{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:YLANTCDMR43IF7EIFQ756S7ZMD","short_pith_number":"pith:YLANTCDM","canonical_record":{"source":{"id":"math/0206098","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.MG","submitted_at":"2002-06-10T11:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"eca1240777d696a91f493e4246bb6227299c96ab3cac26f883b4dae177b3e88d","abstract_canon_sha256":"ec0f9496af05ec5961eecedff3e3a2c261328157f546ba34848dd90ca19d3d2c"},"schema_version":"1.0"},"canonical_sha256":"c2c0d9886c8f3682fc882c3fdf4bf960e43682bef3cf5d9a7fefba99d210f00e","source":{"kind":"arxiv","id":"math/0206098","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0206098","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0206098v2","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0206098","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"YLANTCDMR43I","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"YLANTCDMR43IF7EI","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"YLANTCDM","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:YLANTCDMR43IF7EIFQ756S7ZMD","target":"record","payload":{"canonical_record":{"source":{"id":"math/0206098","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.MG","submitted_at":"2002-06-10T11:40:36Z","cross_cats_sorted":[],"title_canon_sha256":"eca1240777d696a91f493e4246bb6227299c96ab3cac26f883b4dae177b3e88d","abstract_canon_sha256":"ec0f9496af05ec5961eecedff3e3a2c261328157f546ba34848dd90ca19d3d2c"},"schema_version":"1.0"},"canonical_sha256":"c2c0d9886c8f3682fc882c3fdf4bf960e43682bef3cf5d9a7fefba99d210f00e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:59.153674Z","signature_b64":"vzHKfEV0Yefic4LBPbZH77aTtFLSnFPz6z2vpPcYHFUPKunQ3qmV0XpQTviKwTmVOvhL/VLIo8GDwmlTTRbQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2c0d9886c8f3682fc882c3fdf4bf960e43682bef3cf5d9a7fefba99d210f00e","last_reissued_at":"2026-05-17T23:39:59.153168Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:59.153168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0206098","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":"2026-05-17T23:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mUu+k9hWoPZ29CGGU3RU7LiwCjqYBkGe7KBm7rn9DahLGSnKPQJQB6+4NfKtlLMHVQ9nh370MMOw5AiIYCXkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:54:53.096353Z"},"content_sha256":"a2d1956511da141257e51dc0ffcd8ae45e9322bd1f74cdf0c15de82cc79299c6","schema_version":"1.0","event_id":"sha256:a2d1956511da141257e51dc0ffcd8ae45e9322bd1f74cdf0c15de82cc79299c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:YLANTCDMR43IF7EIFQ756S7ZMD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kolakoski-(3,1) is a (deformed) model set","license":"","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Bernd Sing (Univ. Greifswald), Michael Baake","submitted_at":"2002-06-10T11:40:36Z","abstract_excerpt":"Unlike the (classical) Kolakoski sequence on the alphabet {1,2}, its analogue on {1,3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-(3,1) sequence is then obtained as a deformation, without loosing the pure point diffraction property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0206098","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":"2026-05-17T23:39:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oFYPKthv4z8AxqH8/mekZ6fGz9+XZUujF/N38rdojHA8XhTKDOhMmXFim0DsDM/mE5CDykqGHZ6sRibK4E3lDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:54:53.096958Z"},"content_sha256":"cfa60b0ba0285dc630649d73d8e890e9ea1a4ceb63282bef69d0a38009e0d2b9","schema_version":"1.0","event_id":"sha256:cfa60b0ba0285dc630649d73d8e890e9ea1a4ceb63282bef69d0a38009e0d2b9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLANTCDMR43IF7EIFQ756S7ZMD/bundle.json","state_url":"https://pith.science/pith/YLANTCDMR43IF7EIFQ756S7ZMD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLANTCDMR43IF7EIFQ756S7ZMD/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":"2026-05-26T03:54:53Z","links":{"resolver":"https://pith.science/pith/YLANTCDMR43IF7EIFQ756S7ZMD","bundle":"https://pith.science/pith/YLANTCDMR43IF7EIFQ756S7ZMD/bundle.json","state":"https://pith.science/pith/YLANTCDMR43IF7EIFQ756S7ZMD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLANTCDMR43IF7EIFQ756S7ZMD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:YLANTCDMR43IF7EIFQ756S7ZMD","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":"ec0f9496af05ec5961eecedff3e3a2c261328157f546ba34848dd90ca19d3d2c","cross_cats_sorted":[],"license":"","primary_cat":"math.MG","submitted_at":"2002-06-10T11:40:36Z","title_canon_sha256":"eca1240777d696a91f493e4246bb6227299c96ab3cac26f883b4dae177b3e88d"},"schema_version":"1.0","source":{"id":"math/0206098","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0206098","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0206098v2","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0206098","created_at":"2026-05-17T23:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"YLANTCDMR43I","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"YLANTCDMR43IF7EI","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"YLANTCDM","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:cfa60b0ba0285dc630649d73d8e890e9ea1a4ceb63282bef69d0a38009e0d2b9","target":"graph","created_at":"2026-05-17T23:39:59Z","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":"Unlike the (classical) Kolakoski sequence on the alphabet {1,2}, its analogue on {1,3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-(3,1) sequence is then obtained as a deformation, without loosing the pure point diffraction property.","authors_text":"Bernd Sing (Univ. Greifswald), Michael Baake","cross_cats":[],"headline":"","license":"","primary_cat":"math.MG","submitted_at":"2002-06-10T11:40:36Z","title":"Kolakoski-(3,1) is a (deformed) model set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0206098","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:a2d1956511da141257e51dc0ffcd8ae45e9322bd1f74cdf0c15de82cc79299c6","target":"record","created_at":"2026-05-17T23:39:59Z","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":"ec0f9496af05ec5961eecedff3e3a2c261328157f546ba34848dd90ca19d3d2c","cross_cats_sorted":[],"license":"","primary_cat":"math.MG","submitted_at":"2002-06-10T11:40:36Z","title_canon_sha256":"eca1240777d696a91f493e4246bb6227299c96ab3cac26f883b4dae177b3e88d"},"schema_version":"1.0","source":{"id":"math/0206098","kind":"arxiv","version":2}},"canonical_sha256":"c2c0d9886c8f3682fc882c3fdf4bf960e43682bef3cf5d9a7fefba99d210f00e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2c0d9886c8f3682fc882c3fdf4bf960e43682bef3cf5d9a7fefba99d210f00e","first_computed_at":"2026-05-17T23:39:59.153168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:59.153168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vzHKfEV0Yefic4LBPbZH77aTtFLSnFPz6z2vpPcYHFUPKunQ3qmV0XpQTviKwTmVOvhL/VLIo8GDwmlTTRbQCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:59.153674Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0206098","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2d1956511da141257e51dc0ffcd8ae45e9322bd1f74cdf0c15de82cc79299c6","sha256:cfa60b0ba0285dc630649d73d8e890e9ea1a4ceb63282bef69d0a38009e0d2b9"],"state_sha256":"87bc263e1b3895cd02d5f714e5623570c54ad0373798054a6fbd354f235cf7e7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nJD+h35F1tjFlVYtES3OxNFC5b6bRL94mWO3i4adIF6gkm33jqffC8EV7oOD5TWOlYVqC0aQyQqZ3XCJPTaQDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:54:53.100844Z","bundle_sha256":"394a7a67ccb580506a901762eade89fe2d09c9c74acc2467470affc5d4749391"}}