{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:M64PAHPTU2DT6EEMPQZN5CMC7S","short_pith_number":"pith:M64PAHPT","canonical_record":{"source":{"id":"1808.01336","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-03T20:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"24efbe9ee321ceca786c72ab13cd95087f67dafc3c9fe9c792fdec9c9e68f4c1","abstract_canon_sha256":"225a4867418c8d466d86934037f10847f6d37b083fa2751fa47593f11bace7dd"},"schema_version":"1.0"},"canonical_sha256":"67b8f01df3a6873f108c7c32de8982fc8a48e61fb4bdb09da2b63ccdceb52b4c","source":{"kind":"arxiv","id":"1808.01336","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01336","created_at":"2026-05-17T23:47:52Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01336v2","created_at":"2026-05-17T23:47:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01336","created_at":"2026-05-17T23:47:52Z"},{"alias_kind":"pith_short_12","alias_value":"M64PAHPTU2DT","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M64PAHPTU2DT6EEM","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M64PAHPT","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:M64PAHPTU2DT6EEMPQZN5CMC7S","target":"record","payload":{"canonical_record":{"source":{"id":"1808.01336","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-03T20:13:52Z","cross_cats_sorted":[],"title_canon_sha256":"24efbe9ee321ceca786c72ab13cd95087f67dafc3c9fe9c792fdec9c9e68f4c1","abstract_canon_sha256":"225a4867418c8d466d86934037f10847f6d37b083fa2751fa47593f11bace7dd"},"schema_version":"1.0"},"canonical_sha256":"67b8f01df3a6873f108c7c32de8982fc8a48e61fb4bdb09da2b63ccdceb52b4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:52.738264Z","signature_b64":"bvjXZ+nWNiTofVoWz6cBPlbch6eU1BpVI1LN1JFKA7ovO/NOfk+GTS4/h7DGWfBFCpJzT/PiCRLONcM+A9hiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67b8f01df3a6873f108c7c32de8982fc8a48e61fb4bdb09da2b63ccdceb52b4c","last_reissued_at":"2026-05-17T23:47:52.737648Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:52.737648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.01336","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":"2026-05-17T23:47:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YV3mtdx+XwvVPzEmLVNTLk5VmWVtWKxM22vjRmT8NWkIxRXNNBgGaYqrb83oq5oXRdfDNiCnTfgEOquXxgffDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:40:57.961397Z"},"content_sha256":"fbe86ecdc8faa54b1ccdf69f24a7e0385e880ca21a7ec1efad95098d96bc3dc9","schema_version":"1.0","event_id":"sha256:fbe86ecdc8faa54b1ccdf69f24a7e0385e880ca21a7ec1efad95098d96bc3dc9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:M64PAHPTU2DT6EEMPQZN5CMC7S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new proof of the existence of embedded surfaces with Anosov geodesic flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Daniel Visscher, Victor Donnay","submitted_at":"2018-08-03T20:13:52Z","abstract_excerpt":"We give a new proof of the existence of compact surfaces embedded in $R^3$ with Anosov geodesic flows. This proof starts with a non-compact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone condition. Using a sequence of explicit maps based on the standard torus embedding, we produce compact embedded surfaces that can be seen as small perturbations of the Anosov model system and hence are themselves Anosov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01336","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":"2026-05-17T23:47:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mRvsBgjnSyENWeZ04W1TH76d0iRaR9ZRvSLlv5XWW4RbjTrrSc6Pe63goq76VY4QPEzIr9Fjb1rA6CDKHf2oCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T14:40:57.961747Z"},"content_sha256":"4619c7aee49f474a93ae67859fa62968c02d2a0955e8e16342eabfe6747a2670","schema_version":"1.0","event_id":"sha256:4619c7aee49f474a93ae67859fa62968c02d2a0955e8e16342eabfe6747a2670"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M64PAHPTU2DT6EEMPQZN5CMC7S/bundle.json","state_url":"https://pith.science/pith/M64PAHPTU