{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JAF343PSMQD3APSRFQLTBXZ3Q4","short_pith_number":"pith:JAF343PS","canonical_record":{"source":{"id":"1511.03624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-11T19:45:07Z","cross_cats_sorted":[],"title_canon_sha256":"f2d01b056d5eb3321ba086cac7aae3c478f5dceb510026e4f33566aea8aab306","abstract_canon_sha256":"9a4df0fdaec1ce3c140b4f1074b2bae445d83ec1d5cd3b5bb8a8e62d939d2c4c"},"schema_version":"1.0"},"canonical_sha256":"480bbe6df26407b03e512c1730df3b872081f0820a4712cb1af136e983b46f87","source":{"kind":"arxiv","id":"1511.03624","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03624","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03624v1","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03624","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"JAF343PSMQD3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JAF343PSMQD3APSR","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JAF343PS","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JAF343PSMQD3APSRFQLTBXZ3Q4","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03624","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-11T19:45:07Z","cross_cats_sorted":[],"title_canon_sha256":"f2d01b056d5eb3321ba086cac7aae3c478f5dceb510026e4f33566aea8aab306","abstract_canon_sha256":"9a4df0fdaec1ce3c140b4f1074b2bae445d83ec1d5cd3b5bb8a8e62d939d2c4c"},"schema_version":"1.0"},"canonical_sha256":"480bbe6df26407b03e512c1730df3b872081f0820a4712cb1af136e983b46f87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:08.584943Z","signature_b64":"wU/6vwKF6Z79U/ctv9VxwUyRUbnAtLUesqSZm7LOEDsfKVPDEE/3FWHdJ6vpq35W35Cfs+zXCheWiILZjYSHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"480bbe6df26407b03e512c1730df3b872081f0820a4712cb1af136e983b46f87","last_reissued_at":"2026-05-18T01:27:08.584117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:08.584117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03624","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lAlGzvnxvc/LV0F+cY1DnKwRblp4tfHkqBB4uzKoTJoV8rSjsWDgpGNxwYtpmvSOqb9om/E1roCdhKvLkF2JAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:01:16.128431Z"},"content_sha256":"2e3ced29304c6a89eff750d5376968e3b91ed1e5894fbfd0983e7dddeca05d10","schema_version":"1.0","event_id":"sha256:2e3ced29304c6a89eff750d5376968e3b91ed1e5894fbfd0983e7dddeca05d10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JAF343PSMQD3APSRFQLTBXZ3Q4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$B$-Rigidity of flag $2$-spheres without $4$-belt","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Feifei Fan, Jun Ma, Xiangjun Wang","submitted_at":"2015-11-11T19:45:07Z","abstract_excerpt":"Associated to every finite simplicial complex $K$, there is a moment-angle complex $\\mathcal {Z}_{K}$. In this paper, we use some algebraic invariants to solve the $B$-rigidity problem for some special simplicial compelexes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03624","kind":"arxiv","version":1},"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":"2026-05-18T01:27:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YL4l8GKldn2Y7sJXVLcx1eUo098Dcp2IztM2kGcnlB22bJitqCvXJNxrp9RqvR6taiDj0vlZiNGa8XFShSSKAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T18:01:16.129065Z"},"content_sha256":"2d9cc88b2670ba756f55d076c58e05dc1cdb69083786b6e664f17b7d4b0f0a9f","schema_version":"1.0","event_id":"sha256:2d9cc88b2670ba756f55d076c58e05dc1cdb69083786b6e664f17b7d4b0f0a9f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JAF343PSMQD3APSRFQLTBXZ3Q4/bundle.json","state_url":"https://pith.science/pith/JAF343PSMQD3APSRFQLTBXZ3Q4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JAF343PSMQD3APSRFQLTBXZ3Q4/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":"2026-06-06T18:01:16Z","links":{"resolver":"https://pith.science/pith/JAF343PSMQD3APSRFQLTBXZ3Q4","bundle":"https://pith.science/pith/JAF343PSMQD3APSRFQLTBXZ3Q4/bundle.json","state":"https://pith.science/pith/JAF343PSMQD3APSRFQLTBXZ3Q4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JAF343PSMQD3APSRFQLTBXZ3Q4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JAF343PSMQD3APSRFQLTBXZ3Q4","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":"9a4df0fdaec1ce3c140b4f1074b2bae445d83ec1d5cd3b5bb8a8e62d939d2c4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-11T19:45:07Z","title_canon_sha256":"f2d01b056d5eb3321ba086cac7aae3c478f5dceb510026e4f33566aea8aab306"},"schema_version":"1.0","source":{"id":"1511.03624","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03624","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03624v1","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03624","created_at":"2026-05-18T01:27:08Z"},{"alias_kind":"pith_short_12","alias_value":"JAF343PSMQD3","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JAF343PSMQD3APSR","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JAF343PS","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:2d9cc88b2670ba756f55d076c58e05dc1cdb69083786b6e664f17b7d4b0f0a9f","target":"graph","created_at":"2026-05-18T01:27:08Z","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":"Associated to every finite simplicial complex $K$, there is a moment-angle complex $\\mathcal {Z}_{K}$. In this paper, we use some algebraic invariants to solve the $B$-rigidity problem for some special simplicial compelexes.","authors_text":"Feifei Fan, Jun Ma, Xiangjun Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-11T19:45:07Z","title":"$B$-Rigidity of flag $2$-spheres without $4$-belt"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03624","kind":"arxiv","version":1},"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":"sha256:2e3ced29304c6a89eff750d5376968e3b91ed1e5894fbfd0983e7dddeca05d10","target":"record","created_at":"2026-05-18T01:27:08Z","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":"9a4df0fdaec1ce3c140b4f1074b2bae445d83ec1d5cd3b5bb8a8e62d939d2c4c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2015-11-11T19:45:07Z","title_canon_sha256":"f2d01b056d5eb3321ba086cac7aae3c478f5dceb510026e4f33566aea8aab306"},"schema_version":"1.0","source":{"id":"1511.03624","kind":"arxiv","version":1}},"canonical_sha256":"480bbe6df26407b03e512c1730df3b872081f0820a4712cb1af136e983b46f87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"480bbe6df26407b03e512c1730df3b872081f0820a4712cb1af136e983b46f87","first_computed_at":"2026-05-18T01:27:08.584117Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:08.584117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wU/6vwKF6Z79U/ctv9VxwUyRUbnAtLUesqSZm7LOEDsfKVPDEE/3FWHdJ6vpq35W35Cfs+zXCheWiILZjYSHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:08.584943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03624","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e3ced29304c6a89eff750d5376968e3b91ed1e5894fbfd0983e7dddeca05d10","sha256:2d9cc88b2670ba756f55d076c58e05dc1cdb69083786b6e664f17b7d4b0f0a9f"],"state_sha256":"81011aeacd37a05795b32b56f3e65f2fbafd772a17dce9c75a13403b092e0a6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rG2HloafUjDmiJXa2ofgJtGyYK7/FjCP/sFa3R4U73ddml/S1B/7Eemd6iMX4ocWCwJw2y4oJ78UW1K/MytACw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T18:01:16.131823Z","bundle_sha256":"0409384abb8beecddcc5427b76585902d3487ff9e09c88f96d76b81340e266a1"}}