{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:5NV6D5KSSSZ4VEKMJ5DHEYP3VS","short_pith_number":"pith:5NV6D5KS","canonical_record":{"source":{"id":"1306.3777","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-17T09:00:38Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"7018040c719a877ae93fe5064a55e364894179f155541494404ff6b2dc68a1ae","abstract_canon_sha256":"9a21cdaa2104743adeeba247d6a63745bea78cf5eb6696a5ea57c1ad41220ebb"},"schema_version":"1.0"},"canonical_sha256":"eb6be1f55294b3ca914c4f467261fbac8b0483c55e6a0105a70dc3204c6bf64b","source":{"kind":"arxiv","id":"1306.3777","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3777","created_at":"2026-05-18T02:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3777v4","created_at":"2026-05-18T02:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3777","created_at":"2026-05-18T02:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"5NV6D5KSSSZ4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5NV6D5KSSSZ4VEKM","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5NV6D5KS","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:5NV6D5KSSSZ4VEKMJ5DHEYP3VS","target":"record","payload":{"canonical_record":{"source":{"id":"1306.3777","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-17T09:00:38Z","cross_cats_sorted":["cs.FL"],"title_canon_sha256":"7018040c719a877ae93fe5064a55e364894179f155541494404ff6b2dc68a1ae","abstract_canon_sha256":"9a21cdaa2104743adeeba247d6a63745bea78cf5eb6696a5ea57c1ad41220ebb"},"schema_version":"1.0"},"canonical_sha256":"eb6be1f55294b3ca914c4f467261fbac8b0483c55e6a0105a70dc3204c6bf64b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:22.337976Z","signature_b64":"d1UegXeJ4lyz3YTHN3eMsgZCMiSpQUlv7HQpNs/hfAX1r4BQgPgrvWUH3yJippHLu+37WAm1Vro67OAFb2H3AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eb6be1f55294b3ca914c4f467261fbac8b0483c55e6a0105a70dc3204c6bf64b","last_reissued_at":"2026-05-18T02:45:22.337568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:22.337568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.3777","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1CF9o9QLbZtyYYIa5nhg/ATEevtv/YSYD5fdMqe1tZenw6rqwfmq87jVh2TDF4HHLK1yPTzIb0TSzF9UvSQ4DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:14:15.243670Z"},"content_sha256":"35e5e0c6b5580eb4092ecd5a1840ab619b189e41c562cd40a19f9bbdf62c774c","schema_version":"1.0","event_id":"sha256:35e5e0c6b5580eb4092ecd5a1840ab619b189e41c562cd40a19f9bbdf62c774c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:5NV6D5KSSSZ4VEKMJ5DHEYP3VS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Block Maps between Primitive Uniform and Pisot Substitutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.DS","authors_text":"Ilkka T\\\"orm\\\"a, Ville Salo","submitted_at":"2013-06-17T09:00:38Z","abstract_excerpt":"In this article, we prove that for all pairs of primitive Pisot or uniform substitutions with the same dominating eigenvalue, there exists a finite set of block maps such that every block map between the corresponding subshifts is an element of this set, up to a shift."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3777","kind":"arxiv","version":4},"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":"2026-05-18T02:45:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I7mFgUuhC0e16DCfZnuiAYiW3pL800cjFNf72DMwEtIF/LsCu3H1bjs+EtfboCPjBT1hw4xoZwptX6bQf4ivAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T11:14:15.244005Z"},"content_sha256":"00bb8c258f64757b471c2ba78922ba5171d8b4c76b901f7606bbc3c6a0ea8d3d","schema_version":"1.0","event_id":"sha256:00bb8c258f64757b471c2ba78922ba5171d8b4c76b901f7606bbc3c6a0ea8d3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5NV6D5KSSSZ4VEKMJ5DHEYP3VS/bundle.json","state_url":"https://pith.science/pith/5NV6D5KSSSZ4VEKMJ5DHEYP3