{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6DSAE5RQBGVZXIGX5HLBIQTBLG","short_pith_number":"pith:6DSAE5RQ","canonical_record":{"source":{"id":"1804.03434","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-10T10:23:02Z","cross_cats_sorted":["hep-th","math.AP","math.MP"],"title_canon_sha256":"8837cd1e99d29c40d354e5d67d9261e7dc5b8f604b48f44035e1d05648df39ed","abstract_canon_sha256":"5151536b43a7e39e07c4582a6f4705276441ae7b705adb2df2f5715d3973d4c8"},"schema_version":"1.0"},"canonical_sha256":"f0e402763009ab9ba0d7e9d614426159976e6ae5a0f4e50628852404db6f5d7a","source":{"kind":"arxiv","id":"1804.03434","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03434","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03434v3","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03434","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"6DSAE5RQBGVZ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6DSAE5RQBGVZXIGX","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6DSAE5RQ","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6DSAE5RQBGVZXIGX5HLBIQTBLG","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03434","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-10T10:23:02Z","cross_cats_sorted":["hep-th","math.AP","math.MP"],"title_canon_sha256":"8837cd1e99d29c40d354e5d67d9261e7dc5b8f604b48f44035e1d05648df39ed","abstract_canon_sha256":"5151536b43a7e39e07c4582a6f4705276441ae7b705adb2df2f5715d3973d4c8"},"schema_version":"1.0"},"canonical_sha256":"f0e402763009ab9ba0d7e9d614426159976e6ae5a0f4e50628852404db6f5d7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:31.259415Z","signature_b64":"LKMN1aoEQPl9dy7UjHdVdTElYnaAh3jgqOcrlUyPibkGFCYfgwx5oo27XDQ4GioSAVtY/Hz7Hw5iVnMt5BrwBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0e402763009ab9ba0d7e9d614426159976e6ae5a0f4e50628852404db6f5d7a","last_reissued_at":"2026-05-17T23:47:31.258716Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:31.258716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03434","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4cCLssyEf1a6Y/5LVKjvIiUWruAjVibK/QNrrdOSL62pdc1kckg5IhKaAQ2Z2tq1geGGHhydbVUJEve/weFkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:53:46.055852Z"},"content_sha256":"32463add1ff38786fb97c918308ddf33e3e2a9a5d88fcb1b6356f8d9b06a80c4","schema_version":"1.0","event_id":"sha256:32463add1ff38786fb97c918308ddf33e3e2a9a5d88fcb1b6356f8d9b06a80c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6DSAE5RQBGVZXIGX5HLBIQTBLG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Claudio Dappiaggi, Hugo Ferreira, Nicol\\`o Drago","submitted_at":"2018-04-10T10:23:02Z","abstract_excerpt":"We consider the wave operator on static, Lorentzian manifolds with timelike boundary and we discuss the existence of advanced and retarded fundamental solutions in terms of boundary conditions. By means of spectral calculus we prove that answering this question is equivalent to studying the self-adjoint extensions of an associated elliptic operator on a Riemannian manifold with boundary $(M,g)$. The latter is diffeomorphic to any, constant time hypersurface of the underlying background. In turn, assuming that $(M,g)$ is of bounded geometry, this problem can be tackled within the framework of b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03434","kind":"arxiv","version":3},"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":"2026-05-17T23:47:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kGdyuMvWTbLQHgQ9MGlMISDOMOtBMIQQtOwRanD1qMR0jB88Ja4536bPwphBe9CvN4LiATr+jhbxaGDy1iufCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T07:53:46.056627Z"},"content_sha256":"3c5470d8712e0edc869ba587f84eca6238f9b1ed8f37849c8cf8966a08cf23c5","schema_version":"1.0","event_id":"sha256:3c5470d8712e0edc869ba587f84eca6238f9b1ed8f37849c8cf8966a08cf23c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6DSAE5RQBGVZXIGX5HLBIQTBLG/bundle.json","state_url":"https://pith.science/pith/6DSAE5RQBGVZXIGX5HLBIQTBLG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6DSAE5RQBGVZXIGX5HLBIQTBLG/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":"2026-06-11T07:53:46Z","links":{"resolver":"https://pith.science/pith/6DSAE5RQBGVZXIGX5HLBIQTBLG","bundle":"https://pith.science/pith/6DSAE5RQBGVZXIGX5HLBIQTBLG/bundle.json","state":"https://pith.science/pith/6DSAE5RQBGVZXIGX5HLBIQTBLG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6DSAE5RQBGVZXIGX5HLBIQTBLG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6DSAE5RQBGVZXIGX5HLBIQTBLG","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":"5151536b43a7e39e07c4582a6f4705276441ae7b705adb2df2f5715d3973d4c8","cross_cats_sorted":["hep-th","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-10T10:23:02Z","title_canon_sha256":"8837cd1e99d29c40d354e5d67d9261e7dc5b8f604b48f44035e1d05648df39ed"},"schema_version":"1.0","source":{"id":"1804.03434","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03434","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03434v3","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03434","created_at":"2026-05-17T23:47:31Z"},{"alias_kind":"pith_short_12","alias_value":"6DSAE5RQBGVZ","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"6DSAE5RQBGVZXIGX","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"6DSAE5RQ","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:3c5470d8712e0edc869ba587f84eca6238f9b1ed8f37849c8cf8966a08cf23c5","target":"graph","created_at":"2026-05-17T23:47:31Z","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 consider the wave operator on static, Lorentzian manifolds with timelike boundary and we discuss the existence of advanced and retarded fundamental solutions in terms of boundary conditions. By means of spectral calculus we prove that answering this question is equivalent to studying the self-adjoint extensions of an associated elliptic operator on a Riemannian manifold with boundary $(M,g)$. The latter is diffeomorphic to any, constant time hypersurface of the underlying background. In turn, assuming that $(M,g)$ is of bounded geometry, this problem can be tackled within the framework of b","authors_text":"Claudio Dappiaggi, Hugo Ferreira, Nicol\\`o Drago","cross_cats":["hep-th","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-10T10:23:02Z","title":"Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03434","kind":"arxiv","version":3},"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":"sha256:32463add1ff38786fb97c918308ddf33e3e2a9a5d88fcb1b6356f8d9b06a80c4","target":"record","created_at":"2026-05-17T23:47:31Z","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":"5151536b43a7e39e07c4582a6f4705276441ae7b705adb2df2f5715d3973d4c8","cross_cats_sorted":["hep-th","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-04-10T10:23:02Z","title_canon_sha256":"8837cd1e99d29c40d354e5d67d9261e7dc5b8f604b48f44035e1d05648df39ed"},"schema_version":"1.0","source":{"id":"1804.03434","kind":"arxiv","version":3}},"canonical_sha256":"f0e402763009ab9ba0d7e9d614426159976e6ae5a0f4e50628852404db6f5d7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0e402763009ab9ba0d7e9d614426159976e6ae5a0f4e50628852404db6f5d7a","first_computed_at":"2026-05-17T23:47:31.258716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:31.258716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LKMN1aoEQPl9dy7UjHdVdTElYnaAh3jgqOcrlUyPibkGFCYfgwx5oo27XDQ4GioSAVtY/Hz7Hw5iVnMt5BrwBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:31.259415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03434","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32463add1ff38786fb97c918308ddf33e3e2a9a5d88fcb1b6356f8d9b06a80c4","sha256:3c5470d8712e0edc869ba587f84eca6238f9b1ed8f37849c8cf8966a08cf23c5"],"state_sha256":"f121f5618d0c5b400d6099fa5d767acc727716fd8e04e308d2fc6c4138d3909c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LTgQgLqoYPLS/B+TjBrz8KrBy4IBS3E15g76husPJMce0G/9O+YZGj9HxRofMAKoGfC8dvUM0ibnxujMi7AkAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T07:53:46.060743Z","bundle_sha256":"e5a02743cf0413e6d6e56992c14aaecb1e52326cb1ca6a86e65277b442a4eb3b"}}