{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:K2AM5W6YN2XSRV6QLDRIFZTPE5","short_pith_number":"pith:K2AM5W6Y","canonical_record":{"source":{"id":"1509.07647","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-25T09:23:00Z","cross_cats_sorted":[],"title_canon_sha256":"c7b1574472f474df14b926be4703aebc5e2359878977d4478c214b6f9f09a4a5","abstract_canon_sha256":"a95e460e1bd14a449aaa3a258c4613655447231c32bbb09d9459ad45495baded"},"schema_version":"1.0"},"canonical_sha256":"5680cedbd86eaf28d7d058e282e66f2761876d72fe0b93bad64f32f9bb9ebcd3","source":{"kind":"arxiv","id":"1509.07647","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07647","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07647v4","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07647","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"K2AM5W6YN2XS","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"pith_short_16","alias_value":"K2AM5W6YN2XSRV6Q","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"pith_short_8","alias_value":"K2AM5W6Y","created_at":"2026-07-05T00:11:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:K2AM5W6YN2XSRV6QLDRIFZTPE5","target":"record","payload":{"canonical_record":{"source":{"id":"1509.07647","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-25T09:23:00Z","cross_cats_sorted":[],"title_canon_sha256":"c7b1574472f474df14b926be4703aebc5e2359878977d4478c214b6f9f09a4a5","abstract_canon_sha256":"a95e460e1bd14a449aaa3a258c4613655447231c32bbb09d9459ad45495baded"},"schema_version":"1.0"},"canonical_sha256":"5680cedbd86eaf28d7d058e282e66f2761876d72fe0b93bad64f32f9bb9ebcd3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:11:52.873669Z","signature_b64":"3c6JlnOWhuyvfJuuNDk6CNzu8zGLABFHqFONMF8jyI3xpW0nWL6WWoK9PCWejw5g0TBxf9QGYt+cYXpteDSsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5680cedbd86eaf28d7d058e282e66f2761876d72fe0b93bad64f32f9bb9ebcd3","last_reissued_at":"2026-07-05T00:11:52.873237Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:11:52.873237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.07647","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUnB99Tl0dZgbqz8Wt5o8o2Qjm4bL5V3QD0+JwwmMOZgLPZKQ+OoU5iM/+OTENT486eKUwP8Luk7x9JnVjebAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:29:23.719340Z"},"content_sha256":"7e223730120cc5bc41f51e4533d1ee589225157ebb0f64253c30022f7c7f38a2","schema_version":"1.0","event_id":"sha256:7e223730120cc5bc41f51e4533d1ee589225157ebb0f64253c30022f7c7f38a2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:K2AM5W6YN2XSRV6QLDRIFZTPE5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Systolic volume and complexity of 3-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Lizhi Chen","submitted_at":"2015-09-25T09:23:00Z","abstract_excerpt":"In this paper, we prove that the systolic volume of a closed aspherical 3-manifold is bounded below in terms of complexity. Systolic volume is defined as the optimal constant in a systolic inequality. Babenko showed that the systolic volume is a homotopy invariant. Moreover, Gromov proved that the systolic volume depends on topology of the manifold. More precisely, Gromov proved that the systolic volume is related to some topological invariants measuring complicatedness. In this paper, we work along Gromov's spirit to show that systolic volume of 3-manifolds is related to complexity. The compl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07647","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1509.07647/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:11:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E+lw3zeGf6qQBePySqUBbuq2Is0GYAdLajFv5lgufWPY66LgJv7+JtvIXpr6b7NMORJadF0LJgY+JZi9umqkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T14:29:23.719714Z"},"content_sha256":"8fa09a93f5f7e478fa9093641374a5ae34f574a449bc1d9bad1dc1d34fe43c95","schema_version":"1.0","event_id":"sha256:8fa09a93f5f7e478fa9093641374a5ae34f574a449bc1d9bad1dc1d34fe43c95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K2AM5W6YN2XSRV6QLDRIFZTPE5/bundle.json","state_url":"https://pith.science/pith/K2AM5W6YN2XSRV6QLDRIFZTPE5