{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HCQ6FFS66R36W2KJQWXSDZ2VGR","short_pith_number":"pith:HCQ6FFS6","canonical_record":{"source":{"id":"1402.4504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-18T21:42:35Z","cross_cats_sorted":[],"title_canon_sha256":"889cd958c701db4002ef6b020294b9b9d291d9d0af19edee363521c8281c714b","abstract_canon_sha256":"f7a7c8a7376e1e03cc3555aa60956db2504a24fc79126e9ac90a7db2125e9784"},"schema_version":"1.0"},"canonical_sha256":"38a1e2965ef477eb694985af21e755345e2c9eb9bee0f0a7cd3c6180bd90dbdf","source":{"kind":"arxiv","id":"1402.4504","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4504","created_at":"2026-05-18T02:32:30Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4504v3","created_at":"2026-05-18T02:32:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4504","created_at":"2026-05-18T02:32:30Z"},{"alias_kind":"pith_short_12","alias_value":"HCQ6FFS66R36","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HCQ6FFS66R36W2KJ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HCQ6FFS6","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HCQ6FFS66R36W2KJQWXSDZ2VGR","target":"record","payload":{"canonical_record":{"source":{"id":"1402.4504","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-18T21:42:35Z","cross_cats_sorted":[],"title_canon_sha256":"889cd958c701db4002ef6b020294b9b9d291d9d0af19edee363521c8281c714b","abstract_canon_sha256":"f7a7c8a7376e1e03cc3555aa60956db2504a24fc79126e9ac90a7db2125e9784"},"schema_version":"1.0"},"canonical_sha256":"38a1e2965ef477eb694985af21e755345e2c9eb9bee0f0a7cd3c6180bd90dbdf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:30.931664Z","signature_b64":"yVEqZ5xItt8UzWyM6JEuI8bb6kQOH4SyFNOF0RBCui9RclAHtKM2Hn2KFdV0GZTTWugn/rs6ZesWsAPMWBKGCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38a1e2965ef477eb694985af21e755345e2c9eb9bee0f0a7cd3c6180bd90dbdf","last_reissued_at":"2026-05-18T02:32:30.931273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:30.931273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.4504","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9fgF4fS/Yod52/G5p7hfRXk8t8NyF2QhDAMtgMoJzITmGmc1sz+Zz8cyZmMuWF51+jDL7NshT/9LmxU572riBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:06:28.531119Z"},"content_sha256":"5c528e00cf8c15c669ecd31ffa401cab750ecf1a1efe70d842ddf25120c1cb93","schema_version":"1.0","event_id":"sha256:5c528e00cf8c15c669ecd31ffa401cab750ecf1a1efe70d842ddf25120c1cb93"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HCQ6FFS66R36W2KJQWXSDZ2VGR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\mathbb{Z}_{2}$-coefficient homology $(1, 2)$-systolic freedom of $\\mathbb{R}\\mathbb{P}^{3}$ # $\\mathbb{R}\\mathbb{P}^{3}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lizhi Chen","submitted_at":"2014-02-18T21:42:35Z","abstract_excerpt":"We prove the $3$-manifold $\\RP^3 \\# \\RP^3$ is of $\\Z_{2}$-coefficient homology $(1, 2)$-systolic freedom. Given a Riemannian metric on $\\RP^{3}\\# \\RP^{3}$, we define $\\Z_{2}$-coefficient homology $1$-systole as the infimum of lengths of all nonseparating geodesic loops representing nontrivial classes in $H_{1}(\\RP^3\\#\\RP^3; \\Z_{2})$. The $\\Z_{2}$-coefficient homology $2$-systole is defined to be the infimum of areas of all nonseparating surfaces representing nontrivial classes in $H_{2}(\\RP^{3}\\#\\RP^{3}; \\Z_2)$. In the paper we show that there exists a sequence of Riemannian metrics on $\\RP^{3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4504","kind":"arxiv","version":3},"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":"2026-05-18T02:32:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jsQ1BSvl4IeRW9MHJcyjImnbWqbJPZPZACJNI7yxOG27a7e7ZD6vXUd5g6OC0wB4EOSd6MUcNyYshDRtVlJcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T11:06:28.531465Z"},"content_sha256":"807b93d836c53e6814b2f62d7e8377e221121be0859ba83c677a5ac9863d5c32","schema_version":"1.0","event_id":"sha256:807b93d836c53e6814b2f62d7e8377e221121be0859ba83c677a5ac9863d5c32"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HCQ6FFS66R36W2KJQWXSDZ2VGR/bundle.json","state_url":"https://pith.science/pith/HCQ6FFS66R36W2KJQWXSDZ2VGR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HCQ6FFS66R36W2KJQWXSDZ2VGR/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":"2026-07-07T11:06:28Z","links":{"resolver":"https://pith.science/pith/HCQ6FFS66R36W2KJQWXSDZ2VGR","bundle":"https://pith.science/pith/HCQ6FFS66R36W2KJQWXSDZ2VGR/bundle.json","state":"https://pith.science/pith/HCQ6FFS66R36W2KJQWXSDZ2VGR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HCQ6FFS66R36W2KJQWXSDZ2VGR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HCQ6FFS66R36W2KJQWXSDZ2VGR","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":"f7a7c8a7376e1e03cc3555aa60956db2504a24fc79126e9ac90a7db2125e9784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-18T21:42:35Z","title_canon_sha256":"889cd958c701db4002ef6b020294b9b9d291d9d0af19edee363521c8281c714b"},"schema_version":"1.0","source":{"id":"1402.4504","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4504","created_at":"2026-05-18T02:32:30Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4504v3","created_at":"2026-05-18T02:32:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4504","created_at":"2026-05-18T02:32:30Z"},{"alias_kind":"pith_short_12","alias_value":"HCQ6FFS66R36","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HCQ6FFS66R36W2KJ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HCQ6FFS6","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:807b93d836c53e6814b2f62d7e8377e221121be0859ba83c677a5ac9863d5c32","target":"graph","created_at":"2026-05-18T02:32:30Z","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 the $3$-manifold $\\RP^3 \\# \\RP^3$ is of $\\Z_{2}$-coefficient homology $(1, 2)$-systolic freedom. Given a Riemannian metric on $\\RP^{3}\\# \\RP^{3}$, we define $\\Z_{2}$-coefficient homology $1$-systole as the infimum of lengths of all nonseparating geodesic loops representing nontrivial classes in $H_{1}(\\RP^3\\#\\RP^3; \\Z_{2})$. The $\\Z_{2}$-coefficient homology $2$-systole is defined to be the infimum of areas of all nonseparating surfaces representing nontrivial classes in $H_{2}(\\RP^{3}\\#\\RP^{3}; \\Z_2)$. In the paper we show that there exists a sequence of Riemannian metrics on $\\RP^{3","authors_text":"Lizhi Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-18T21:42:35Z","title":"$\\mathbb{Z}_{2}$-coefficient homology $(1, 2)$-systolic freedom of $\\mathbb{R}\\mathbb{P}^{3}$ # $\\mathbb{R}\\mathbb{P}^{3}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4504","kind":"arxiv","version":3},"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":"sha256:5c528e00cf8c15c669ecd31ffa401cab750ecf1a1efe70d842ddf25120c1cb93","target":"record","created_at":"2026-05-18T02:32:30Z","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":"f7a7c8a7376e1e03cc3555aa60956db2504a24fc79126e9ac90a7db2125e9784","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-02-18T21:42:35Z","title_canon_sha256":"889cd958c701db4002ef6b020294b9b9d291d9d0af19edee363521c8281c714b"},"schema_version":"1.0","source":{"id":"1402.4504","kind":"arxiv","version":3}},"canonical_sha256":"38a1e2965ef477eb694985af21e755345e2c9eb9bee0f0a7cd3c6180bd90dbdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38a1e2965ef477eb694985af21e755345e2c9eb9bee0f0a7cd3c6180bd90dbdf","first_computed_at":"2026-05-18T02:32:30.931273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:30.931273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yVEqZ5xItt8UzWyM6JEuI8bb6kQOH4SyFNOF0RBCui9RclAHtKM2Hn2KFdV0GZTTWugn/rs6ZesWsAPMWBKGCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:30.931664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4504","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c528e00cf8c15c669ecd31ffa401cab750ecf1a1efe70d842ddf25120c1cb93","sha256:807b93d836c53e6814b2f62d7e8377e221121be0859ba83c677a5ac9863d5c32"],"state_sha256":"4354d1ea50a7b7f210577e68d9f93ccc6a4f46758dc5595ee63a9b7d953508f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PLhRTEljPScHPXOLVwxqT3v9MVErryk7ZHePJtR4zR5g7Rb99flZbIodM4uMYaSCW9uGyOAw1dA1cvbnEB6kBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T11:06:28.533230Z","bundle_sha256":"2ec72e662e876a13d4f76b2a1c44f5b586adc7d2411cd0350c7a4478edf2894b"}}