{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DJD4L4PAY5JMBV7CW2OS5MJTNR","short_pith_number":"pith:DJD4L4PA","canonical_record":{"source":{"id":"1505.00439","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-03T15:13:19Z","cross_cats_sorted":[],"title_canon_sha256":"1d0392926b3b7f86647c861ef5227a9fb7682694ec32319b19a47e655eacee7e","abstract_canon_sha256":"8835c177c53152e6202db804b2d6e0094e8c9b4c531e7ded026a517db4db1045"},"schema_version":"1.0"},"canonical_sha256":"1a47c5f1e0c752c0d7e2b69d2eb1336c55d266ef645202f16c7c5e4ef6f05cab","source":{"kind":"arxiv","id":"1505.00439","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00439","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00439v4","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00439","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"DJD4L4PAY5JM","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DJD4L4PAY5JMBV7C","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DJD4L4PA","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DJD4L4PAY5JMBV7CW2OS5MJTNR","target":"record","payload":{"canonical_record":{"source":{"id":"1505.00439","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-03T15:13:19Z","cross_cats_sorted":[],"title_canon_sha256":"1d0392926b3b7f86647c861ef5227a9fb7682694ec32319b19a47e655eacee7e","abstract_canon_sha256":"8835c177c53152e6202db804b2d6e0094e8c9b4c531e7ded026a517db4db1045"},"schema_version":"1.0"},"canonical_sha256":"1a47c5f1e0c752c0d7e2b69d2eb1336c55d266ef645202f16c7c5e4ef6f05cab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:16.132297Z","signature_b64":"lwrI/UAKKj/ewkUlVJCjx6ZgHZrpLFhA4WSwCRJgyp/9/BA5go30ugg4+rlitcuuLg5NNfBLCL31ySGv+aoSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a47c5f1e0c752c0d7e2b69d2eb1336c55d266ef645202f16c7c5e4ef6f05cab","last_reissued_at":"2026-05-18T01:19:16.131905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:16.131905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.00439","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W0MJH8O2H0Yf5YKiiPsHupFYFsOkOi759IbZNTR+GMlhrZZ15MyulzaffdfqSO6/8cqaONs1kMlC8P7ADW0PBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:10:55.333698Z"},"content_sha256":"5371bfead6c6e2d2537f3905924045ccfd1c2a01e03e3506ecfd3c2e3e8a15b4","schema_version":"1.0","event_id":"sha256:5371bfead6c6e2d2537f3905924045ccfd1c2a01e03e3506ecfd3c2e3e8a15b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DJD4L4PAY5JMBV7CW2OS5MJTNR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sobolev spaces and Bochner Laplacian on complex projective varieties and stratified pseudomanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francesco Bei","submitted_at":"2015-05-03T15:13:19Z","abstract_excerpt":"Let $V\\subset \\mathbb{C}\\mathbb{P}^n$ be an irreducible complex projective variety of complex dimension $v$ and let $g$ be the K\\\"ahler metric on $\\reg(V)$, the regular part of $V$, induced by the Fubini Study metric of $\\mathbb{C}\\mathbb{P}^n$. In this setting Li and Tian proved that $W^{1,2}_0(\\reg(V),g)=W^{1,2}(\\reg(V),g)$, that the natural inclusion $W^{1,2}(\\reg(V),g)\\hookrightarrow L^2(\\reg(V),g)$ is a compact operator and that the heat operator associated to the Friedrich extension of the scalar Laplacian $\\Delta_0:C^{\\infty}_c(\\reg(V))\\rightarrow C^{\\infty}_c(\\reg(V))$, that is $e^{-t\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00439","kind":"arxiv","version":4},"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":"2026-05-18T01:19:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXIu/MXvNKoiVPgUah/CkBVKJvzqq40cyojBDGQg+sj+vY7o6KoHAoYPhxm4DX5iAeEnlf3ppoYpBn6XPJH/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T04:10:55.334354Z"},"content_sha256":"f3b7c8547575680d16edb1e5f48f3281afb6374d31ca0abfda4dc938bfe132e5","schema_version":"1.0","event_id":"sha256:f3b7c8547575680d16edb1e5f48f3281afb6374d31ca0abfda4dc938bfe132e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DJD4L4PAY5JMBV7CW2OS5MJTNR/bundle.json","state_url":"https://pith.science/pith/DJD4L4PAY5JMBV7CW2OS5MJTNR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