2DT6EEMPQZN5CMC7S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M64PAHPTU2DT6EEMPQZN5CMC7S/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":"2026-06-24T14:40:57Z","links":{"resolver":"https://pith.science/pith/M64PAHPTU2DT6EEMPQZN5CMC7S","bundle":"https://pith.science/pith/M64PAHPTU2DT6EEMPQZN5CMC7S/bundle.json","state":"https://pith.science/pith/M64PAHPTU2DT6EEMPQZN5CMC7S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M64PAHPTU2DT6EEMPQZN5CMC7S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:M64PAHPTU2DT6EEMPQZN5CMC7S","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":"225a4867418c8d466d86934037f10847f6d37b083fa2751fa47593f11bace7dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-03T20:13:52Z","title_canon_sha256":"24efbe9ee321ceca786c72ab13cd95087f67dafc3c9fe9c792fdec9c9e68f4c1"},"schema_version":"1.0","source":{"id":"1808.01336","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.01336","created_at":"2026-05-17T23:47:52Z"},{"alias_kind":"arxiv_version","alias_value":"1808.01336v2","created_at":"2026-05-17T23:47:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.01336","created_at":"2026-05-17T23:47:52Z"},{"alias_kind":"pith_short_12","alias_value":"M64PAHPTU2DT","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M64PAHPTU2DT6EEM","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M64PAHPT","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:4619c7aee49f474a93ae67859fa62968c02d2a0955e8e16342eabfe6747a2670","target":"graph","created_at":"2026-05-17T23:47:52Z","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 give a new proof of the existence of compact surfaces embedded in $R^3$ with Anosov geodesic flows. This proof starts with a non-compact model surface whose geodesic flow is shown to be Anosov using a uniformly strictly invariant cone condition. Using a sequence of explicit maps based on the standard torus embedding, we produce compact embedded surfaces that can be seen as small perturbations of the Anosov model system and hence are themselves Anosov.","authors_text":"Daniel Visscher, Victor Donnay","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-03T20:13:52Z","title":"A new proof of the existence of embedded surfaces with Anosov geodesic flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.01336","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:fbe86ecdc8faa54b1ccdf69f24a7e0385e880ca21a7ec1efad95098d96bc3dc9","target":"record","created_at":"2026-05-17T23:47:52Z","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":"225a4867418c8d466d86934037f10847f6d37b083fa2751fa47593f11bace7dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-03T20:13:52Z","title_canon_sha256":"24efbe9ee321ceca786c72ab13cd95087f67dafc3c9fe9c792fdec9c9e68f4c1"},"schema_version":"1.0","source":{"id":"1808.01336","kind":"arxiv","version":2}},"canonical_sha256":"67b8f01df3a6873f108c7c32de8982fc8a48e61fb4bdb09da2b63ccdceb52b4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67b8f01df3a6873f108c7c32de8982fc8a48e61fb4bdb09da2b63ccdceb52b4c","first_computed_at":"2026-05-17T23:47:52.737648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:52.737648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bvjXZ+nWNiTofVoWz6cBPlbch6eU1BpVI1LN1JFKA7ovO/NOfk+GTS4/h7DGWfBFCpJzT/PiCRLONcM+A9hiBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:52.738264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.01336","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fbe86ecdc8faa54b1ccdf69f24a7e0385e880ca21a7ec1efad95098d96bc3dc9","sha256:4619c7aee49f474a93ae67859fa62968c02d2a0955e8e16342eabfe6747a2670"],"state_sha256":"fec8c586c717d446f652e689a0d0c6991749095ef8dc1849fd20be4c1b4d5a73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Nh3gFEaY9s/Ctp84SK3o9vK8LqChxBTRfE/N1s882SLShmhyDGCAJOpR3YCVMsL9aw8DWl/VHYMMYDT3uOICg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T14:40:57.963687Z","bundle_sha256":"35e138578f6d16a83a09c65fc325733ed5392f8b4c195ed639b425748109fb99"}}