{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:VYF2IWZ5HOOROO7ZCCDTBSTLPZ","short_pith_number":"pith:VYF2IWZ5","canonical_record":{"source":{"id":"math/0504008","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-04-01T06:32:08Z","cross_cats_sorted":["math.AT","math.GT","math.MG"],"title_canon_sha256":"86ea0c08e7ef6420ece4bcec8de643e5b6b0bc2e120e97c9cc140a00b8033aed","abstract_canon_sha256":"8e8da770615d27520408ffc4636f024b6d2c4e9741a64cf403edc21601ee5d5d"},"schema_version":"1.0"},"canonical_sha256":"ae0ba45b3d3b9d173bf9108730ca6b7e6134ecd4275b48a54a0a4c75c18ef749","source":{"kind":"arxiv","id":"math/0504008","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504008","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504008v2","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504008","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"VYF2IWZ5HOOR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"VYF2IWZ5HOOROO7Z","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"VYF2IWZ5","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:VYF2IWZ5HOOROO7ZCCDTBSTLPZ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0504008","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2005-04-01T06:32:08Z","cross_cats_sorted":["math.AT","math.GT","math.MG"],"title_canon_sha256":"86ea0c08e7ef6420ece4bcec8de643e5b6b0bc2e120e97c9cc140a00b8033aed","abstract_canon_sha256":"8e8da770615d27520408ffc4636f024b6d2c4e9741a64cf403edc21601ee5d5d"},"schema_version":"1.0"},"canonical_sha256":"ae0ba45b3d3b9d173bf9108730ca6b7e6134ecd4275b48a54a0a4c75c18ef749","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:51.119621Z","signature_b64":"Ho2EePHTwqdf9QtjlkWnTsfr38uuVHK2AtoeGuFSvLCK9xp+SM6TC6PoG56OVjw3UAZRxCPthUS5VoSrF6sbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae0ba45b3d3b9d173bf9108730ca6b7e6134ecd4275b48a54a0a4c75c18ef749","last_reissued_at":"2026-05-18T02:57:51.119061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:51.119061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0504008","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":"2026-05-18T02:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KkQ9m9BfA/NbgsMCqq3j6aQ+Ccybt/kCako5YZBYkIiqUm/oTAwBI7Z8iKgorXTdQGxhGmFELqD/hEqBXVWSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:58:26.024332Z"},"content_sha256":"99dbdb9fa81ba2d7c7ac2269ab3bb6858fd05429982bbeb96a75c9b2dbbe1c8c","schema_version":"1.0","event_id":"sha256:99dbdb9fa81ba2d7c7ac2269ab3bb6858fd05429982bbeb96a75c9b2dbbe1c8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:VYF2IWZ5HOOROO7ZCCDTBSTLPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounding volume by systoles of 3-manifolds","license":"","headline":"","cross_cats":["math.AT","math.GT","math.MG"],"primary_cat":"math.DG","authors_text":"Mikhail G. Katz, Yuli B. Rudyak","submitted_at":"2005-04-01T06:32:08Z","abstract_excerpt":"We prove a new systolic volume lower bound for non-orientable n-manifolds, involving the stable 1-systole and the codimension 1 systole with coefficients in Z_2. As an application, we prove that Lusternik-Schnirelmann category and systolic category agree for non-orientable closed manifolds of dimension 3, extending our earlier result in the orientable case. Finally, we prove the homotopy invariance of systolic category."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504008","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":"2026-05-18T02:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BMLhTIE0Et/wV1dzga6WSt5xcf0W1sbbq2ELlbVNbkX38/MN8IBGJdhpcKt+8vTeUIQsHC7StkuP6FH3iIxwCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T10:58:26.024932Z"},"content_sha256":"705d31299476de57a3ebac1ee4b6966088a3f7d8163ef11cdfcc3348cedbd0bf","schema_version":"1.0","event_id":"sha256:705d31299476de57a3ebac1ee4b6966088a3f7d8163ef11cdfcc3348cedbd0bf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/bundle.json","state_url":