{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NDGSHTIPYF35QDROOX76G4TJX6","short_pith_number":"pith:NDGSHTIP","canonical_record":{"source":{"id":"1703.04302","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-13T09:35:38Z","cross_cats_sorted":[],"title_canon_sha256":"ec110eaed6cf417706e677bc431773dad91f43589a8aa321526696c08666c389","abstract_canon_sha256":"c406f3d69cfedeeeaa8edd8a4912d222831087cadd9dd36de9ad1b4b3dde3c24"},"schema_version":"1.0"},"canonical_sha256":"68cd23cd0fc177d80e2e75ffe37269bf83daaf90e704d22d0e94a4cfb0784b09","source":{"kind":"arxiv","id":"1703.04302","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04302","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04302v3","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04302","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"NDGSHTIPYF35","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NDGSHTIPYF35QDRO","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NDGSHTIP","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NDGSHTIPYF35QDROOX76G4TJX6","target":"record","payload":{"canonical_record":{"source":{"id":"1703.04302","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-13T09:35:38Z","cross_cats_sorted":[],"title_canon_sha256":"ec110eaed6cf417706e677bc431773dad91f43589a8aa321526696c08666c389","abstract_canon_sha256":"c406f3d69cfedeeeaa8edd8a4912d222831087cadd9dd36de9ad1b4b3dde3c24"},"schema_version":"1.0"},"canonical_sha256":"68cd23cd0fc177d80e2e75ffe37269bf83daaf90e704d22d0e94a4cfb0784b09","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:11.770119Z","signature_b64":"Cwltue0JG7V1z+l+npihSEj7GQCdbF2/kfGQvfaYVwXPEEWYGean4r7DF4wUpriJWWTxem3jo0fO72R3jswoAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68cd23cd0fc177d80e2e75ffe37269bf83daaf90e704d22d0e94a4cfb0784b09","last_reissued_at":"2026-05-18T00:11:11.769404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:11.769404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.04302","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h7s9Zy4HEtCP7eMDO/oInxfHImPVq9WxDMC4404nA2qdc7Vdt9kpiAMwvtybQumHKZ/lJh9A1OLKPMLB8PA8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T07:59:38.719716Z"},"content_sha256":"1d3c5204f002f1a3db133ee9b39dea7e761661d5f49a208143d201b3886e367f","schema_version":"1.0","event_id":"sha256:1d3c5204f002f1a3db133ee9b39dea7e761661d5f49a208143d201b3886e367f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NDGSHTIPYF35QDROOX76G4TJX6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$HD(M\\setminus L)>0.353$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Gustavo Moreira, Carlos Matheus","submitted_at":"2017-03-13T09:35:38Z","abstract_excerpt":"The complement $M\\setminus L$ of the Lagrange spectrum $L$ in the Markov spectrum $M$ was studied by many authors (including Freiman, Berstein, Cusick and Flahive). After their works, we disposed of a countable collection of points in $M\\setminus L$.\n  In this article, we describe the structure of $M\\setminus L$ near a non-isolated point $\\alpha_{\\infty}$ found by Freiman in 1973, and we use this description to exhibit a concrete Cantor set $X$ whose Hausdorff dimension coincides with the Hausdorff dimension of $M\\setminus L$ near $\\alpha_{\\infty}$.\n  A consequence of our results is the lower "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04302","kind":"arxiv","version":3},"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":"2026-05-18T00:11:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSjXEdgnnKmP8zA8hxZmaoii9mZkO/euc0DQ6MvzeHv74W3s6mYvH4PuXR1w8lOWkdqwWKJgnInT909FCBSYAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T07:59:38.720097Z"},"content_sha256":"95a690999e7387b1ac891c0ccbf2afb155c4fc01e735b91065481f6f21b308d3","schema_version":"1.0","event_id":"sha256:95a690999e7387b1ac891c0ccbf2afb155c4fc01e735b91065481f6f21b308d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NDGSHTIPYF35QDROOX76G4TJX6/bundle.json","state_url":"https://pith.science/pith/NDGSHTIPYF35QDROOX76G4TJX6