{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3QQY4KKBYZ3C7FDBXRNGVQCCPB","short_pith_number":"pith:3QQY4KKB","canonical_record":{"source":{"id":"1408.6048","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-26T08:31:09Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6c5dd801f721c3634404e70b4eea0c59b6009da3d02705ef04950b08307043a3","abstract_canon_sha256":"468646c511c3cc452cf35347369c1ee8d9e9fc69f0fd0b7a50d40385859795f4"},"schema_version":"1.0"},"canonical_sha256":"dc218e2941c6762f9461bc5a6ac04278525c6dd836823119e5f186e73d77cfc0","source":{"kind":"arxiv","id":"1408.6048","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6048","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6048v2","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6048","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"3QQY4KKBYZ3C","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3QQY4KKBYZ3C7FDB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3QQY4KKB","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3QQY4KKBYZ3C7FDBXRNGVQCCPB","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6048","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-26T08:31:09Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6c5dd801f721c3634404e70b4eea0c59b6009da3d02705ef04950b08307043a3","abstract_canon_sha256":"468646c511c3cc452cf35347369c1ee8d9e9fc69f0fd0b7a50d40385859795f4"},"schema_version":"1.0"},"canonical_sha256":"dc218e2941c6762f9461bc5a6ac04278525c6dd836823119e5f186e73d77cfc0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:55.940940Z","signature_b64":"4bwBWUZopKK3SA5fD/aUR/9Shg3/wwR7XIsaPIH8WFkXIBaSO37lL0zvAqeJbanUDrDMgwXw5GZc18QM3KtzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc218e2941c6762f9461bc5a6ac04278525c6dd836823119e5f186e73d77cfc0","last_reissued_at":"2026-05-18T01:21:55.940225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:55.940225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6048","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":"2026-05-18T01:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"psPRZLtbeZ9k35Y/aTMtQr6N5kV5RdbBMNP4kstBJ+AjEpV2LMnr9+weYhfp6lWcGFhlfKs4ljRrxN6iGhsCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:38:08.795391Z"},"content_sha256":"36194d2743579b792fff73f76dc97999c80bd8ac073317144f6d622131b3b2f8","schema_version":"1.0","event_id":"sha256:36194d2743579b792fff73f76dc97999c80bd8ac073317144f6d622131b3b2f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3QQY4KKBYZ3C7FDBXRNGVQCCPB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Systoles and kissing numbers of finite area hyperbolic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Federica Fanoni, Hugo Parlier","submitted_at":"2014-08-26T08:31:09Z","abstract_excerpt":"We study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main result is a bound which only depends on the topology of the surface and which grows subquadratically in the genus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6048","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":"2026-05-18T01:21:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bkt2cuDZC2ZpwJlTMkg02kL5UXlQBBxpPFuYkMDy0Y+ChRGt3cmh9L5w9VJH2n0uFTTcVFR2gqrsaWRklR3sBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:38:08.796023Z"},"content_sha256":"661da35ddc90128d8c51b53b8c63f2d5759d455af35db21e5f124cadca9b44f9","schema_version":"1.0","event_id":"sha256:661da35ddc90128d8c51b53b8c63f2d5759d455af35db21e5f124cadca9b44f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3QQY4KKBYZ3C7FDBXRNGVQCCPB/bundle.json","state_url":"https://pith.science/pith/3QQY4KKBYZ3C7FDBXRNGVQCCPB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3QQY4KKBYZ3C7FDBXRNGVQCCPB/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":"2026-05-25T20:38:08Z","links":{"resolver":"https://pith.science/pith/3QQY4KKBYZ3C7FDBXRNGVQCCPB","bundle":"https://pith.science/pith/3QQY4KKBYZ3C7FDBXRNGVQCCPB/bundle.json","state":"https://pith.science/pith/3QQY4KKBYZ3C7FDBXRNGVQCCPB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3QQY4KKBYZ3C7FDBXRNGVQCCPB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3QQY4KKBYZ3C7FDBXRNGVQCCPB","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":"468646c511c3cc452cf35347369c1ee8d9e9fc69f0fd0b7a50d40385859795f4","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-26T08:31:09Z","title_canon_sha256":"6c5dd801f721c3634404e70b4eea0c59b6009da3d02705ef04950b08307043a3"},"schema_version":"1.0","source":{"id":"1408.6048","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6048","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6048v2","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6048","created_at":"2026-05-18T01:21:55Z"},{"alias_kind":"pith_short_12","alias_value":"3QQY4KKBYZ3C","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3QQY4KKBYZ3C7FDB","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3QQY4KKB","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:661da35ddc90128d8c51b53b8c63f2d5759d455af35db21e5f124cadca9b44f9","target":"graph","created_at":"2026-05-18T01:21:55Z","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 study the number and the length of systoles on complete finite area orientable hyperbolic surfaces. In particular, we prove upper bounds on the number of systoles that a surface can have (the so-called kissing number for hyperbolic surfaces). Our main result is a bound which only depends on the topology of the surface and which grows subquadratically in the genus.","authors_text":"Federica Fanoni, Hugo Parlier","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-26T08:31:09Z","title":"Systoles and kissing numbers of finite area hyperbolic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6048","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":"sha256:36194d2743579b792fff73f76dc97999c80bd8ac073317144f6d622131b3b2f8","target":"record","created_at":"2026-05-18T01:21:55Z","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":"468646c511c3cc452cf35347369c1ee8d9e9fc69f0fd0b7a50d40385859795f4","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-26T08:31:09Z","title_canon_sha256":"6c5dd801f721c3634404e70b4eea0c59b6009da3d02705ef04950b08307043a3"},"schema_version":"1.0","source":{"id":"1408.6048","kind":"arxiv","version":2}},"canonical_sha256":"dc218e2941c6762f9461bc5a6ac04278525c6dd836823119e5f186e73d77cfc0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc218e2941c6762f9461bc5a6ac04278525c6dd836823119e5f186e73d77cfc0","first_computed_at":"2026-05-18T01:21:55.940225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:55.940225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4bwBWUZopKK3SA5fD/aUR/9Shg3/wwR7XIsaPIH8WFkXIBaSO37lL0zvAqeJbanUDrDMgwXw5GZc18QM3KtzDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:55.940940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6048","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36194d2743579b792fff73f76dc97999c80bd8ac073317144f6d622131b3b2f8","sha256:661da35ddc90128d8c51b53b8c63f2d5759d455af35db21e5f124cadca9b44f9"],"state_sha256":"2902ef6fa46d4d0c1b6792d475ae9cf0eb0442748104fd80220167dcfc2c7942"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5+z1Ta/UxlgY9PZM4bzsM7wLCrscfyPdGs4HcooqtQZONGjsw58y0InPIXSCm4Us1msarDV/TFN+8FuM4ECIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:38:08.799615Z","bundle_sha256":"23ce04b958536fb4a90e744a78d42c45a7742836b0d2994b5005c8c7a7ebbd70"}}