{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KJLCC2HMQ5U3GTVA4SXVXVTOMM","short_pith_number":"pith:KJLCC2HM","canonical_record":{"source":{"id":"1811.04311","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-10T20:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"cf56b2297a5933bc21c9433c833384c135958ef0ce5385dd00f88a1681dc08d4","abstract_canon_sha256":"fc5a8788fd1c35eaea3f562833aebb6e2f0029da27ddd3567bab921c98d251c1"},"schema_version":"1.0"},"canonical_sha256":"52562168ec8769b34ea0e4af5bd66e6329ce92f6ef028436bfabb3801eb576d2","source":{"kind":"arxiv","id":"1811.04311","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04311","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04311v2","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04311","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"KJLCC2HMQ5U3","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KJLCC2HMQ5U3GTVA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KJLCC2HM","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KJLCC2HMQ5U3GTVA4SXVXVTOMM","target":"record","payload":{"canonical_record":{"source":{"id":"1811.04311","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-10T20:38:18Z","cross_cats_sorted":[],"title_canon_sha256":"cf56b2297a5933bc21c9433c833384c135958ef0ce5385dd00f88a1681dc08d4","abstract_canon_sha256":"fc5a8788fd1c35eaea3f562833aebb6e2f0029da27ddd3567bab921c98d251c1"},"schema_version":"1.0"},"canonical_sha256":"52562168ec8769b34ea0e4af5bd66e6329ce92f6ef028436bfabb3801eb576d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:22.091767Z","signature_b64":"xPJdDKdsrL3gU470/17CoE1BaPBjKLrLRaOCnUmaislMXPlsy3YH/PULqVhT5//aWDL4zUCZ2KbqeWAcAbi+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52562168ec8769b34ea0e4af5bd66e6329ce92f6ef028436bfabb3801eb576d2","last_reissued_at":"2026-05-17T23:54:22.091085Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:22.091085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.04311","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":"2026-05-17T23:54:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1mAzaxmV/EQ/Q//+hCPolWcS7G7PTJbP8I34rYv9ejfCQ4Giflnoom+Yyl2Dbm5sVOjnPde6K+HsYZdj0MdDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:49:26.463668Z"},"content_sha256":"56855dd1bf74fa317bedc8f60d14fc0acb9c6532aaa72448bb284e6f7349a804","schema_version":"1.0","event_id":"sha256:56855dd1bf74fa317bedc8f60d14fc0acb9c6532aaa72448bb284e6f7349a804"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KJLCC2HMQ5U3GTVA4SXVXVTOMM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scalar Curvature of Manifolds with Boundaries: Natural Questions and Artificial Constructions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Misha Gromov","submitted_at":"2018-11-10T20:38:18Z","abstract_excerpt":"We present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04311","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":"2026-05-17T23:54:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CROo0SM0nXghttl391Q3qG8DYwPPlp+1HVwPKGfIHEX/CFILMvsO+76/PkfLAo6WYP/U9vxsbzX1zz118HTtDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:49:26.464659Z"},"content_sha256":"6f628219e80497d12668224fc11376dd653c8e44fbdf5da2a17d0a3ea974bd64","schema_version":"1.0","event_id":"sha256:6f628219e80497d12668224fc11376dd653c8e44fbdf5da2a17d0a3ea974bd64"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KJLCC2HMQ5U3GTVA4SXVXVTOMM/bundle.json","state_url":"https://pith.science/pith/KJLCC2HMQ5U3GTVA4SXVXVTOMM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KJLCC2HMQ5U3GTVA4SXVXVTOMM/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":"2026-08-09T15:49:26Z","links":{"resolver":"https://pith.science/pith/KJLCC2HMQ5U3GTVA4SXVXVTOMM","bundle":"https://pith.science/pith/KJLCC2HMQ5U3GTVA4SXVXVTOMM/bundle.json","state":"https://pith.science/pith/KJLCC2HMQ5U3GTVA4SXVXVTOMM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KJLCC2HMQ5U3GTVA4SXVXVTOMM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KJLCC2HMQ5U3GTVA4SXVXVTOMM","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":"fc5a8788fd1c35eaea3f562833aebb6e2f0029da27ddd3567bab921c98d251c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-10T20:38:18Z","title_canon_sha256":"cf56b2297a5933bc21c9433c833384c135958ef0ce5385dd00f88a1681dc08d4"},"schema_version":"1.0","source":{"id":"1811.04311","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04311","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04311v2","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04311","created_at":"2026-05-17T23:54:22Z"},{"alias_kind":"pith_short_12","alias_value":"KJLCC2HMQ5U3","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KJLCC2HMQ5U3GTVA","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KJLCC2HM","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:6f628219e80497d12668224fc11376dd653c8e44fbdf5da2a17d0a3ea974bd64","target":"graph","created_at":"2026-05-17T23:54:22Z","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 present several problems and results relating the scalar curvatures of manifolds with mean curvatures of their boundaries","authors_text":"Misha Gromov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-10T20:38:18Z","title":"Scalar Curvature of Manifolds with Boundaries: Natural Questions and Artificial Constructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04311","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":"sha256:56855dd1bf74fa317bedc8f60d14fc0acb9c6532aaa72448bb284e6f7349a804","target":"record","created_at":"2026-05-17T23:54:22Z","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":"fc5a8788fd1c35eaea3f562833aebb6e2f0029da27ddd3567bab921c98d251c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-11-10T20:38:18Z","title_canon_sha256":"cf56b2297a5933bc21c9433c833384c135958ef0ce5385dd00f88a1681dc08d4"},"schema_version":"1.0","source":{"id":"1811.04311","kind":"arxiv","version":2}},"canonical_sha256":"52562168ec8769b34ea0e4af5bd66e6329ce92f6ef028436bfabb3801eb576d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"52562168ec8769b34ea0e4af5bd66e6329ce92f6ef028436bfabb3801eb576d2","first_computed_at":"2026-05-17T23:54:22.091085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:22.091085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xPJdDKdsrL3gU470/17CoE1BaPBjKLrLRaOCnUmaislMXPlsy3YH/PULqVhT5//aWDL4zUCZ2KbqeWAcAbi+CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:22.091767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04311","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56855dd1bf74fa317bedc8f60d14fc0acb9c6532aaa72448bb284e6f7349a804","sha256:6f628219e80497d12668224fc11376dd653c8e44fbdf5da2a17d0a3ea974bd64"],"state_sha256":"9554e3f3ed977e17b08cbeff6ed91093e77e26f807545a6c8ce8210e278cde4c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j+FR1HbO0E6DAALJ2cgBSAHXVUVqwtateQaujbj5hApkp7linaVLguH3y5dSBe50eqqXxug/pifKv+a75MiPBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T15:49:26.471798Z","bundle_sha256":"3ad25c0381e624d155e4fd623d083fbeb2f7296cc335b4b5fb66f218904364b2"}}