{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LBFPNISP772Z5MGSPV3MQFUPKI","short_pith_number":"pith:LBFPNISP","canonical_record":{"source":{"id":"1507.00714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-02T19:49:01Z","cross_cats_sorted":[],"title_canon_sha256":"a918678166af48970eb052fbbc38655d639156a1a02ae146e27cbb35f96bad3a","abstract_canon_sha256":"205003cbd240efe8f47f1a42258b7d65e697b3281aefa1f4f9c24a2249009e49"},"schema_version":"1.0"},"canonical_sha256":"584af6a24ffff59eb0d27d76c8168f52336db4ad7e6a698d753f54864f44972b","source":{"kind":"arxiv","id":"1507.00714","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00714","created_at":"2026-05-18T01:37:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00714v1","created_at":"2026-05-18T01:37:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00714","created_at":"2026-05-18T01:37:23Z"},{"alias_kind":"pith_short_12","alias_value":"LBFPNISP772Z","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBFPNISP772Z5MGS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBFPNISP","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LBFPNISP772Z5MGSPV3MQFUPKI","target":"record","payload":{"canonical_record":{"source":{"id":"1507.00714","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-02T19:49:01Z","cross_cats_sorted":[],"title_canon_sha256":"a918678166af48970eb052fbbc38655d639156a1a02ae146e27cbb35f96bad3a","abstract_canon_sha256":"205003cbd240efe8f47f1a42258b7d65e697b3281aefa1f4f9c24a2249009e49"},"schema_version":"1.0"},"canonical_sha256":"584af6a24ffff59eb0d27d76c8168f52336db4ad7e6a698d753f54864f44972b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:23.790377Z","signature_b64":"0L6DVPJbvqpBtJjz604/8Q6L9Kp/2x+A5zIYYjd6ppEJSEn5HuOmDyQ7ACniBeEXuUP7KeBB2FLXpS31rPTBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"584af6a24ffff59eb0d27d76c8168f52336db4ad7e6a698d753f54864f44972b","last_reissued_at":"2026-05-18T01:37:23.789614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:23.789614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.00714","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":"2026-05-18T01:37:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZKdbmA9rstH5xKgNTtTVWPJwy2iL8zNTH67LtveiwnBZ6kvmsQZAE51akMc5Vyu0tW8d88D7UjKC0BXbMDydAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:19:39.668474Z"},"content_sha256":"4143697798b1dc17686e44e34e1a5a7a2e42bc96e1aa5b7f8a29705a6f4ac74e","schema_version":"1.0","event_id":"sha256:4143697798b1dc17686e44e34e1a5a7a2e42bc96e1aa5b7f8a29705a6f4ac74e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LBFPNISP772Z5MGSPV3MQFUPKI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hereditary subshifts whose simplex of invariant measures is Poulsen","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Benjamin Weiss, Joanna Ku{\\l}aga-Przymus, Mariusz Lema\\'nczyk","submitted_at":"2015-07-02T19:49:01Z","abstract_excerpt":"We give a sufficient condition for the simplex of invariant measures for a hereditary system to be Poulsen. In particular, we show that this simplex is Poulsen in case of positive entropy $\\mathscr{B}$-free systems. We also give an example of a positive entropy hereditary system whose simplex of invariant measures is not Poulsen."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00714","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":"2026-05-18T01:37:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FdwH9hMCKIsop5HfydT5uP9sKUi5XJUfm5ZQCNY3DXz+0YZxiTQOFFlCENP348eN3Rp/vs3BrtDV3HpFd4QTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T12:19:39.668807Z"},"content_sha256":"33abd0339f7ef80b716ea70e4692e93b8c8fe3988a0869ad1f0bb3c06d342d0d","schema_version":"1.0","event_id":"sha256:33abd0339f7ef80b716ea70e4692e93b8c8fe3988a0869ad1f0bb3c06d342d0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBFPNISP772Z5MGSPV3MQFUPKI/bundle.json","state_url":"https://pith.science