{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:DBUL25WXJH6XIKIRP4LRM4N5RU","short_pith_number":"pith:DBUL25WX","canonical_record":{"source":{"id":"1709.04143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-13T05:36:29Z","cross_cats_sorted":[],"title_canon_sha256":"253e43787114ecfb488e2beba4c54c7eebeb8d51b29fb4c65c8f2593d7774162","abstract_canon_sha256":"459b15538a8293ba669526803f5520aad54f6da0b493b162ab9780a0db5b831c"},"schema_version":"1.0"},"canonical_sha256":"1868bd76d749fd7429117f171671bd8d034aef64a3c1d885143216dd166be213","source":{"kind":"arxiv","id":"1709.04143","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04143","created_at":"2026-05-17T23:55:43Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04143v1","created_at":"2026-05-17T23:55:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04143","created_at":"2026-05-17T23:55:43Z"},{"alias_kind":"pith_short_12","alias_value":"DBUL25WXJH6X","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DBUL25WXJH6XIKIR","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DBUL25WX","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:DBUL25WXJH6XIKIRP4LRM4N5RU","target":"record","payload":{"canonical_record":{"source":{"id":"1709.04143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-13T05:36:29Z","cross_cats_sorted":[],"title_canon_sha256":"253e43787114ecfb488e2beba4c54c7eebeb8d51b29fb4c65c8f2593d7774162","abstract_canon_sha256":"459b15538a8293ba669526803f5520aad54f6da0b493b162ab9780a0db5b831c"},"schema_version":"1.0"},"canonical_sha256":"1868bd76d749fd7429117f171671bd8d034aef64a3c1d885143216dd166be213","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:43.221073Z","signature_b64":"bWSw1i3NalEcIh4QTKlJoAS38LLDkWOpVIM6Abg4NXUFmBT0pR3D7vJcCchV01C4w2X7si9i0udqX1KfFeSiAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1868bd76d749fd7429117f171671bd8d034aef64a3c1d885143216dd166be213","last_reissued_at":"2026-05-17T23:55:43.220412Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:43.220412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.04143","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":"2026-05-17T23:55:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2prIVV6EF57wxrGcMZodow24MPwlbbI4LVPzuJQN0AB+j0B7RRhki29UguKW7MIN/G865CqrrwP7a4oBGWAzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:39:57.726960Z"},"content_sha256":"1252a4e0fc5fde0459f32dd6e054b3e7b6dea86c95ce6dfa2f38a87074a4e217","schema_version":"1.0","event_id":"sha256:1252a4e0fc5fde0459f32dd6e054b3e7b6dea86c95ce6dfa2f38a87074a4e217"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:DBUL25WXJH6XIKIRP4LRM4N5RU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Periodic representations in algebraic bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Tom\\'a\\v{s} V\\'avra, V\\'it\\v{e}zslav Kala","submitted_at":"2017-09-13T05:36:29Z","abstract_excerpt":"We study periodic representations in number systems with an algebraic base $\\beta$ (not a rational integer). We show that if $\\beta$ has no Galois conjugate on the unit circle, then there exists a finite integer alphabet $\\mathcal A$ such that every element of $\\mathbb Q(\\beta)$ admits an eventually periodic representation with base $\\beta$ and digits in $\\mathcal A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04143","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":"2026-05-17T23:55:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EgBvrfWdDO2s1t8VM8S4ADIaxyptin5tScze5mX+gmYAApmyhXUmJcZpA7BdkQNNRiGEEMJatGBot2nu/LdwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T12:39:57.727306Z"},"content_sha256":"44fd618437a5da6fc25a8afe8e7c5bd74777e472d8b677918bb054e1f9081726","schema_version":"1.0","event_id":"sha256:44fd618437a5da6fc25a8afe8e7c5bd74777e472d8b677918bb054e1f9081726"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DBUL25WXJH6XIKIRP4LRM4N5RU/bundle.json","state_url":"https://pith.science