{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EY2DAPRSWTFCRRMBNFQUVSXMGW","short_pith_number":"pith:EY2DAPRS","canonical_record":{"source":{"id":"1402.2002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-02-09T23:08:03Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"ecb7a116ed5704f2626f79f7b516228be52e18d85da44812d01122c854de770a","abstract_canon_sha256":"919ea90f58da1378a1490506e3a59bf39d2180c5130290ac6ae462d2b48d992f"},"schema_version":"1.0"},"canonical_sha256":"2634303e32b4ca28c58169614acaec35bbc22c4ef33e8d25a98f6251a04c1b2a","source":{"kind":"arxiv","id":"1402.2002","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2002","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2002v1","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2002","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"EY2DAPRSWTFC","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EY2DAPRSWTFCRRMB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EY2DAPRS","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EY2DAPRSWTFCRRMBNFQUVSXMGW","target":"record","payload":{"canonical_record":{"source":{"id":"1402.2002","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-02-09T23:08:03Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"ecb7a116ed5704f2626f79f7b516228be52e18d85da44812d01122c854de770a","abstract_canon_sha256":"919ea90f58da1378a1490506e3a59bf39d2180c5130290ac6ae462d2b48d992f"},"schema_version":"1.0"},"canonical_sha256":"2634303e32b4ca28c58169614acaec35bbc22c4ef33e8d25a98f6251a04c1b2a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:39.192380Z","signature_b64":"UDCC6vux3uDRiO5Z2U+SV+XXV4eWLSqznyMq43biYW7edQkY0LsJyb3g4NdZ+8t0tUHy8b9x1DTEQ7Snee+uBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2634303e32b4ca28c58169614acaec35bbc22c4ef33e8d25a98f6251a04c1b2a","last_reissued_at":"2026-05-18T02:54:39.191850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:39.191850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.2002","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":"2026-05-18T02:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"urgdlGELwhNRouM9XwwX9OSlIFOKY1YUeYiQgsRVGxal/iP+k2AQ8rXxAoqyGzJJ6krduAlOe4u1W4koDFLLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:52:13.999001Z"},"content_sha256":"5bd5345ca10750b593c81e39f29f0105d2ce1da92533cdad7a38478c11860dc6","schema_version":"1.0","event_id":"sha256:5bd5345ca10750b593c81e39f29f0105d2ce1da92533cdad7a38478c11860dc6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EY2DAPRSWTFCRRMBNFQUVSXMGW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The geometry of non-unit Pisot substitutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"J\\\"org Thuswaldner, Milton Minervino","submitted_at":"2014-02-09T23:08:03Z","abstract_excerpt":"Let $\\sigma$ be a non-unit Pisot substitution and let $\\alpha$ be the associated Pisot number. It is known that one can associate certain fractal tiles, so-called \\emph{Rauzy fractals}, with $\\sigma$. In our setting, these fractals are subsets of a certain open subring of the ad\\`ele ring $\\mathbb{A}_{\\mathbb{Q}(\\alpha)}$. We present several approaches on how to define Rauzy fractals and discuss the relations between them. In particular, we consider Rauzy fractals as the natural geometric objects of certain numeration systems, define them in terms of the one-dimensional realization of $\\sigma$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2002","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":"2026-05-18T02:54:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52ITbkkh6I8dgL7D8fv3RhX3Y1HtBaV4mLR8SIZsnS6ch4Pd6PElhxTN28zqXlnTBoc7YwR1RwKr5uCX2BozCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:52:13.999696Z"},"content_sha256":"46a030d76fe854653bd748ac932493d6e40dadb3ea2bb699fed8b0a8e5a85f5b","schema_version":"1.0","event_id":"sha256:46a030d76fe854653bd748ac932493d6e40dadb3ea2bb699fed8b0a8e5a85f5b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EY2DAPRSWTFCRRMBNFQUVSXMGW/bundle.json","state_url":"https://pith.science/pith/EY2DAPRSWTFCRRMBNFQUVSXMGW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EY2DAPRSWTFCRRMBNFQUVSXMGW/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":"2026-06-05T19:52:14Z","links":{"resolver":"https://pith.science/pith/EY2DAPRSWTFCRRMBNFQUVSXMGW","bundle":"https://pith.science/pith/EY2DAPRSWTFCRRMBNFQUVSXMGW/bundle.json","state":"https://pith.science/pith/EY2DAPRSWTFCRRMBNFQUVSXMGW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EY2DAPRSWTFCRRMBNFQUVSXMGW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EY2DAPRSWTFCRRMBNFQUVSXMGW","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":"919ea90f58da1378a1490506e3a59bf39d2180c5130290ac6ae462d2b48d992f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-02-09T23:08:03Z","title_canon_sha256":"ecb7a116ed5704f2626f79f7b516228be52e18d85da44812d01122c854de770a"},"schema_version":"1.0","source":{"id":"1402.2002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.2002","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"arxiv_version","alias_value":"1402.2002v1","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.2002","created_at":"2026-05-18T02:54:39Z"},{"alias_kind":"pith_short_12","alias_value":"EY2DAPRSWTFC","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EY2DAPRSWTFCRRMB","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EY2DAPRS","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:46a030d76fe854653bd748ac932493d6e40dadb3ea2bb699fed8b0a8e5a85f5b","target":"graph","created_at":"2026-05-18T02:54:39Z","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":"Let $\\sigma$ be a non-unit Pisot substitution and let $\\alpha$ be the associated Pisot number. It is known that one can associate certain fractal tiles, so-called \\emph{Rauzy fractals}, with $\\sigma$. In our setting, these fractals are subsets of a certain open subring of the ad\\`ele ring $\\mathbb{A}_{\\mathbb{Q}(\\alpha)}$. We present several approaches on how to define Rauzy fractals and discuss the relations between them. In particular, we consider Rauzy fractals as the natural geometric objects of certain numeration systems, define them in terms of the one-dimensional realization of $\\sigma$","authors_text":"J\\\"org Thuswaldner, Milton Minervino","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-02-09T23:08:03Z","title":"The geometry of non-unit Pisot substitutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2002","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":"sha256:5bd5345ca10750b593c81e39f29f0105d2ce1da92533cdad7a38478c11860dc6","target":"record","created_at":"2026-05-18T02:54:39Z","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":"919ea90f58da1378a1490506e3a59bf39d2180c5130290ac6ae462d2b48d992f","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-02-09T23:08:03Z","title_canon_sha256":"ecb7a116ed5704f2626f79f7b516228be52e18d85da44812d01122c854de770a"},"schema_version":"1.0","source":{"id":"1402.2002","kind":"arxiv","version":1}},"canonical_sha256":"2634303e32b4ca28c58169614acaec35bbc22c4ef33e8d25a98f6251a04c1b2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2634303e32b4ca28c58169614acaec35bbc22c4ef33e8d25a98f6251a04c1b2a","first_computed_at":"2026-05-18T02:54:39.191850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:39.191850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UDCC6vux3uDRiO5Z2U+SV+XXV4eWLSqznyMq43biYW7edQkY0LsJyb3g4NdZ+8t0tUHy8b9x1DTEQ7Snee+uBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:39.192380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.2002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bd5345ca10750b593c81e39f29f0105d2ce1da92533cdad7a38478c11860dc6","sha256:46a030d76fe854653bd748ac932493d6e40dadb3ea2bb699fed8b0a8e5a85f5b"],"state_sha256":"4f40083b952c5cd59a3166ef4bbf4d4cd7cac6fa23e6daa6bbab02e7d009d3c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pd4fLZfQPWJW+qBoftcgSqVmluPu12Wa4YO04kukEJEEsomZfIBle4UkmYvZQgyE2OhTCbp4iL5AtCTV3lB9CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:52:14.004310Z","bundle_sha256":"7e86b45bddfc2042ad60f08a5fa891c58e87df91baeffbf1303441fb75a1f885"}}