{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JP4PYDRMXXMCXCYVT2XSZNDJYF","short_pith_number":"pith:JP4PYDRM","canonical_record":{"source":{"id":"1610.01408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-05T13:22:51Z","cross_cats_sorted":[],"title_canon_sha256":"d33b0fd6e56a1f1d9258833c15fdca6b435683c969e2b08a0caf32c2d55e3690","abstract_canon_sha256":"22635eb03906b83c35732b1967c3c6f59f5e57ff4125ee9b60bc1e83ec0d414c"},"schema_version":"1.0"},"canonical_sha256":"4bf8fc0e2cbdd82b8b159eaf2cb469c15520e5da0fe696d4e1a7183a6b176636","source":{"kind":"arxiv","id":"1610.01408","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01408","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01408v2","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01408","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"pith_short_12","alias_value":"JP4PYDRMXXMC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JP4PYDRMXXMCXCYV","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JP4PYDRM","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JP4PYDRMXXMCXCYVT2XSZNDJYF","target":"record","payload":{"canonical_record":{"source":{"id":"1610.01408","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-05T13:22:51Z","cross_cats_sorted":[],"title_canon_sha256":"d33b0fd6e56a1f1d9258833c15fdca6b435683c969e2b08a0caf32c2d55e3690","abstract_canon_sha256":"22635eb03906b83c35732b1967c3c6f59f5e57ff4125ee9b60bc1e83ec0d414c"},"schema_version":"1.0"},"canonical_sha256":"4bf8fc0e2cbdd82b8b159eaf2cb469c15520e5da0fe696d4e1a7183a6b176636","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:05.310962Z","signature_b64":"2xLmMKE7/qs72ZO3xUKWLaoBhsZ12QejMYhgojsnMcGXoJhyOkeCqgX5S7dbsxyO++K7n5CdPL8k2XsSKkGyDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bf8fc0e2cbdd82b8b159eaf2cb469c15520e5da0fe696d4e1a7183a6b176636","last_reissued_at":"2026-05-18T01:00:05.310465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:05.310465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.01408","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":"2026-05-18T01:00:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F6C6CAT8snL3n6KqrZgC2XE8VahlC1xdw78JiNMAj6PZtc/D2thWTqn25svxyTook19rAaWtS+ltGvCEyEjQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:36:16.962128Z"},"content_sha256":"c6723d968105c128f2622ae9ce5c8cbe8f7a7185a92921bbe84d05382f16f480","schema_version":"1.0","event_id":"sha256:c6723d968105c128f2622ae9ce5c8cbe8f7a7185a92921bbe84d05382f16f480"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JP4PYDRMXXMCXCYVT2XSZNDJYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projective properties of Lorentzian surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Pierre Mounoud (IMB)","submitted_at":"2016-10-05T13:22:51Z","abstract_excerpt":"We investigate projective properties of Lorentzian surfaces. In particular, we prove that if T is a non flat torus, then the index of its isometry group in its projective group is at most two. We also prove that any topologically finite noncompact surface can be endowed with a metric having a non isometric projective transformation of infinite order."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01408","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":"2026-05-18T01:00:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qSLpx8dZgWCkSoOOHGB8GzzOBe5XOeyHfcKS+KpoIrevy9GVXyCzdOrKAFj95a424Rntdo/9ZNf5onMKqudBDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:36:16.962489Z"},"content_sha256":"cd4a2ddaf4622a181f1bb6a7017a3f9377f17d6c9528286497a10fea344b7ddf","schema_version":"1.0","event_id":"sha256:cd4a2ddaf4622a181f1bb6a7017a3f9377f17d6c9528286497a10fea344b7ddf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JP4PYDRMXXMCXCYVT2XSZNDJYF/bundle.json","state_url":"https://pith.science/pith/JP4PYDRMXXMCXCYVT2XSZNDJYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JP4PYDRMXXMCXCYVT2XSZNDJYF/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":"2026-06-01T10:36:16Z","links":{"resolver":"https://pith.science/pith/JP4PYDRMXXMCXCYVT2XSZNDJYF","bundle":"https://pith.science/pith/JP4PYDRMXXMCXCYVT2XSZNDJYF/bundle.json","state":"https://pith.science/pith/JP4PYDRMXXMCXCYVT2XSZNDJYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JP4PYDRMXXMCXCYVT2XSZNDJYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JP4PYDRMXXMCXCYVT2XSZNDJYF","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":"22635eb03906b83c35732b1967c3c6f59f5e57ff4125ee9b60bc1e83ec0d414c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-05T13:22:51Z","title_canon_sha256":"d33b0fd6e56a1f1d9258833c15fdca6b435683c969e2b08a0caf32c2d55e3690"},"schema_version":"1.0","source":{"id":"1610.01408","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01408","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01408v2","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01408","created_at":"2026-05-18T01:00:05Z"},{"alias_kind":"pith_short_12","alias_value":"JP4PYDRMXXMC","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JP4PYDRMXXMCXCYV","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JP4PYDRM","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:cd4a2ddaf4622a181f1bb6a7017a3f9377f17d6c9528286497a10fea344b7ddf","target":"graph","created_at":"2026-05-18T01:00:05Z","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 investigate projective properties of Lorentzian surfaces. In particular, we prove that if T is a non flat torus, then the index of its isometry group in its projective group is at most two. We also prove that any topologically finite noncompact surface can be endowed with a metric having a non isometric projective transformation of infinite order.","authors_text":"Pierre Mounoud (IMB)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-05T13:22:51Z","title":"Projective properties of Lorentzian surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01408","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:c6723d968105c128f2622ae9ce5c8cbe8f7a7185a92921bbe84d05382f16f480","target":"record","created_at":"2026-05-18T01:00:05Z","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":"22635eb03906b83c35732b1967c3c6f59f5e57ff4125ee9b60bc1e83ec0d414c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-05T13:22:51Z","title_canon_sha256":"d33b0fd6e56a1f1d9258833c15fdca6b435683c969e2b08a0caf32c2d55e3690"},"schema_version":"1.0","source":{"id":"1610.01408","kind":"arxiv","version":2}},"canonical_sha256":"4bf8fc0e2cbdd82b8b159eaf2cb469c15520e5da0fe696d4e1a7183a6b176636","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bf8fc0e2cbdd82b8b159eaf2cb469c15520e5da0fe696d4e1a7183a6b176636","first_computed_at":"2026-05-18T01:00:05.310465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:05.310465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2xLmMKE7/qs72ZO3xUKWLaoBhsZ12QejMYhgojsnMcGXoJhyOkeCqgX5S7dbsxyO++K7n5CdPL8k2XsSKkGyDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:05.310962Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01408","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6723d968105c128f2622ae9ce5c8cbe8f7a7185a92921bbe84d05382f16f480","sha256:cd4a2ddaf4622a181f1bb6a7017a3f9377f17d6c9528286497a10fea344b7ddf"],"state_sha256":"c290e3dda28068663d25e8ee80d075862dc9f500a747779b886608ab9a840834"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Er3QHJD6sjCC/P36S/7Uxb6ELsIvaOow0R9JCZiEw049P8NUY9agK9A6tKFe9kiPhVMCNVXP1eHtyv2ysKtpDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:36:16.964488Z","bundle_sha256":"31a5d1a89ac35b8434cc8877855a23a17f724df83ef9739994ac44b0850a1579"}}