{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:QXPTN7C3N2LKHFTIHEZOG3CCII","short_pith_number":"pith:QXPTN7C3","canonical_record":{"source":{"id":"1412.7326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-23T11:34:48Z","cross_cats_sorted":[],"title_canon_sha256":"88de16efdbf931b434c2d7c6f5665c4dea668eb38eac2efcc1b82a806cda34dc","abstract_canon_sha256":"84bd851fc4d7d8425be1e6d6f27c4315bd636c408d6a52b458c4ad22b9e518af"},"schema_version":"1.0"},"canonical_sha256":"85df36fc5b6e96a396683932e36c42423752c0d7bb5dc3d82068eed35f5c4cc7","source":{"kind":"arxiv","id":"1412.7326","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7326","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7326v1","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7326","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"QXPTN7C3N2LK","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QXPTN7C3N2LKHFTI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QXPTN7C3","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:QXPTN7C3N2LKHFTIHEZOG3CCII","target":"record","payload":{"canonical_record":{"source":{"id":"1412.7326","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-23T11:34:48Z","cross_cats_sorted":[],"title_canon_sha256":"88de16efdbf931b434c2d7c6f5665c4dea668eb38eac2efcc1b82a806cda34dc","abstract_canon_sha256":"84bd851fc4d7d8425be1e6d6f27c4315bd636c408d6a52b458c4ad22b9e518af"},"schema_version":"1.0"},"canonical_sha256":"85df36fc5b6e96a396683932e36c42423752c0d7bb5dc3d82068eed35f5c4cc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:39.133084Z","signature_b64":"kTlZ8Q/Y75i8H5f3gOJpd6GXSLXJqvXpgFn8P2NPzjGVXc6HvuGomddD9R/bB7wUDcfBKxkQqobGCdhrVAEdBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85df36fc5b6e96a396683932e36c42423752c0d7bb5dc3d82068eed35f5c4cc7","last_reissued_at":"2026-05-18T02:30:39.132648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:39.132648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.7326","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":"2026-05-18T02:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HSSOKJLllLNmCP3wcj4Hox+qMtPNcafEbIegdJpgyp8qHEtc/ImTCNecJNH8psRuOkS0KAwkblJuQOoSPNRSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:02:33.577665Z"},"content_sha256":"d8fde1e996d876f928662f2f2e3ae81fc2835c4b54af3a438a15866dfd2c3628","schema_version":"1.0","event_id":"sha256:d8fde1e996d876f928662f2f2e3ae81fc2835c4b54af3a438a15866dfd2c3628"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:QXPTN7C3N2LKHFTIHEZOG3CCII","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"m-Microlocal elliptic pseudodifferential operators acting on $L^p_{\\rm loc}(\\Omega)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alessandro Morando, Gianluca Garello","submitted_at":"2014-12-23T11:34:48Z","abstract_excerpt":"In the first part of the paper the authors study the minimal and maximal extension of a class of weighted pseudodifferential operators in the Fr\\'echet space $L^p_{\\rm loc}(\\Omega)$. In the second one non homogeneous microlocal properties are introduced and propagation of Sobolev singularities for solutions to (pseudo)differential equations is given. For both the arguments actual examples are provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7326","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":"2026-05-18T02:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LsTsjKjaW+pdtFtu9fwF0L0OCY7INDABGHBzl04be8xeryRgUzQwxKzLHCVC+SEmSr13/BkuL3jbC+z5mw6fCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:02:33.578012Z"},"content_sha256":"d265401103c31756082226ff09cccf4fd72d096c78b3ec91990c5af35bbd2c50","schema_version":"1.0","event_id":"sha256:d265401103c31756082226ff09cccf4fd72d096c78b3ec91990c5af35bbd2c50"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QXPTN7C3N2LKHFTIHEZOG3CCII/bundle.json","state_url":"https://pith.science/pith/QXPTN7C3N2LKHFTIHEZOG3CCII/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QXPTN7C3N2LKHFTIHEZOG3CCII/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":"2026-06-01T19:02:33Z","links":{"resolver":"https://pith.science/pith/QXPTN7C3N2LKHFTIHEZOG3CCII","bundle":"https://pith.science/pith/QXPTN7C3N2LKHFTIHEZOG3CCII/bundle.json","state":"https://pith.science/pith/QXPTN7C3N2LKHFTIHEZOG3CCII/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QXPTN7C3N2LKHFTIHEZOG3CCII/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QXPTN7C3N2LKHFTIHEZOG3CCII","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":"84bd851fc4d7d8425be1e6d6f27c4315bd636c408d6a52b458c4ad22b9e518af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-23T11:34:48Z","title_canon_sha256":"88de16efdbf931b434c2d7c6f5665c4dea668eb38eac2efcc1b82a806cda34dc"},"schema_version":"1.0","source":{"id":"1412.7326","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7326","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7326v1","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7326","created_at":"2026-05-18T02:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"QXPTN7C3N2LK","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QXPTN7C3N2LKHFTI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QXPTN7C3","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:d265401103c31756082226ff09cccf4fd72d096c78b3ec91990c5af35bbd2c50","target":"graph","created_at":"2026-05-18T02:30:39Z","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":"In the first part of the paper the authors study the minimal and maximal extension of a class of weighted pseudodifferential operators in the Fr\\'echet space $L^p_{\\rm loc}(\\Omega)$. In the second one non homogeneous microlocal properties are introduced and propagation of Sobolev singularities for solutions to (pseudo)differential equations is given. For both the arguments actual examples are provided.","authors_text":"Alessandro Morando, Gianluca Garello","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-23T11:34:48Z","title":"m-Microlocal elliptic pseudodifferential operators acting on $L^p_{\\rm loc}(\\Omega)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7326","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:d8fde1e996d876f928662f2f2e3ae81fc2835c4b54af3a438a15866dfd2c3628","target":"record","created_at":"2026-05-18T02:30:39Z","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":"84bd851fc4d7d8425be1e6d6f27c4315bd636c408d6a52b458c4ad22b9e518af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-23T11:34:48Z","title_canon_sha256":"88de16efdbf931b434c2d7c6f5665c4dea668eb38eac2efcc1b82a806cda34dc"},"schema_version":"1.0","source":{"id":"1412.7326","kind":"arxiv","version":1}},"canonical_sha256":"85df36fc5b6e96a396683932e36c42423752c0d7bb5dc3d82068eed35f5c4cc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85df36fc5b6e96a396683932e36c42423752c0d7bb5dc3d82068eed35f5c4cc7","first_computed_at":"2026-05-18T02:30:39.132648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:39.132648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kTlZ8Q/Y75i8H5f3gOJpd6GXSLXJqvXpgFn8P2NPzjGVXc6HvuGomddD9R/bB7wUDcfBKxkQqobGCdhrVAEdBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:39.133084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7326","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8fde1e996d876f928662f2f2e3ae81fc2835c4b54af3a438a15866dfd2c3628","sha256:d265401103c31756082226ff09cccf4fd72d096c78b3ec91990c5af35bbd2c50"],"state_sha256":"d7d931fa2146840179b757c4094f8980fdc99e1e28f3029aebf6bb44ac450c0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"us7LwKc4cgMJXxC+6kjibjYrA3cKQX7maz78R+evQ2qu+0Q+fEdSnaMmPFp3WOPO4UhMw/jkUEEJSoKcrcM3Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:02:33.579952Z","bundle_sha256":"c01d8d5a0f787cf89f71dd03deadf7ea61800a7ecd6ac3cc437d4019599faa48"}}