{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:JADIAXTBECBM2EDI36THUMG5OF","short_pith_number":"pith:JADIAXTB","canonical_record":{"source":{"id":"1307.7501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-29T08:47:21Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"66168810356c8560a6d0ddbd6b8f8646275d28c00662f90aa16fc13020e8c7e5","abstract_canon_sha256":"e0402cc8070d78c36fb633f00720def5a35a4e5fd36ec8cdf5f2480080e91732"},"schema_version":"1.0"},"canonical_sha256":"4806805e612082cd1068dfa67a30dd7153fc4716e9d74a761391350fcd9342ad","source":{"kind":"arxiv","id":"1307.7501","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7501","created_at":"2026-05-18T01:27:37Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7501v1","created_at":"2026-05-18T01:27:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7501","created_at":"2026-05-18T01:27:37Z"},{"alias_kind":"pith_short_12","alias_value":"JADIAXTBECBM","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JADIAXTBECBM2EDI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JADIAXTB","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:JADIAXTBECBM2EDI36THUMG5OF","target":"record","payload":{"canonical_record":{"source":{"id":"1307.7501","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-29T08:47:21Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"66168810356c8560a6d0ddbd6b8f8646275d28c00662f90aa16fc13020e8c7e5","abstract_canon_sha256":"e0402cc8070d78c36fb633f00720def5a35a4e5fd36ec8cdf5f2480080e91732"},"schema_version":"1.0"},"canonical_sha256":"4806805e612082cd1068dfa67a30dd7153fc4716e9d74a761391350fcd9342ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:37.059713Z","signature_b64":"m9XUCcPCfIivguUteItcqQ8TMqfqmQ7uj3SE6cmSPh6zh+FYTAIjxXGiM60MMGmlKwkM6THDtHRm00MUmKYZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4806805e612082cd1068dfa67a30dd7153fc4716e9d74a761391350fcd9342ad","last_reissued_at":"2026-05-18T01:27:37.059098Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:37.059098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.7501","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":"2026-05-18T01:27:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iQPolBiy6P3QExeshnIZG3b0Oz0TRMSAylAnpn9aKJaWK7Iz1yjgL2KzSYW02XifS0WBDJNNIOFCKxWY6tolDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:41:02.100538Z"},"content_sha256":"efc9ecb2732ceab41208f0e5d6f7118f760b9c95c9e6714f2f652cc847181e64","schema_version":"1.0","event_id":"sha256:efc9ecb2732ceab41208f0e5d6f7118f760b9c95c9e6714f2f652cc847181e64"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:JADIAXTBECBM2EDI36THUMG5OF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic differential operators on Lipschitz domains and abstract boundary value problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Jussi Behrndt, Till Micheler","submitted_at":"2013-07-29T08:47:21Z","abstract_excerpt":"This paper consists of two parts. In the first part, which is of more abstract nature, the notion of quasi boundary triples and associated Weyl functions is developed further in such a way that it can be applied to elliptic boundary value problems on non-smooth domains. A key feature is the extension of the boundary maps by continuity to the duals of certain range spaces, which directly leads to a description of all self-adjoint extensions of the underlying symmetric operator with the help of abstract boundary values. In the second part of the paper a complete description is obtained of all se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7501","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":""},"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":"2026-05-18T01:27:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sVnuY6hGe3xkTvJlOlK2lbycaNZlOOxS4f6rQLD017LjMHb3Ib9JUMib/hAatsv/7k4cFds2n/i7aCKXQxcbBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:41:02.100884Z"},"content_sha256":"b0135d97f1a6e060cd34f52d0a7801a67ef827f8716b51f34e966a12b8792472","schema_version":"1.0","event_id":"sha256:b0135d97f1a6e060cd34f52d0a7801a67ef827f8716b51f34e966a12b8792472"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JADIAXTBECBM2EDI36THUMG5OF/bundle.json","state