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NDGSHTIPYF35QDROOX76G4TJX6/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":"2026-05-24T07:59:38Z","links":{"resolver":"https://pith.science/pith/NDGSHTIPYF35QDROOX76G4TJX6","bundle":"https://pith.science/pith/NDGSHTIPYF35QDROOX76G4TJX6/bundle.json","state":"https://pith.science/pith/NDGSHTIPYF35QDROOX76G4TJX6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NDGSHTIPYF35QDROOX76G4TJX6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NDGSHTIPYF35QDROOX76G4TJX6","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":"c406f3d69cfedeeeaa8edd8a4912d222831087cadd9dd36de9ad1b4b3dde3c24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-13T09:35:38Z","title_canon_sha256":"ec110eaed6cf417706e677bc431773dad91f43589a8aa321526696c08666c389"},"schema_version":"1.0","source":{"id":"1703.04302","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04302","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04302v3","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04302","created_at":"2026-05-18T00:11:11Z"},{"alias_kind":"pith_short_12","alias_value":"NDGSHTIPYF35","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"NDGSHTIPYF35QDRO","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"NDGSHTIP","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:95a690999e7387b1ac891c0ccbf2afb155c4fc01e735b91065481f6f21b308d3","target":"graph","created_at":"2026-05-18T00:11:11Z","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":"The complement $M\\setminus L$ of the Lagrange spectrum $L$ in the Markov spectrum $M$ was studied by many authors (including Freiman, Berstein, Cusick and Flahive). After their works, we disposed of a countable collection of points in $M\\setminus L$.\n  In this article, we describe the structure of $M\\setminus L$ near a non-isolated point $\\alpha_{\\infty}$ found by Freiman in 1973, and we use this description to exhibit a concrete Cantor set $X$ whose Hausdorff dimension coincides with the Hausdorff dimension of $M\\setminus L$ near $\\alpha_{\\infty}$.\n  A consequence of our results is the lower ","authors_text":"Carlos Gustavo Moreira, Carlos Matheus","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-13T09:35:38Z","title":"$HD(M\\setminus L)>0.353$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04302","kind":"arxiv","version":3},"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":"sha256:1d3c5204f002f1a3db133ee9b39dea7e761661d5f49a208143d201b3886e367f","target":"record","created_at":"2026-05-18T00:11:11Z","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":"c406f3d69cfedeeeaa8edd8a4912d222831087cadd9dd36de9ad1b4b3dde3c24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-13T09:35:38Z","title_canon_sha256":"ec110eaed6cf417706e677bc431773dad91f43589a8aa321526696c08666c389"},"schema_version":"1.0","source":{"id":"1703.04302","kind":"arxiv","version":3}},"canonical_sha256":"68cd23cd0fc177d80e2e75ffe37269bf83daaf90e704d22d0e94a4cfb0784b09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68cd23cd0fc177d80e2e75ffe37269bf83daaf90e704d22d0e94a4cfb0784b09","first_computed_at":"2026-05-18T00:11:11.769404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:11.769404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cwltue0JG7V1z+l+npihSEj7GQCdbF2/kfGQvfaYVwXPEEWYGean4r7DF4wUpriJWWTxem3jo0fO72R3jswoAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:11.770119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04302","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d3c5204f002f1a3db133ee9b39dea7e761661d5f49a208143d201b3886e367f","sha256:95a690999e7387b1ac891c0ccbf2afb155c4fc01e735b91065481f6f21b308d3"],"state_sha256":"b7dcefc6ecf4b147f5cf318ccd21382ff5e5f591a40513d4370aa9460ae52263"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4p98SElIZHFoZxYthu88uA+Lm3eCpEMPn4RDwVM5whig/UBnnerRiSl61rTgZXpmHGBqjM7AoBUkudl2D4FDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T07:59:38.723304Z","bundle_sha256":"efb9a0e0095845c123cc9ab2d6914fff53329c1e1624317f531e70841c166a92"}}