{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:WQR6FI56XB73Z72Z62TQCLKVSM","short_pith_number":"pith:WQR6FI56","canonical_record":{"source":{"id":"1602.02126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-05T19:25:07Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0389ba8114b7002d3d95e144fd32e5438002a141c805ee116c872cbe8b39b962","abstract_canon_sha256":"f0da2348bd18dce36924199d3049932ecea31791ba2909c6089940729ee18159"},"schema_version":"1.0"},"canonical_sha256":"b423e2a3beb87fbcff59f6a7012d55931f48a3c036c252af69e10047e3aaba7d","source":{"kind":"arxiv","id":"1602.02126","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02126","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02126v1","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02126","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"pith_short_12","alias_value":"WQR6FI56XB73","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WQR6FI56XB73Z72Z","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WQR6FI56","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:WQR6FI56XB73Z72Z62TQCLKVSM","target":"record","payload":{"canonical_record":{"source":{"id":"1602.02126","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-05T19:25:07Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"0389ba8114b7002d3d95e144fd32e5438002a141c805ee116c872cbe8b39b962","abstract_canon_sha256":"f0da2348bd18dce36924199d3049932ecea31791ba2909c6089940729ee18159"},"schema_version":"1.0"},"canonical_sha256":"b423e2a3beb87fbcff59f6a7012d55931f48a3c036c252af69e10047e3aaba7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:14.468946Z","signature_b64":"tm6ROiQvm7rNVQC5kGAoy855ZWX7q8Ke7f9PGE75zs/ADPgk3RDjYE/rj7uzLrf0jDsubsq/hvH9aTIwV4AqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b423e2a3beb87fbcff59f6a7012d55931f48a3c036c252af69e10047e3aaba7d","last_reissued_at":"2026-05-18T01:21:14.468225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:14.468225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.02126","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":"2026-05-18T01:21:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9y5cf8hOcCqcUS2vM1hwaThUl0IyWCKO4xDcGfxmiJl2YIKuD1HDPG4G6aA7zdRoR2pb8drDWUFxg3QuuJCrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:33:46.034787Z"},"content_sha256":"87483edf147340801b30154a061d2f20844976226e2e042dd2b5fd590ad7dd52","schema_version":"1.0","event_id":"sha256:87483edf147340801b30154a061d2f20844976226e2e042dd2b5fd590ad7dd52"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:WQR6FI56XB73Z72Z62TQCLKVSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Lagrange spectrum of some square-tiled surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.DS","authors_text":"Corinna Ulcigrai, Luca Marchese, Pascal Hubert, Samuel Leli\\`evre","submitted_at":"2016-02-05T19:25:07Z","abstract_excerpt":"Lagrange spectra have been defined for closed submanifolds of the moduli space of translation surfaces which are invariant under the action of SL(2,R). We consider the closed orbit generated by a specific covering of degree 7 of the standard torus, which is an element of the stratum H(2). We give an explicit formula for the values in the spectrum, in terms of a cocycle over the classical continued fraction. Differently from the classical case of the modular surface, where the lowest part of the Lagrange spectrum is discrete, we find an isolated minimum, and a set with a rich structure right ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02126","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":"2026-05-18T01:21:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"us/frrZ1nRX4bT5czpRRHP4WY1QAcZfjYu/DBpciBpR9uO7Ugc5HsHOicB8R2K3PzTX5UdOyLIB6nI3fzr3KAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:33:46.035130Z"},"content_sha256":"384c40ab4b91eaf5b9fd452da502c805bcc9c61a104a5e5b10b7c8365e83db27","schema_version":"1.0","event_id":"sha256:384c40ab4b91eaf5b9fd452da502c805bcc9c61a104a5e5b10b7c8365e83db27"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WQR6FI56XB73Z72Z62TQCLKVSM/bundle.json","state_url":"https://pith.science/pith/WQR6FI56XB73Z72Z62TQCLKVSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WQR6FI56XB73Z72Z62TQCLKVSM/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":"2026-05-31T02:33:46Z","links":{"resolver":"https://pith.science/pith/WQR6FI56XB73Z72Z62TQCLKVSM","bundle":"https://pith.science/pith/WQR6FI56XB73Z72Z62TQCLKVSM/bundle.json","state":"https://pith.science/pith/WQR6FI56XB73Z72Z62TQCLKVSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WQR6FI56XB73Z72Z62TQCLKVSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:WQR6FI56XB73Z72Z62TQCLKVSM","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":"f0da2348bd18dce36924199d3049932ecea31791ba2909c6089940729ee18159","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-05T19:25:07Z","title_canon_sha256":"0389ba8114b7002d3d95e144fd32e5438002a141c805ee116c872cbe8b39b962"},"schema_version":"1.0","source":{"id":"1602.02126","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.02126","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"arxiv_version","alias_value":"1602.02126v1","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.02126","created_at":"2026-05-18T01:21:14Z"},{"alias_kind":"pith_short_12","alias_value":"WQR6FI56XB73","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"WQR6FI56XB73Z72Z","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"WQR6FI56","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:384c40ab4b91eaf5b9fd452da502c805bcc9c61a104a5e5b10b7c8365e83db27","target":"graph","created_at":"2026-05-18T01:21:14Z","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":"Lagrange spectra have been defined for closed submanifolds of the moduli space of translation surfaces which are invariant under the action of SL(2,R). We consider the closed orbit generated by a specific covering of degree 7 of the standard torus, which is an element of the stratum H(2). We give an explicit formula for the values in the spectrum, in terms of a cocycle over the classical continued fraction. Differently from the classical case of the modular surface, where the lowest part of the Lagrange spectrum is discrete, we find an isolated minimum, and a set with a rich structure right ab","authors_text":"Corinna Ulcigrai, Luca Marchese, Pascal Hubert, Samuel Leli\\`evre","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-05T19:25:07Z","title":"The Lagrange spectrum of some square-tiled surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02126","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":"sha256:87483edf147340801b30154a061d2f20844976226e2e042dd2b5fd590ad7dd52","target":"record","created_at":"2026-05-18T01:21:14Z","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":"f0da2348bd18dce36924199d3049932ecea31791ba2909c6089940729ee18159","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-02-05T19:25:07Z","title_canon_sha256":"0389ba8114b7002d3d95e144fd32e5438002a141c805ee116c872cbe8b39b962"},"schema_version":"1.0","source":{"id":"1602.02126","kind":"arxiv","version":1}},"canonical_sha256":"b423e2a3beb87fbcff59f6a7012d55931f48a3c036c252af69e10047e3aaba7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b423e2a3beb87fbcff59f6a7012d55931f48a3c036c252af69e10047e3aaba7d","first_computed_at":"2026-05-18T01:21:14.468225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:14.468225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tm6ROiQvm7rNVQC5kGAoy855ZWX7q8Ke7f9PGE75zs/ADPgk3RDjYE/rj7uzLrf0jDsubsq/hvH9aTIwV4AqAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:14.468946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.02126","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87483edf147340801b30154a061d2f20844976226e2e042dd2b5fd590ad7dd52","sha256:384c40ab4b91eaf5b9fd452da502c805bcc9c61a104a5e5b10b7c8365e83db27"],"state_sha256":"9285d46247c8d357f721855d34dbae6447b36cae64b9d15ad7309500764accdb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ygaspHN8Zw5TMSV+NwbyQUvXMpdc93uAj8ZMbRhXKtJSTLfKMhelpA6taEQNs2WMllRbYUDWss6BtlqlYqJODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:33:46.037202Z","bundle_sha256":"95ef7a62b179d5889bc907a996de7502cb6a32b6c9f3806de253e959fff56417"}}