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K2AM5W6YN2XSRV6QLDRIFZTPE5/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":"2026-07-06T14:29:23Z","links":{"resolver":"https://pith.science/pith/K2AM5W6YN2XSRV6QLDRIFZTPE5","bundle":"https://pith.science/pith/K2AM5W6YN2XSRV6QLDRIFZTPE5/bundle.json","state":"https://pith.science/pith/K2AM5W6YN2XSRV6QLDRIFZTPE5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K2AM5W6YN2XSRV6QLDRIFZTPE5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:K2AM5W6YN2XSRV6QLDRIFZTPE5","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":"a95e460e1bd14a449aaa3a258c4613655447231c32bbb09d9459ad45495baded","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-25T09:23:00Z","title_canon_sha256":"c7b1574472f474df14b926be4703aebc5e2359878977d4478c214b6f9f09a4a5"},"schema_version":"1.0","source":{"id":"1509.07647","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07647","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07647v4","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07647","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"pith_short_12","alias_value":"K2AM5W6YN2XS","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"pith_short_16","alias_value":"K2AM5W6YN2XSRV6Q","created_at":"2026-07-05T00:11:52Z"},{"alias_kind":"pith_short_8","alias_value":"K2AM5W6Y","created_at":"2026-07-05T00:11:52Z"}],"graph_snapshots":[{"event_id":"sha256:8fa09a93f5f7e478fa9093641374a5ae34f574a449bc1d9bad1dc1d34fe43c95","target":"graph","created_at":"2026-07-05T00:11:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1509.07647/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that the systolic volume of a closed aspherical 3-manifold is bounded below in terms of complexity. Systolic volume is defined as the optimal constant in a systolic inequality. Babenko showed that the systolic volume is a homotopy invariant. Moreover, Gromov proved that the systolic volume depends on topology of the manifold. More precisely, Gromov proved that the systolic volume is related to some topological invariants measuring complicatedness. In this paper, we work along Gromov's spirit to show that systolic volume of 3-manifolds is related to complexity. The compl","authors_text":"Lizhi Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-25T09:23:00Z","title":"Systolic volume and complexity of 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07647","kind":"arxiv","version":4},"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":"sha256:7e223730120cc5bc41f51e4533d1ee589225157ebb0f64253c30022f7c7f38a2","target":"record","created_at":"2026-07-05T00:11:52Z","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":"a95e460e1bd14a449aaa3a258c4613655447231c32bbb09d9459ad45495baded","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2015-09-25T09:23:00Z","title_canon_sha256":"c7b1574472f474df14b926be4703aebc5e2359878977d4478c214b6f9f09a4a5"},"schema_version":"1.0","source":{"id":"1509.07647","kind":"arxiv","version":4}},"canonical_sha256":"5680cedbd86eaf28d7d058e282e66f2761876d72fe0b93bad64f32f9bb9ebcd3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5680cedbd86eaf28d7d058e282e66f2761876d72fe0b93bad64f32f9bb9ebcd3","first_computed_at":"2026-07-05T00:11:52.873237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:11:52.873237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3c6JlnOWhuyvfJuuNDk6CNzu8zGLABFHqFONMF8jyI3xpW0nWL6WWoK9PCWejw5g0TBxf9QGYt+cYXpteDSsCw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:11:52.873669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07647","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e223730120cc5bc41f51e4533d1ee589225157ebb0f64253c30022f7c7f38a2","sha256:8fa09a93f5f7e478fa9093641374a5ae34f574a449bc1d9bad1dc1d34fe43c95"],"state_sha256":"6508c9e4a631e0285a93117ec2a76184e04d2d201ba89a77e1ea4432732351b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tyq//z/SrT2yUJ2y8F8sTaaqcFcND9I08TLvSZfhSuVPLBazdtIMiO4TWRp061fo0ELThYE3BmUrxvhs8bKyCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T14:29:23.721684Z","bundle_sha256":"10b85ba11d1884f531a2822989762d65ae013bd36e4cddb69c9a8608f13e637f"}}