VS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5NV6D5KSSSZ4VEKMJ5DHEYP3VS/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":"2026-06-09T11:14:15Z","links":{"resolver":"https://pith.science/pith/5NV6D5KSSSZ4VEKMJ5DHEYP3VS","bundle":"https://pith.science/pith/5NV6D5KSSSZ4VEKMJ5DHEYP3VS/bundle.json","state":"https://pith.science/pith/5NV6D5KSSSZ4VEKMJ5DHEYP3VS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5NV6D5KSSSZ4VEKMJ5DHEYP3VS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:5NV6D5KSSSZ4VEKMJ5DHEYP3VS","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":"9a21cdaa2104743adeeba247d6a63745bea78cf5eb6696a5ea57c1ad41220ebb","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-17T09:00:38Z","title_canon_sha256":"7018040c719a877ae93fe5064a55e364894179f155541494404ff6b2dc68a1ae"},"schema_version":"1.0","source":{"id":"1306.3777","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.3777","created_at":"2026-05-18T02:45:22Z"},{"alias_kind":"arxiv_version","alias_value":"1306.3777v4","created_at":"2026-05-18T02:45:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.3777","created_at":"2026-05-18T02:45:22Z"},{"alias_kind":"pith_short_12","alias_value":"5NV6D5KSSSZ4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"5NV6D5KSSSZ4VEKM","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"5NV6D5KS","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:00bb8c258f64757b471c2ba78922ba5171d8b4c76b901f7606bbc3c6a0ea8d3d","target":"graph","created_at":"2026-05-18T02:45:22Z","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":"In this article, we prove that for all pairs of primitive Pisot or uniform substitutions with the same dominating eigenvalue, there exists a finite set of block maps such that every block map between the corresponding subshifts is an element of this set, up to a shift.","authors_text":"Ilkka T\\\"orm\\\"a, Ville Salo","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-17T09:00:38Z","title":"Block Maps between Primitive Uniform and Pisot Substitutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.3777","kind":"arxiv","version":4},"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":"sha256:35e5e0c6b5580eb4092ecd5a1840ab619b189e41c562cd40a19f9bbdf62c774c","target":"record","created_at":"2026-05-18T02:45:22Z","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":"9a21cdaa2104743adeeba247d6a63745bea78cf5eb6696a5ea57c1ad41220ebb","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-06-17T09:00:38Z","title_canon_sha256":"7018040c719a877ae93fe5064a55e364894179f155541494404ff6b2dc68a1ae"},"schema_version":"1.0","source":{"id":"1306.3777","kind":"arxiv","version":4}},"canonical_sha256":"eb6be1f55294b3ca914c4f467261fbac8b0483c55e6a0105a70dc3204c6bf64b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb6be1f55294b3ca914c4f467261fbac8b0483c55e6a0105a70dc3204c6bf64b","first_computed_at":"2026-05-18T02:45:22.337568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:22.337568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d1UegXeJ4lyz3YTHN3eMsgZCMiSpQUlv7HQpNs/hfAX1r4BQgPgrvWUH3yJippHLu+37WAm1Vro67OAFb2H3AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:22.337976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.3777","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35e5e0c6b5580eb4092ecd5a1840ab619b189e41c562cd40a19f9bbdf62c774c","sha256:00bb8c258f64757b471c2ba78922ba5171d8b4c76b901f7606bbc3c6a0ea8d3d"],"state_sha256":"523610d772f0f108a68922032717d917846e05495eecc33d824c91d0fbbd4ad1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OSdSX2rfUzVaPxY/VHK9hN9Eo0WzwSY9WLw9JCzvVPoEHfuyWbZQ/Itl56TS/HXk91eHixQgXMO8RiFmsdkuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T11:14:15.245908Z","bundle_sha256":"a097af09ed95b2a39e7b8b559ee6af28f3c34f5e2b5b1ccd6133d544c0d4d3df"}}