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/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":"2026-07-01T10:58:26Z","links":{"resolver":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ","bundle":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/bundle.json","state":"https://pith.science/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VYF2IWZ5HOOROO7ZCCDTBSTLPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:VYF2IWZ5HOOROO7ZCCDTBSTLPZ","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":"8e8da770615d27520408ffc4636f024b6d2c4e9741a64cf403edc21601ee5d5d","cross_cats_sorted":["math.AT","math.GT","math.MG"],"license":"","primary_cat":"math.DG","submitted_at":"2005-04-01T06:32:08Z","title_canon_sha256":"86ea0c08e7ef6420ece4bcec8de643e5b6b0bc2e120e97c9cc140a00b8033aed"},"schema_version":"1.0","source":{"id":"math/0504008","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504008","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504008v2","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504008","created_at":"2026-05-18T02:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"VYF2IWZ5HOOR","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"VYF2IWZ5HOOROO7Z","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"VYF2IWZ5","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:705d31299476de57a3ebac1ee4b6966088a3f7d8163ef11cdfcc3348cedbd0bf","target":"graph","created_at":"2026-05-18T02:57:51Z","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 prove a new systolic volume lower bound for non-orientable n-manifolds, involving the stable 1-systole and the codimension 1 systole with coefficients in Z_2. As an application, we prove that Lusternik-Schnirelmann category and systolic category agree for non-orientable closed manifolds of dimension 3, extending our earlier result in the orientable case. Finally, we prove the homotopy invariance of systolic category.","authors_text":"Mikhail G. Katz, Yuli B. Rudyak","cross_cats":["math.AT","math.GT","math.MG"],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2005-04-01T06:32:08Z","title":"Bounding volume by systoles of 3-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504008","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":"sha256:99dbdb9fa81ba2d7c7ac2269ab3bb6858fd05429982bbeb96a75c9b2dbbe1c8c","target":"record","created_at":"2026-05-18T02:57:51Z","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":"8e8da770615d27520408ffc4636f024b6d2c4e9741a64cf403edc21601ee5d5d","cross_cats_sorted":["math.AT","math.GT","math.MG"],"license":"","primary_cat":"math.DG","submitted_at":"2005-04-01T06:32:08Z","title_canon_sha256":"86ea0c08e7ef6420ece4bcec8de643e5b6b0bc2e120e97c9cc140a00b8033aed"},"schema_version":"1.0","source":{"id":"math/0504008","kind":"arxiv","version":2}},"canonical_sha256":"ae0ba45b3d3b9d173bf9108730ca6b7e6134ecd4275b48a54a0a4c75c18ef749","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae0ba45b3d3b9d173bf9108730ca6b7e6134ecd4275b48a54a0a4c75c18ef749","first_computed_at":"2026-05-18T02:57:51.119061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:51.119061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ho2EePHTwqdf9QtjlkWnTsfr38uuVHK2AtoeGuFSvLCK9xp+SM6TC6PoG56OVjw3UAZRxCPthUS5VoSrF6sbAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:51.119621Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504008","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99dbdb9fa81ba2d7c7ac2269ab3bb6858fd05429982bbeb96a75c9b2dbbe1c8c","sha256:705d31299476de57a3ebac1ee4b6966088a3f7d8163ef11cdfcc3348cedbd0bf"],"state_sha256":"c0749a2515ef7c206ddb5403cc34b04d2d4237f2556b539b19b76144e2faa906"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/KFBSJC8y0yyox6r1sTSK4OeP1N4HhVK4AyVUBEqgrGrX8YL52j5MPs/7J0ezORAb6ZgBiddZeuehrcHbLHbAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T10:58:26.027807Z","bundle_sha256":"7b6f759921686d11516779626731b061240455c2979c8f82cafd3b83f5672f4d"}}