{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PJFZRWZQ2XU5IAIMINF3ZQTWFL","short_pith_number":"pith:PJFZRWZQ","canonical_record":{"source":{"id":"1705.07021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T14:30:11Z","cross_cats_sorted":[],"title_canon_sha256":"8de8832baf2df7d1bf8ccf07b153e0a5bc6733a24cbcdf0af1b1a370edfa8f57","abstract_canon_sha256":"d48eddb7977b17bb02e7a674cca1958d5340b2df2cf6ff399ec2ba274f990e03"},"schema_version":"1.0"},"canonical_sha256":"7a4b98db30d5e9d4010c434bbcc2762ad979391357cde689b05f2e71c522d027","source":{"kind":"arxiv","id":"1705.07021","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07021","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07021v1","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07021","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"PJFZRWZQ2XU5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PJFZRWZQ2XU5IAIM","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PJFZRWZQ","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PJFZRWZQ2XU5IAIMINF3ZQTWFL","target":"record","payload":{"canonical_record":{"source":{"id":"1705.07021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T14:30:11Z","cross_cats_sorted":[],"title_canon_sha256":"8de8832baf2df7d1bf8ccf07b153e0a5bc6733a24cbcdf0af1b1a370edfa8f57","abstract_canon_sha256":"d48eddb7977b17bb02e7a674cca1958d5340b2df2cf6ff399ec2ba274f990e03"},"schema_version":"1.0"},"canonical_sha256":"7a4b98db30d5e9d4010c434bbcc2762ad979391357cde689b05f2e71c522d027","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:10.788017Z","signature_b64":"aMeTJkZZXYqUex7y4oHuqOcWRptW0J2tIKmk2HRv1nH82EUtCuQDr7bDWM8W/F9wXvmGoy5Isoh0dLpy2XFMDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a4b98db30d5e9d4010c434bbcc2762ad979391357cde689b05f2e71c522d027","last_reissued_at":"2026-05-18T00:44:10.787425Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:10.787425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.07021","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":"2026-05-18T00:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xjA9JclVznN2xDQ5WLNC+Y9hJvRLI1R2ZzWysmo0l0mqlj4MRo+yJBRhyzm+rnVE3HD+aiO5Dg/sVgtKbGCCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:30:01.353972Z"},"content_sha256":"5990bc0821f3e960565fcec6d9d9e0eea00451a225b5dfa2082935f4e47c0f47","schema_version":"1.0","event_id":"sha256:5990bc0821f3e960565fcec6d9d9e0eea00451a225b5dfa2082935f4e47c0f47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PJFZRWZQ2XU5IAIMINF3ZQTWFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automorphisms of Toeplitz $\\mathscr{B}$-free systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aurelia Bartnicka","submitted_at":"2017-05-19T14:30:11Z","abstract_excerpt":"For each $\\mathscr{B}$-free subshift given by $\\mathscr{B}=\\{2^ib_i\\}_{i\\in\\mathbb{N}}$, where $\\{b_i\\}_{i\\in\\mathbb{N}}$ is a set of pairwise coprime odd numbers greater than one, it is shown that its automorphism group consists solely of powers of the shift."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07021","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":"2026-05-18T00:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cx6WgXm6qpVe6DgldWblv0IZjV4QiuOdOcDBwpXiDl3WZbFNkbVAdaf2aPUyE/VDhuZ19jTqMLCCAIMLZkanDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T00:30:01.354309Z"},"content_sha256":"d3554b919083ba16bc327b6812497539a16b2158267441ebf92e3f9445b406fc","schema_version":"1.0","event_id":"sha256:d3554b919083ba16bc327b6812497539a16b2158267441ebf92e3f9445b406fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PJFZRWZQ2XU5IAIMINF3ZQTWFL/bundle.json","state_url":"https://pith.science/pith/PJFZRWZQ2XU5IAIMINF3ZQTWFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PJFZRWZQ2XU5IAIMINF3ZQTWFL/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":"2026-06-02T00:30:01Z","links":{"resolver":"https://pith.science/pith/PJFZRWZQ2XU5IAIMINF3ZQTWFL","bundle":"https://pith.science/pith/PJFZRWZQ2XU5IAIMINF3ZQTWFL/bundle.json","state":"https://pith.science/pith/PJFZRWZQ2XU5IAIMINF3ZQTWFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PJFZRWZQ2XU5IAIMINF3ZQTWFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PJFZRWZQ2XU5IAIMINF3ZQTWFL","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":"d48eddb7977b17bb02e7a674cca1958d5340b2df2cf6ff399ec2ba274f990e03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T14:30:11Z","title_canon_sha256":"8de8832baf2df7d1bf8ccf07b153e0a5bc6733a24cbcdf0af1b1a370edfa8f57"},"schema_version":"1.0","source":{"id":"1705.07021","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.07021","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"1705.07021v1","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.07021","created_at":"2026-05-18T00:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"PJFZRWZQ2XU5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PJFZRWZQ2XU5IAIM","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PJFZRWZQ","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:d3554b919083ba16bc327b6812497539a16b2158267441ebf92e3f9445b406fc","target":"graph","created_at":"2026-05-18T00:44:10Z","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":"For each $\\mathscr{B}$-free subshift given by $\\mathscr{B}=\\{2^ib_i\\}_{i\\in\\mathbb{N}}$, where $\\{b_i\\}_{i\\in\\mathbb{N}}$ is a set of pairwise coprime odd numbers greater than one, it is shown that its automorphism group consists solely of powers of the shift.","authors_text":"Aurelia Bartnicka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T14:30:11Z","title":"Automorphisms of Toeplitz $\\mathscr{B}$-free systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.07021","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":"sha256:5990bc0821f3e960565fcec6d9d9e0eea00451a225b5dfa2082935f4e47c0f47","target":"record","created_at":"2026-05-18T00:44:10Z","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":"d48eddb7977b17bb02e7a674cca1958d5340b2df2cf6ff399ec2ba274f990e03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-05-19T14:30:11Z","title_canon_sha256":"8de8832baf2df7d1bf8ccf07b153e0a5bc6733a24cbcdf0af1b1a370edfa8f57"},"schema_version":"1.0","source":{"id":"1705.07021","kind":"arxiv","version":1}},"canonical_sha256":"7a4b98db30d5e9d4010c434bbcc2762ad979391357cde689b05f2e71c522d027","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a4b98db30d5e9d4010c434bbcc2762ad979391357cde689b05f2e71c522d027","first_computed_at":"2026-05-18T00:44:10.787425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:10.787425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMeTJkZZXYqUex7y4oHuqOcWRptW0J2tIKmk2HRv1nH82EUtCuQDr7bDWM8W/F9wXvmGoy5Isoh0dLpy2XFMDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:10.788017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.07021","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5990bc0821f3e960565fcec6d9d9e0eea00451a225b5dfa2082935f4e47c0f47","sha256:d3554b919083ba16bc327b6812497539a16b2158267441ebf92e3f9445b406fc"],"state_sha256":"427ef509485b4bf59c847b5802920ea9156dc07d4f43e4fd777fa248105e8c6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cWZJaonfJZMLRX9SD5GP4GHOBv/uyipvpR5T9TzJPn+ofrFBVguGctI9fWnGT1cvys6OYeeCjtF/LAHVE7HvDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T00:30:01.356248Z","bundle_sha256":"293740c44a770f5c01bc1eabe33543b4c715b790d27aa80c350d45c294008549"}}