{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Z3CHFSTIGWO3X5WCXUIE6UYPZ5","short_pith_number":"pith:Z3CHFSTI","canonical_record":{"source":{"id":"1308.2871","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-13T14:06:25Z","cross_cats_sorted":[],"title_canon_sha256":"01b0dc8763e181139c9f9e30fe20e38bbd36680325975add0314d4b50a9c2030","abstract_canon_sha256":"8401041dba150c7dd0c18677ddf51f0e7e1a30a48980a4031c1fcd75d914a472"},"schema_version":"1.0"},"canonical_sha256":"cec472ca68359dbbf6c2bd104f530fcf7fb82d6b5535f192a46a1356271fdf17","source":{"kind":"arxiv","id":"1308.2871","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2871","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2871v3","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2871","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z3CHFSTIGWO3","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z3CHFSTIGWO3X5WC","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z3CHFSTI","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Z3CHFSTIGWO3X5WCXUIE6UYPZ5","target":"record","payload":{"canonical_record":{"source":{"id":"1308.2871","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-13T14:06:25Z","cross_cats_sorted":[],"title_canon_sha256":"01b0dc8763e181139c9f9e30fe20e38bbd36680325975add0314d4b50a9c2030","abstract_canon_sha256":"8401041dba150c7dd0c18677ddf51f0e7e1a30a48980a4031c1fcd75d914a472"},"schema_version":"1.0"},"canonical_sha256":"cec472ca68359dbbf6c2bd104f530fcf7fb82d6b5535f192a46a1356271fdf17","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:59.849710Z","signature_b64":"a+uFR09yjFbbtKNbDRRFalJLsXiIDyjW0iSHtNnUtISelgZ0xtslqyU5ecgkMlqiSlJ80CZ83PuTuc8KeGVpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cec472ca68359dbbf6c2bd104f530fcf7fb82d6b5535f192a46a1356271fdf17","last_reissued_at":"2026-05-18T01:12:59.849376Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:59.849376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.2871","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":"2026-05-18T01:12:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G0yOICnSkaWibKg+HXBXriD2g5TMhFc+Bjc1MZYQ693GOlrbsjSmU04cV7QYjkFN4807woKP572ncMTJjZx8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T13:02:24.641528Z"},"content_sha256":"978dfed8c8f74c64fe9c86ea323eec3e17d1e23a1d9360460fd3770b01e040a4","schema_version":"1.0","event_id":"sha256:978dfed8c8f74c64fe9c86ea323eec3e17d1e23a1d9360460fd3770b01e040a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Z3CHFSTIGWO3X5WCXUIE6UYPZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some examples of isotropic SL(2,R)-invariant subbundles of the Hodge bundle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Matheus, Gabriela Weitze-Schmithuesen","submitted_at":"2013-08-13T14:06:25Z","abstract_excerpt":"We construct some examples of origamis (square-tiled surfaces) such that the Hodge bundles over the corresponding SL(2,R)-orbits on the moduli space admit non-trivial isotropic SL(2,R)-invariant subbundles. This answers a question posed to the authors by A. Eskin and G. Forni."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2871","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":"2026-05-18T01:12:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6io9m3RpC6rEUlOhnt5q3JqrTGZxGKEYC0Nvq8YRKeFhP/zZ8jdC88v6VbfXhqjDFFMS2JvRLZWAOzV27pNCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T13:02:24.642158Z"},"content_sha256":"6f352657b7094cbe49beec1d949bcfaa096412f0cfae72079fb0a7f7b2b8002f","schema_version":"1.0","event_id":"sha256:6f352657b7094cbe49beec1d949bcfaa096412f0cfae72079fb0a7f7b2b8002f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3CHFSTIGWO3X5WCXUIE6UYPZ5/bundle.json","state_url":"https://pith.science/pith/Z3CHFSTIGWO3X5WCXUIE6UYPZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3CHFSTIGWO3X5WCXUIE6UYPZ5/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":"2026-05-24T13:02:24Z","links":{"resolver":"https://pith.science/pith/Z3CHFSTIGWO3X5WCXUIE6UYPZ5","bundle":"https://pith.science/pith/Z3CHFSTIGWO3X5WCXUIE6UYPZ5/bundle.json","state":"https://pith.science/pith/Z3CHFSTIGWO3X5WCXUIE6UYPZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3CHFSTIGWO3X5WCXUIE6UYPZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z3CHFSTIGWO3X5WCXUIE6UYPZ5","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":"8401041dba150c7dd0c18677ddf51f0e7e1a30a48980a4031c1fcd75d914a472","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-13T14:06:25Z","title_canon_sha256":"01b0dc8763e181139c9f9e30fe20e38bbd36680325975add0314d4b50a9c2030"},"schema_version":"1.0","source":{"id":"1308.2871","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.2871","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"arxiv_version","alias_value":"1308.2871v3","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2871","created_at":"2026-05-18T01:12:59Z"},{"alias_kind":"pith_short_12","alias_value":"Z3CHFSTIGWO3","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z3CHFSTIGWO3X5WC","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z3CHFSTI","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:6f352657b7094cbe49beec1d949bcfaa096412f0cfae72079fb0a7f7b2b8002f","target":"graph","created_at":"2026-05-18T01:12:59Z","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":"We construct some examples of origamis (square-tiled surfaces) such that the Hodge bundles over the corresponding SL(2,R)-orbits on the moduli space admit non-trivial isotropic SL(2,R)-invariant subbundles. This answers a question posed to the authors by A. Eskin and G. Forni.","authors_text":"Carlos Matheus, Gabriela Weitze-Schmithuesen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-13T14:06:25Z","title":"Some examples of isotropic SL(2,R)-invariant subbundles of the Hodge bundle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2871","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":"sha256:978dfed8c8f74c64fe9c86ea323eec3e17d1e23a1d9360460fd3770b01e040a4","target":"record","created_at":"2026-05-18T01:12:59Z","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":"8401041dba150c7dd0c18677ddf51f0e7e1a30a48980a4031c1fcd75d914a472","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-08-13T14:06:25Z","title_canon_sha256":"01b0dc8763e181139c9f9e30fe20e38bbd36680325975add0314d4b50a9c2030"},"schema_version":"1.0","source":{"id":"1308.2871","kind":"arxiv","version":3}},"canonical_sha256":"cec472ca68359dbbf6c2bd104f530fcf7fb82d6b5535f192a46a1356271fdf17","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cec472ca68359dbbf6c2bd104f530fcf7fb82d6b5535f192a46a1356271fdf17","first_computed_at":"2026-05-18T01:12:59.849376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:59.849376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a+uFR09yjFbbtKNbDRRFalJLsXiIDyjW0iSHtNnUtISelgZ0xtslqyU5ecgkMlqiSlJ80CZ83PuTuc8KeGVpAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:59.849710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.2871","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:978dfed8c8f74c64fe9c86ea323eec3e17d1e23a1d9360460fd3770b01e040a4","sha256:6f352657b7094cbe49beec1d949bcfaa096412f0cfae72079fb0a7f7b2b8002f"],"state_sha256":"fda3c11570ec7269be07a8433e90811d7891994bc0ba3d81b037d7affaa058ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YLErEej9oBXFwnNKb1NU09FbDCU4i+i4vO2YIsOwIbcgCT5U6Hli7POzX9VNIqVnJIrmAp6/NSK/OWW0NHPQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T13:02:24.645505Z","bundle_sha256":"365ac6cfa0dc63bd522cd5cfd1705a831a063a2f81b93f9d1ce37e89076b65aa"}}