f37e531f4b4d7fad61a1935d4652a5437f1","sha256:e043ba2e2e92ea63678c8e1583293b0ae3d63dd4a651f18ad2b1efbb9f24eeb5"],"state_sha256":"eb872fbbbbf527c2637ae96d2e1e97e07ef08a8afb4dce51c2aabb215da22ee6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"++8gSOX087pODRAiGBE/mxmVkiKr1/UJssMsqV2exFRqc0itRN0xY6WfNoK4HlZxMcxkHmkfFgcZdVPirVjjCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T08:09:01.673368Z","bundle_sha256":"a68d8cdde1794cbe35b041d53a700946a27ba45ea298c689d45f0f2a4cdc0f1a"}}