{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MDGPLRXVGGT4I7KVFVDIZP3WS6","short_pith_number":"pith:MDGPLRXV","canonical_record":{"source":{"id":"1801.08885","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-26T16:20:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2a51b38eee12583bf8886dd2477329d928c5c9c9ed2b68d1948c506e23eee9b7","abstract_canon_sha256":"9ae211f6ee03086ea9f24b3b2acda3a47d88c6194a64c32c2e0e51a31c3a48d0"},"schema_version":"1.0"},"canonical_sha256":"60ccf5c6f531a7c47d552d468cbf76979b74c66ff45ecc6d0036dfd7a3a7dfbb","source":{"kind":"arxiv","id":"1801.08885","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08885","created_at":"2026-05-18T00:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08885v6","created_at":"2026-05-18T00:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08885","created_at":"2026-05-18T00:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"MDGPLRXVGGT4","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MDGPLRXVGGT4I7KV","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MDGPLRXV","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MDGPLRXVGGT4I7KVFVDIZP3WS6","target":"record","payload":{"canonical_record":{"source":{"id":"1801.08885","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-26T16:20:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2a51b38eee12583bf8886dd2477329d928c5c9c9ed2b68d1948c506e23eee9b7","abstract_canon_sha256":"9ae211f6ee03086ea9f24b3b2acda3a47d88c6194a64c32c2e0e51a31c3a48d0"},"schema_version":"1.0"},"canonical_sha256":"60ccf5c6f531a7c47d552d468cbf76979b74c66ff45ecc6d0036dfd7a3a7dfbb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:15.525980Z","signature_b64":"ixbh1w16Da61lKauDTLLZPD4asNwVvGOLF59/+qOqJheNgye/PBfsl5KnPPfbjaOI8oJ822DImbi6RNB0estBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60ccf5c6f531a7c47d552d468cbf76979b74c66ff45ecc6d0036dfd7a3a7dfbb","last_reissued_at":"2026-05-18T00:08:15.525465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:15.525465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.08885","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1p9X45ijGyfEI2A17IM1MBHYpXoxUMnZvYAYFK4O5iSLGLDy9hApAC+zNp/Cd/d1rgEYamKB1BbpQJO0Ea+hAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:20:26.532194Z"},"content_sha256":"3f243a1a0e0314e19dd41fba662337dd5fe7f78c419d08344455dba9b54005e7","schema_version":"1.0","event_id":"sha256:3f243a1a0e0314e19dd41fba662337dd5fe7f78c419d08344455dba9b54005e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MDGPLRXVGGT4I7KVFVDIZP3WS6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional powers and singular perturbations of quantum differential Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Alessandro Michelangeli, Andrea Ottolini, Raffaele Scandone","submitted_at":"2018-01-26T16:20:56Z","abstract_excerpt":"We consider the fractional powers of singular (point-like) perturbations of the Laplacian, and the singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schr\\\"{o}dinger equations for the corresponding operators we outline a programme of relevant questions that deserve being investigated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08885","kind":"arxiv","version":6},"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":"2026-05-18T00:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WFqvXfc9q+HuDJH0ZSXefgU3DIk1GlZZ72SQXWJWFXdKoRuWcCkhVxcxxAURa+QbGY0vNJDIKZHn7LGoDq+AAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T05:20:26.533124Z"},"content_sha256":"06f479adc49e40293f7af514dc07cecf5a09f39653e99ab0fa43589c63f68114","schema_version":"1.0","event_id":"sha256:06f479adc49e40293f7af514dc07cecf5a09f39653e99ab0fa43589c63f68114"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDGPLRXVGGT4I7KVFVDIZP3WS6/bundle.json","state_url":"https://pith.science/pith/MDGPLRXVGGT4I7KVFVDIZP3WS6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDGPLRXVGGT4I7KVFVDIZP3WS6/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":"2026-05-30T05:20:26Z","links":{"resolver":"https://pith.science/pith/MDGPLRXVGGT4I7KVFVDIZP3WS6","bundle":"https://pith.science/pith/MDGPLRXVGGT4I7KVFVDIZP3WS6/bundle.json","state":"https://pith.science/pith/MDGPLRXVGGT4I7KVFVDIZP3WS6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDGPLRXVGGT4I7KVFVDIZP3WS6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MDGPLRXVGGT4I7KVFVDIZP3WS6","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":"9ae211f6ee03086ea9f24b3b2acda3a47d88c6194a64c32c2e0e51a31c3a48d0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-26T16:20:56Z","title_canon_sha256":"2a51b38eee12583bf8886dd2477329d928c5c9c9ed2b68d1948c506e23eee9b7"},"schema_version":"1.0","source":{"id":"1801.08885","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.08885","created_at":"2026-05-18T00:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"1801.08885v6","created_at":"2026-05-18T00:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.08885","created_at":"2026-05-18T00:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"MDGPLRXVGGT4","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MDGPLRXVGGT4I7KV","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MDGPLRXV","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:06f479adc49e40293f7af514dc07cecf5a09f39653e99ab0fa43589c63f68114","target":"graph","created_at":"2026-05-18T00:08:15Z","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 fractional powers of singular (point-like) perturbations of the Laplacian, and the singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schr\\\"{o}dinger equations for the corresponding operators we outline a programme of relevant questions that deserve being investigated.","authors_text":"Alessandro Michelangeli, Andrea Ottolini, Raffaele Scandone","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-26T16:20:56Z","title":"Fractional powers and singular perturbations of quantum differential Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.08885","kind":"arxiv","version":6},"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":"sha256:3f243a1a0e0314e19dd41fba662337dd5fe7f78c419d08344455dba9b54005e7","target":"record","created_at":"2026-05-18T00:08:15Z","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":"9ae211f6ee03086ea9f24b3b2acda3a47d88c6194a64c32c2e0e51a31c3a48d0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-01-26T16:20:56Z","title_canon_sha256":"2a51b38eee12583bf8886dd2477329d928c5c9c9ed2b68d1948c506e23eee9b7"},"schema_version":"1.0","source":{"id":"1801.08885","kind":"arxiv","version":6}},"canonical_sha256":"60ccf5c6f531a7c47d552d468cbf76979b74c66ff45ecc6d0036dfd7a3a7dfbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60ccf5c6f531a7c47d552d468cbf76979b74c66ff45ecc6d0036dfd7a3a7dfbb","first_computed_at":"2026-05-18T00:08:15.525465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:15.525465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ixbh1w16Da61lKauDTLLZPD4asNwVvGOLF59/+qOqJheNgye/PBfsl5KnPPfbjaOI8oJ822DImbi6RNB0estBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:15.525980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.08885","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f243a1a0e0314e19dd41fba662337dd5fe7f78c419d08344455dba9b54005e7","sha256:06f479adc49e40293f7af514dc07cecf5a09f39653e99ab0fa43589c63f68114"],"state_sha256":"4a390686a8a9e03c2b43a380af381c5cf939137d88aee2705a3053f6c636179d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yw/gyh/uMOxCNHfHAWyLWijvFoaU1HC2dnRDlRJvMkm8UJVcQOB6yThJiz9KEx2SBPeFSTKZLMD9o7ROhWf+BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T05:20:26.537327Z","bundle_sha256":"22d8a72ad9f17b56eef47a56d9a0f0cdabaaa542278bda588a1a2bcd4caa2848"}}