DJD4L4PAY5JMBV7CW2OS5MJTNR/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":"2026-06-06T04:10:55Z","links":{"resolver":"https://pith.science/pith/DJD4L4PAY5JMBV7CW2OS5MJTNR","bundle":"https://pith.science/pith/DJD4L4PAY5JMBV7CW2OS5MJTNR/bundle.json","state":"https://pith.science/pith/DJD4L4PAY5JMBV7CW2OS5MJTNR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DJD4L4PAY5JMBV7CW2OS5MJTNR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DJD4L4PAY5JMBV7CW2OS5MJTNR","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":"8835c177c53152e6202db804b2d6e0094e8c9b4c531e7ded026a517db4db1045","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-03T15:13:19Z","title_canon_sha256":"1d0392926b3b7f86647c861ef5227a9fb7682694ec32319b19a47e655eacee7e"},"schema_version":"1.0","source":{"id":"1505.00439","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.00439","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"arxiv_version","alias_value":"1505.00439v4","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00439","created_at":"2026-05-18T01:19:16Z"},{"alias_kind":"pith_short_12","alias_value":"DJD4L4PAY5JM","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DJD4L4PAY5JMBV7C","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DJD4L4PA","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:f3b7c8547575680d16edb1e5f48f3281afb6374d31ca0abfda4dc938bfe132e5","target":"graph","created_at":"2026-05-18T01:19:16Z","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":"Let $V\\subset \\mathbb{C}\\mathbb{P}^n$ be an irreducible complex projective variety of complex dimension $v$ and let $g$ be the K\\\"ahler metric on $\\reg(V)$, the regular part of $V$, induced by the Fubini Study metric of $\\mathbb{C}\\mathbb{P}^n$. In this setting Li and Tian proved that $W^{1,2}_0(\\reg(V),g)=W^{1,2}(\\reg(V),g)$, that the natural inclusion $W^{1,2}(\\reg(V),g)\\hookrightarrow L^2(\\reg(V),g)$ is a compact operator and that the heat operator associated to the Friedrich extension of the scalar Laplacian $\\Delta_0:C^{\\infty}_c(\\reg(V))\\rightarrow C^{\\infty}_c(\\reg(V))$, that is $e^{-t\\","authors_text":"Francesco Bei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-03T15:13:19Z","title":"Sobolev spaces and Bochner Laplacian on complex projective varieties and stratified pseudomanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00439","kind":"arxiv","version":4},"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":"sha256:5371bfead6c6e2d2537f3905924045ccfd1c2a01e03e3506ecfd3c2e3e8a15b4","target":"record","created_at":"2026-05-18T01:19:16Z","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":"8835c177c53152e6202db804b2d6e0094e8c9b4c531e7ded026a517db4db1045","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-03T15:13:19Z","title_canon_sha256":"1d0392926b3b7f86647c861ef5227a9fb7682694ec32319b19a47e655eacee7e"},"schema_version":"1.0","source":{"id":"1505.00439","kind":"arxiv","version":4}},"canonical_sha256":"1a47c5f1e0c752c0d7e2b69d2eb1336c55d266ef645202f16c7c5e4ef6f05cab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a47c5f1e0c752c0d7e2b69d2eb1336c55d266ef645202f16c7c5e4ef6f05cab","first_computed_at":"2026-05-18T01:19:16.131905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:16.131905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lwrI/UAKKj/ewkUlVJCjx6ZgHZrpLFhA4WSwCRJgyp/9/BA5go30ugg4+rlitcuuLg5NNfBLCL31ySGv+aoSDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:16.132297Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.00439","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5371bfead6c6e2d2537f3905924045ccfd1c2a01e03e3506ecfd3c2e3e8a15b4","sha256:f3b7c8547575680d16edb1e5f48f3281afb6374d31ca0abfda4dc938bfe132e5"],"state_sha256":"4c2508fb205c6dbbb38aaa3b27b5b43813449dbe5db1152659eb3539534f2850"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xh4rjXlgyisIi139Zq5o96DRNVO+dj//GpHaz65v9lUl9EGKhZTTcoCPn94dW8bD3+q2wcfZgPLwOqH9/cFBDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T04:10:55.337940Z","bundle_sha256":"ec60b764f40903f89500e207df9a4c1a591b87b3fabc3e3efdbc072c600a356a"}}