/pith/DBUL25WXJH6XIKIRP4LRM4N5RU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DBUL25WXJH6XIKIRP4LRM4N5RU/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":"2026-06-04T12:39:57Z","links":{"resolver":"https://pith.science/pith/DBUL25WXJH6XIKIRP4LRM4N5RU","bundle":"https://pith.science/pith/DBUL25WXJH6XIKIRP4LRM4N5RU/bundle.json","state":"https://pith.science/pith/DBUL25WXJH6XIKIRP4LRM4N5RU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DBUL25WXJH6XIKIRP4LRM4N5RU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DBUL25WXJH6XIKIRP4LRM4N5RU","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":"459b15538a8293ba669526803f5520aad54f6da0b493b162ab9780a0db5b831c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-13T05:36:29Z","title_canon_sha256":"253e43787114ecfb488e2beba4c54c7eebeb8d51b29fb4c65c8f2593d7774162"},"schema_version":"1.0","source":{"id":"1709.04143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.04143","created_at":"2026-05-17T23:55:43Z"},{"alias_kind":"arxiv_version","alias_value":"1709.04143v1","created_at":"2026-05-17T23:55:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04143","created_at":"2026-05-17T23:55:43Z"},{"alias_kind":"pith_short_12","alias_value":"DBUL25WXJH6X","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DBUL25WXJH6XIKIR","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DBUL25WX","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:44fd618437a5da6fc25a8afe8e7c5bd74777e472d8b677918bb054e1f9081726","target":"graph","created_at":"2026-05-17T23:55:43Z","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 study periodic representations in number systems with an algebraic base $\\beta$ (not a rational integer). We show that if $\\beta$ has no Galois conjugate on the unit circle, then there exists a finite integer alphabet $\\mathcal A$ such that every element of $\\mathbb Q(\\beta)$ admits an eventually periodic representation with base $\\beta$ and digits in $\\mathcal A$.","authors_text":"Tom\\'a\\v{s} V\\'avra, V\\'it\\v{e}zslav Kala","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-13T05:36:29Z","title":"Periodic representations in algebraic bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04143","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":"sha256:1252a4e0fc5fde0459f32dd6e054b3e7b6dea86c95ce6dfa2f38a87074a4e217","target":"record","created_at":"2026-05-17T23:55:43Z","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":"459b15538a8293ba669526803f5520aad54f6da0b493b162ab9780a0db5b831c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-09-13T05:36:29Z","title_canon_sha256":"253e43787114ecfb488e2beba4c54c7eebeb8d51b29fb4c65c8f2593d7774162"},"schema_version":"1.0","source":{"id":"1709.04143","kind":"arxiv","version":1}},"canonical_sha256":"1868bd76d749fd7429117f171671bd8d034aef64a3c1d885143216dd166be213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1868bd76d749fd7429117f171671bd8d034aef64a3c1d885143216dd166be213","first_computed_at":"2026-05-17T23:55:43.220412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:43.220412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bWSw1i3NalEcIh4QTKlJoAS38LLDkWOpVIM6Abg4NXUFmBT0pR3D7vJcCchV01C4w2X7si9i0udqX1KfFeSiAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:43.221073Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.04143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1252a4e0fc5fde0459f32dd6e054b3e7b6dea86c95ce6dfa2f38a87074a4e217","sha256:44fd618437a5da6fc25a8afe8e7c5bd74777e472d8b677918bb054e1f9081726"],"state_sha256":"9ef836a07c7c0c8d7c29c9083e1d6ca69f7f81f5a76d2e636fc29350c101c0bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X6Rvlrpzwcx4DdtE8PDGYL9uyiBuNpXo72M7kZi0nerGNS6sVukEpVfxS0WGNagYLYoz4BXGSmirBvcLmtkTAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T12:39:57.729287Z","bundle_sha256":"7bf66fd7608ba45338b659f4505505b84107a4955f6edaa5005f4fc6d56aa5d5"}}