{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:NFM5EQS3UZY7XWGPJLI6AJL6OJ","short_pith_number":"pith:NFM5EQS3","canonical_record":{"source":{"id":"2205.01379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2022-05-03T09:07:09Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.PR"],"title_canon_sha256":"9c4ecc18eb547fa61af64e8a5da7d96770ec148019ec99d562223d94ce578431","abstract_canon_sha256":"419873e08a2d100909f7d547cc34a76007b4968460c2fce202bbda83e36dc51a"},"schema_version":"1.0"},"canonical_sha256":"6959d2425ba671fbd8cf4ad1e0257e72788955c5a62030277752fc23b08e0a1a","source":{"kind":"arxiv","id":"2205.01379","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.01379","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"arxiv_version","alias_value":"2205.01379v1","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.01379","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_12","alias_value":"NFM5EQS3UZY7","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_16","alias_value":"NFM5EQS3UZY7XWGP","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_8","alias_value":"NFM5EQS3","created_at":"2026-07-05T04:20:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:NFM5EQS3UZY7XWGPJLI6AJL6OJ","target":"record","payload":{"canonical_record":{"source":{"id":"2205.01379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2022-05-03T09:07:09Z","cross_cats_sorted":["math-ph","math.FA","math.MP","math.PR"],"title_canon_sha256":"9c4ecc18eb547fa61af64e8a5da7d96770ec148019ec99d562223d94ce578431","abstract_canon_sha256":"419873e08a2d100909f7d547cc34a76007b4968460c2fce202bbda83e36dc51a"},"schema_version":"1.0"},"canonical_sha256":"6959d2425ba671fbd8cf4ad1e0257e72788955c5a62030277752fc23b08e0a1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:20:04.067173Z","signature_b64":"RbjuxnEsSzaXPlkyyXEjsLpBbmOzLrxKa8IHgpSSHink6zZE3ifGJhTqEjpvZSDQOKMpGf5K2T+15e50alxKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6959d2425ba671fbd8cf4ad1e0257e72788955c5a62030277752fc23b08e0a1a","last_reissued_at":"2026-07-05T04:20:04.066781Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:20:04.066781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.01379","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":"2026-07-05T04:20:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mE69e1luy9cgkohncsVM8WgKpRZKUiUkVUzc+z0g0VjqSXXdoEm6k6nK66TyiBl1opoyhhS0E+v5IY/76DegBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:28:18.499718Z"},"content_sha256":"2ed58b0ce2c6dcc48f706f50e1ac3170692f0b2f5aa3bfea7c8c954a691b9e50","schema_version":"1.0","event_id":"sha256:2ed58b0ce2c6dcc48f706f50e1ac3170692f0b2f5aa3bfea7c8c954a691b9e50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:NFM5EQS3UZY7XWGPJLI6AJL6OJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Configuration Spaces over Singular Spaces -- II. Curvature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.PR"],"primary_cat":"math.MG","authors_text":"Kohei Suzuki, Lorenzo Dello Schiavo","submitted_at":"2022-05-03T09:07:09Z","abstract_excerpt":"This is the second paper of a series on configuration spaces $\\Upsilon$ over singular spaces $X$. Here, we focus on geometric aspects of the extended metric measure space $(\\Upsilon, \\mathsf{d}_{\\Upsilon}, \\mu)$ equipped with the $L^2$-transportation distance $\\mathsf{d}_{\\Upsilon}$, and a mixed Poisson measure $\\mu$. Firstly, we establish the essential self-adjointness and the $L^p$-uniqueness for the Laplacian on $\\Upsilon$ lifted from $X$. Secondly, we prove the equivalence of Bakry-\\'Emery curvature bounds on $X$ and on $\\Upsilon$, without any metric assumption on $X$. We further prove the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01379","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/2205.01379/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":"2026-07-05T04:20:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A3jRlwZoHGOzF4ToA9NgaZhrldStYEx9UqHMMQJf50CvnigND5+njS5V8Sg3WXyXhf1ICROdM/IAgHkivealAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T09:28:18.500532Z"},"content_sha256":"d6d9187e4174cfdaa775e9a7b7c5856b96aa470968bc4c5b50ab4a57905d9e1b","schema_version":"1.0","event_id":"sha256:d6d9187e4174cfdaa775e9a7b7c5856b96aa470968bc4c5b50ab4a57905d9e1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NFM5EQS3UZY7XWGPJLI6AJL6OJ/bundle.json","state_url":"https://pith.science