/pith/LBFPNISP772Z5MGSPV3MQFUPKI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBFPNISP772Z5MGSPV3MQFUPKI/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":"2026-06-02T12:19:39Z","links":{"resolver":"https://pith.science/pith/LBFPNISP772Z5MGSPV3MQFUPKI","bundle":"https://pith.science/pith/LBFPNISP772Z5MGSPV3MQFUPKI/bundle.json","state":"https://pith.science/pith/LBFPNISP772Z5MGSPV3MQFUPKI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBFPNISP772Z5MGSPV3MQFUPKI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LBFPNISP772Z5MGSPV3MQFUPKI","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":"205003cbd240efe8f47f1a42258b7d65e697b3281aefa1f4f9c24a2249009e49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-02T19:49:01Z","title_canon_sha256":"a918678166af48970eb052fbbc38655d639156a1a02ae146e27cbb35f96bad3a"},"schema_version":"1.0","source":{"id":"1507.00714","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00714","created_at":"2026-05-18T01:37:23Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00714v1","created_at":"2026-05-18T01:37:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00714","created_at":"2026-05-18T01:37:23Z"},{"alias_kind":"pith_short_12","alias_value":"LBFPNISP772Z","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBFPNISP772Z5MGS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBFPNISP","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:33abd0339f7ef80b716ea70e4692e93b8c8fe3988a0869ad1f0bb3c06d342d0d","target":"graph","created_at":"2026-05-18T01:37:23Z","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 give a sufficient condition for the simplex of invariant measures for a hereditary system to be Poulsen. In particular, we show that this simplex is Poulsen in case of positive entropy $\\mathscr{B}$-free systems. We also give an example of a positive entropy hereditary system whose simplex of invariant measures is not Poulsen.","authors_text":"Benjamin Weiss, Joanna Ku{\\l}aga-Przymus, Mariusz Lema\\'nczyk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-02T19:49:01Z","title":"Hereditary subshifts whose simplex of invariant measures is Poulsen"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00714","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":"sha256:4143697798b1dc17686e44e34e1a5a7a2e42bc96e1aa5b7f8a29705a6f4ac74e","target":"record","created_at":"2026-05-18T01:37:23Z","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":"205003cbd240efe8f47f1a42258b7d65e697b3281aefa1f4f9c24a2249009e49","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-07-02T19:49:01Z","title_canon_sha256":"a918678166af48970eb052fbbc38655d639156a1a02ae146e27cbb35f96bad3a"},"schema_version":"1.0","source":{"id":"1507.00714","kind":"arxiv","version":1}},"canonical_sha256":"584af6a24ffff59eb0d27d76c8168f52336db4ad7e6a698d753f54864f44972b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"584af6a24ffff59eb0d27d76c8168f52336db4ad7e6a698d753f54864f44972b","first_computed_at":"2026-05-18T01:37:23.789614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:23.789614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0L6DVPJbvqpBtJjz604/8Q6L9Kp/2x+A5zIYYjd6ppEJSEn5HuOmDyQ7ACniBeEXuUP7KeBB2FLXpS31rPTBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:23.790377Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00714","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4143697798b1dc17686e44e34e1a5a7a2e42bc96e1aa5b7f8a29705a6f4ac74e","sha256:33abd0339f7ef80b716ea70e4692e93b8c8fe3988a0869ad1f0bb3c06d342d0d"],"state_sha256":"ea99248143e48d7503e2aefb6d780f8c4e2a99e2b4248038207dcc73890d3d83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WRAZBR0JC2ymZtcOhvhPwBVFQDu5PV/JTdqGXuotswmXz7yTswcKS0hdOgHU/g3kwkRQP2m9ejHcZDlb4cHuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T12:19:39.670703Z","bundle_sha256":"212fa6dd2741449b570284e37f7fab69a2b0e346c449b569434b652d604cd014"}}