{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:BEZIQEIKENOL4H2F77ZXSZ3KTC","short_pith_number":"pith:BEZIQEIK","canonical_record":{"source":{"id":"2003.09919","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-03-22T15:10:42Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"fb127c7f4ffd25bb6299d7fb1e1a696e932211f0139911d73f5833f6c95dd6a4","abstract_canon_sha256":"9431f2a72f0e62c27409a2d3ae3c1f62dfe70e9e107d752667b43c6ca2b9df3c"},"schema_version":"1.0"},"canonical_sha256":"093288110a235cbe1f45fff379676a98bd45c3adb9f2a377718c08efa204a0af","source":{"kind":"arxiv","id":"2003.09919","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.09919","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"2003.09919v1","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.09919","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"BEZIQEIKENOL","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"pith_short_16","alias_value":"BEZIQEIKENOL4H2F","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"pith_short_8","alias_value":"BEZIQEIK","created_at":"2026-07-05T00:49:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:BEZIQEIKENOL4H2F77ZXSZ3KTC","target":"record","payload":{"canonical_record":{"source":{"id":"2003.09919","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-03-22T15:10:42Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"fb127c7f4ffd25bb6299d7fb1e1a696e932211f0139911d73f5833f6c95dd6a4","abstract_canon_sha256":"9431f2a72f0e62c27409a2d3ae3c1f62dfe70e9e107d752667b43c6ca2b9df3c"},"schema_version":"1.0"},"canonical_sha256":"093288110a235cbe1f45fff379676a98bd45c3adb9f2a377718c08efa204a0af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:49:48.097690Z","signature_b64":"VWGPDXk4c/J47y1J7o/l/EAe4z14S2/0OVObZ4mR46wVaYPB0NlEcRzsPHnNgGRtH1RY4K/ngFpQh2CNg+zcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"093288110a235cbe1f45fff379676a98bd45c3adb9f2a377718c08efa204a0af","last_reissued_at":"2026-07-05T00:49:48.097330Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:49:48.097330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2003.09919","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":"2026-07-05T00:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D6vCe1UUnoChbxv49cerVC35RF4pewY+6MJgAbKvNu0kl4P1R0pA9FGxihjTZb0eCMD8O4iYo6JItKvzSrw8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T07:19:25.471732Z"},"content_sha256":"4c667353708be980d8dec24662ad6131d348c48417043791eda6fd73debbaf3d","schema_version":"1.0","event_id":"sha256:4c667353708be980d8dec24662ad6131d348c48417043791eda6fd73debbaf3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:BEZIQEIKENOL4H2F77ZXSZ3KTC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gluing of multiple Alexandrov spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Jian Ge, Nan Li","submitted_at":"2020-03-22T15:10:42Z","abstract_excerpt":"In this paper we discuss the sufficient and necessary conditions for multiple Alexandrov spaces being glued to an Alexandrov space. We propose a Gluing Conjecture, which says that the finite gluing of Alexandrov spaces is an Alexandrov space, if and only if the gluing is by path isometry along the boundaries and the tangent cones are glued to Alexandrov spaces. This generalizes Petrunin's Gluing Theorem. Under the assumptions of the Gluing Conjecture, we classify the $2$-point gluing over $(n-1,\\epsilon)$-regular points as local separable gluing and the gluing near un-glued $(n-1,\\epsilon)$-re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.09919","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2003.09919/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":"2026-07-05T00:49:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cR3Z9eCE+KnVFKbezAHXsZa/CbMPLBzhqEFfLw2/tWGiFln+HXlwmN1HLAff9BccZyviHIMfmorEyHLBnCUBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T07:19:25.472263Z"},"content_sha256":"722414019e424755e2256a1a6d2da2e2ced51f57842eb68b20c1b0669ffd62f2","schema_version":"1.0","event_id":"sha256:722414019e424755e2256a1a6d2da2e2ced51f57842eb68b20c1b0669ffd62f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BEZIQEIKENOL4H2F77ZXSZ3KTC/bundle.json","state_url":"https://pith.science/pith/BEZIQEIKENOL4H2F77ZXSZ3KTC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BEZIQEIKENOL4H2F77ZXSZ3KTC/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":"2026-08-06T07:19:25Z","links":{"resolver":"https://pith.science/pith/BEZIQEIKENOL4H2F77ZXSZ3KTC","bundle":"https://pith.science/pith/BEZIQEIKENOL4H2F77ZXSZ3KTC/bundle.json","state":"https://pith.science/pith/BEZIQEIKENOL4H2F77ZXSZ3KTC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BEZIQEIKENOL4H2F77ZXSZ3KTC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:BEZIQEIKENOL4H2F77ZXSZ3KTC","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":"9431f2a72f0e62c27409a2d3ae3c1f62dfe70e9e107d752667b43c6ca2b9df3c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-03-22T15:10:42Z","title_canon_sha256":"fb127c7f4ffd25bb6299d7fb1e1a696e932211f0139911d73f5833f6c95dd6a4"},"schema_version":"1.0","source":{"id":"2003.09919","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2003.09919","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"arxiv_version","alias_value":"2003.09919v1","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2003.09919","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"pith_short_12","alias_value":"BEZIQEIKENOL","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"pith_short_16","alias_value":"BEZIQEIKENOL4H2F","created_at":"2026-07-05T00:49:48Z"},{"alias_kind":"pith_short_8","alias_value":"BEZIQEIK","created_at":"2026-07-05T00:49:48Z"}],"graph_snapshots":[{"event_id":"sha256:722414019e424755e2256a1a6d2da2e2ced51f57842eb68b20c1b0669ffd62f2","target":"graph","created_at":"2026-07-05T00:49:48Z","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/2003.09919/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we discuss the sufficient and necessary conditions for multiple Alexandrov spaces being glued to an Alexandrov space. We propose a Gluing Conjecture, which says that the finite gluing of Alexandrov spaces is an Alexandrov space, if and only if the gluing is by path isometry along the boundaries and the tangent cones are glued to Alexandrov spaces. This generalizes Petrunin's Gluing Theorem. Under the assumptions of the Gluing Conjecture, we classify the $2$-point gluing over $(n-1,\\epsilon)$-regular points as local separable gluing and the gluing near un-glued $(n-1,\\epsilon)$-re","authors_text":"Jian Ge, Nan Li","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-03-22T15:10:42Z","title":"Gluing of multiple Alexandrov spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2003.09919","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":"sha256:4c667353708be980d8dec24662ad6131d348c48417043791eda6fd73debbaf3d","target":"record","created_at":"2026-07-05T00:49:48Z","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":"9431f2a72f0e62c27409a2d3ae3c1f62dfe70e9e107d752667b43c6ca2b9df3c","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2020-03-22T15:10:42Z","title_canon_sha256":"fb127c7f4ffd25bb6299d7fb1e1a696e932211f0139911d73f5833f6c95dd6a4"},"schema_version":"1.0","source":{"id":"2003.09919","kind":"arxiv","version":1}},"canonical_sha256":"093288110a235cbe1f45fff379676a98bd45c3adb9f2a377718c08efa204a0af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"093288110a235cbe1f45fff379676a98bd45c3adb9f2a377718c08efa204a0af","first_computed_at":"2026-07-05T00:49:48.097330Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:49:48.097330Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VWGPDXk4c/J47y1J7o/l/EAe4z14S2/0OVObZ4mR46wVaYPB0NlEcRzsPHnNgGRtH1RY4K/ngFpQh2CNg+zcCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:49:48.097690Z","signed_message":"canonical_sha256_bytes"},"source_id":"2003.09919","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c667353708be980d8dec24662ad6131d348c48417043791eda6fd73debbaf3d","sha256:722414019e424755e2256a1a6d2da2e2ced51f57842eb68b20c1b0669ffd62f2"],"state_sha256":"c594bcc317a9b36656c53bf710477e0e5531c5b4ea42b64db69986b982c4e0b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6bDf3vco6sA6C/xCJy90i9tLxZLwMgbJWhn3rJsm2RtCHmF9OTb+Mvoq4Q50ttEhJ7AUKMOK+IlTAPHfB8H2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T07:19:25.485393Z","bundle_sha256":"c85e5e279f22d0e48cc0af2d3c0ba7a054dc08dd6c3d566602d4865bbe2b2ed5"}}