/pith/NFM5EQS3UZY7XWGPJLI6AJL6OJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NFM5EQS3UZY7XWGPJLI6AJL6OJ/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":"2026-08-13T09:28:18Z","links":{"resolver":"https://pith.science/pith/NFM5EQS3UZY7XWGPJLI6AJL6OJ","bundle":"https://pith.science/pith/NFM5EQS3UZY7XWGPJLI6AJL6OJ/bundle.json","state":"https://pith.science/pith/NFM5EQS3UZY7XWGPJLI6AJL6OJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NFM5EQS3UZY7XWGPJLI6AJL6OJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:NFM5EQS3UZY7XWGPJLI6AJL6OJ","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":"419873e08a2d100909f7d547cc34a76007b4968460c2fce202bbda83e36dc51a","cross_cats_sorted":["math-ph","math.FA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2022-05-03T09:07:09Z","title_canon_sha256":"9c4ecc18eb547fa61af64e8a5da7d96770ec148019ec99d562223d94ce578431"},"schema_version":"1.0","source":{"id":"2205.01379","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.01379","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"arxiv_version","alias_value":"2205.01379v1","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.01379","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_12","alias_value":"NFM5EQS3UZY7","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_16","alias_value":"NFM5EQS3UZY7XWGP","created_at":"2026-07-05T04:20:04Z"},{"alias_kind":"pith_short_8","alias_value":"NFM5EQS3","created_at":"2026-07-05T04:20:04Z"}],"graph_snapshots":[{"event_id":"sha256:d6d9187e4174cfdaa775e9a7b7c5856b96aa470968bc4c5b50ab4a57905d9e1b","target":"graph","created_at":"2026-07-05T04:20:04Z","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/2205.01379/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is the second paper of a series on configuration spaces $\\Upsilon$ over singular spaces $X$. Here, we focus on geometric aspects of the extended metric measure space $(\\Upsilon, \\mathsf{d}_{\\Upsilon}, \\mu)$ equipped with the $L^2$-transportation distance $\\mathsf{d}_{\\Upsilon}$, and a mixed Poisson measure $\\mu$. Firstly, we establish the essential self-adjointness and the $L^p$-uniqueness for the Laplacian on $\\Upsilon$ lifted from $X$. Secondly, we prove the equivalence of Bakry-\\'Emery curvature bounds on $X$ and on $\\Upsilon$, without any metric assumption on $X$. We further prove the","authors_text":"Kohei Suzuki, Lorenzo Dello Schiavo","cross_cats":["math-ph","math.FA","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2022-05-03T09:07:09Z","title":"Configuration Spaces over Singular Spaces -- II. Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01379","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":"sha256:2ed58b0ce2c6dcc48f706f50e1ac3170692f0b2f5aa3bfea7c8c954a691b9e50","target":"record","created_at":"2026-07-05T04:20:04Z","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":"419873e08a2d100909f7d547cc34a76007b4968460c2fce202bbda83e36dc51a","cross_cats_sorted":["math-ph","math.FA","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2022-05-03T09:07:09Z","title_canon_sha256":"9c4ecc18eb547fa61af64e8a5da7d96770ec148019ec99d562223d94ce578431"},"schema_version":"1.0","source":{"id":"2205.01379","kind":"arxiv","version":1}},"canonical_sha256":"6959d2425ba671fbd8cf4ad1e0257e72788955c5a62030277752fc23b08e0a1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6959d2425ba671fbd8cf4ad1e0257e72788955c5a62030277752fc23b08e0a1a","first_computed_at":"2026-07-05T04:20:04.066781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:20:04.066781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RbjuxnEsSzaXPlkyyXEjsLpBbmOzLrxKa8IHgpSSHink6zZE3ifGJhTqEjpvZSDQOKMpGf5K2T+15e50alxKCA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:20:04.067173Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.01379","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ed58b0ce2c6dcc48f706f50e1ac3170692f0b2f5aa3bfea7c8c954a691b9e50","sha256:d6d9187e4174cfdaa775e9a7b7c5856b96aa470968bc4c5b50ab4a57905d9e1b"],"state_sha256":"290ee8e49e58599f220c26500b79d5abe20f7eb64c15a9ff32df1141fd84dd56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kBguwpJu+j5JgU1NGgV1bhnhOT1Oe4i8kAVUbaSEKbcl+NdgYjc1Ad2JHkM1ZNS1fga62N+Kn/XiLZ/VXem4DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T09:28:18.512155Z","bundle_sha256":"0cb6122a86e8d4669e9afc093fb86f2e5c0a3e2f68d4b19ba49295fd3a6d56c5"}}