_url":"https://pith.science/pith/JADIAXTBECBM2EDI36THUMG5OF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JADIAXTBECBM2EDI36THUMG5OF/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":"2026-06-01T18:41:02Z","links":{"resolver":"https://pith.science/pith/JADIAXTBECBM2EDI36THUMG5OF","bundle":"https://pith.science/pith/JADIAXTBECBM2EDI36THUMG5OF/bundle.json","state":"https://pith.science/pith/JADIAXTBECBM2EDI36THUMG5OF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JADIAXTBECBM2EDI36THUMG5OF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:JADIAXTBECBM2EDI36THUMG5OF","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":"e0402cc8070d78c36fb633f00720def5a35a4e5fd36ec8cdf5f2480080e91732","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-29T08:47:21Z","title_canon_sha256":"66168810356c8560a6d0ddbd6b8f8646275d28c00662f90aa16fc13020e8c7e5"},"schema_version":"1.0","source":{"id":"1307.7501","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.7501","created_at":"2026-05-18T01:27:37Z"},{"alias_kind":"arxiv_version","alias_value":"1307.7501v1","created_at":"2026-05-18T01:27:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.7501","created_at":"2026-05-18T01:27:37Z"},{"alias_kind":"pith_short_12","alias_value":"JADIAXTBECBM","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"JADIAXTBECBM2EDI","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"JADIAXTB","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:b0135d97f1a6e060cd34f52d0a7801a67ef827f8716b51f34e966a12b8792472","target":"graph","created_at":"2026-05-18T01:27:37Z","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":"This paper consists of two parts. In the first part, which is of more abstract nature, the notion of quasi boundary triples and associated Weyl functions is developed further in such a way that it can be applied to elliptic boundary value problems on non-smooth domains. A key feature is the extension of the boundary maps by continuity to the duals of certain range spaces, which directly leads to a description of all self-adjoint extensions of the underlying symmetric operator with the help of abstract boundary values. In the second part of the paper a complete description is obtained of all se","authors_text":"Jussi Behrndt, Till Micheler","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-29T08:47:21Z","title":"Elliptic differential operators on Lipschitz domains and abstract boundary value problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7501","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:efc9ecb2732ceab41208f0e5d6f7118f760b9c95c9e6714f2f652cc847181e64","target":"record","created_at":"2026-05-18T01:27:37Z","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":"e0402cc8070d78c36fb633f00720def5a35a4e5fd36ec8cdf5f2480080e91732","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-29T08:47:21Z","title_canon_sha256":"66168810356c8560a6d0ddbd6b8f8646275d28c00662f90aa16fc13020e8c7e5"},"schema_version":"1.0","source":{"id":"1307.7501","kind":"arxiv","version":1}},"canonical_sha256":"4806805e612082cd1068dfa67a30dd7153fc4716e9d74a761391350fcd9342ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4806805e612082cd1068dfa67a30dd7153fc4716e9d74a761391350fcd9342ad","first_computed_at":"2026-05-18T01:27:37.059098Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:37.059098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m9XUCcPCfIivguUteItcqQ8TMqfqmQ7uj3SE6cmSPh6zh+FYTAIjxXGiM60MMGmlKwkM6THDtHRm00MUmKYZAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:37.059713Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.7501","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efc9ecb2732ceab41208f0e5d6f7118f760b9c95c9e6714f2f652cc847181e64","sha256:b0135d97f1a6e060cd34f52d0a7801a67ef827f8716b51f34e966a12b8792472"],"state_sha256":"c3f9e15941211ac6bee0b22c6dfb8e0e437299a01904c9b7304e0f3133e91184"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i0vjnOks3gdOpHBMZuBU2T37ePr4wD9/1mjXNch6W1/KU8ZkP3LPMsGWXKX6xfje/AzcHwx0Ozpq3cdXGZaaBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:41:02.102783Z","bundle_sha256":"036c7a1d17e6d1e1def60d2c9387f81d0e07a0d5f1927dcf1ad6fd47ef4273ea"}}