{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ZK7PJQ4PXAXG4IQMINBB46CWKV","short_pith_number":"pith:ZK7PJQ4P","canonical_record":{"source":{"id":"1711.04418","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T04:23:50Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"ac7254112b8198d0c3914f028dbba77e932cc2fd910336aa8567aa37fff39647","abstract_canon_sha256":"afcb9d62b93d25f5fffed893719adaf9e78bef55566c999ec53627a1b9a4a355"},"schema_version":"1.0"},"canonical_sha256":"cabef4c38fb82e6e220c43421e7856557a26c3cb988cbf4749db4c7fd6161768","source":{"kind":"arxiv","id":"1711.04418","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04418","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04418v3","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04418","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"ZK7PJQ4PXAXG","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZK7PJQ4PXAXG4IQM","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZK7PJQ4P","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ZK7PJQ4PXAXG4IQMINBB46CWKV","target":"record","payload":{"canonical_record":{"source":{"id":"1711.04418","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T04:23:50Z","cross_cats_sorted":["math-ph","math.FA","math.MP"],"title_canon_sha256":"ac7254112b8198d0c3914f028dbba77e932cc2fd910336aa8567aa37fff39647","abstract_canon_sha256":"afcb9d62b93d25f5fffed893719adaf9e78bef55566c999ec53627a1b9a4a355"},"schema_version":"1.0"},"canonical_sha256":"cabef4c38fb82e6e220c43421e7856557a26c3cb988cbf4749db4c7fd6161768","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:11.102378Z","signature_b64":"uXi4gBAKMqj2TEczQ5oV3fGwKth3ZQZDPQauuFaFv9/DlLYQPXBJhADnu9L6tRYKUV+iA9g+HXMy5DWvXCGXDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cabef4c38fb82e6e220c43421e7856557a26c3cb988cbf4749db4c7fd6161768","last_reissued_at":"2026-05-18T00:10:11.101676Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:11.101676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.04418","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":"2026-05-18T00:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2TB/FDwHEYbfNrC1bWPGeeHKteNFWxzIGgrv/YTdPlBhg/FOWH9hGEoWKh2P8OK9Pi7aqATfN7WLAYukCbhPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:21:55.044906Z"},"content_sha256":"20dafb24cc2156d2ad0892f8c95ffbee3b023885fe7878d9b94aeed771e2da78","schema_version":"1.0","event_id":"sha256:20dafb24cc2156d2ad0892f8c95ffbee3b023885fe7878d9b94aeed771e2da78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ZK7PJQ4PXAXG4IQMINBB46CWKV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The singular Hartree equation in fractional perturbed Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"math.AP","authors_text":"Alessandro Michelangeli, Alessandro Olgiati, Raffaele Scandone","submitted_at":"2017-11-13T04:23:50Z","abstract_excerpt":"We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schr\\\"odinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04418","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":"2026-05-18T00:10:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7Y8qhcNoOlYKzPtsKwFTq7u9DN+5PqWlS05rpsA7Va1xQyh1GbgkEOHcfGK4X9gY1rG7lKl5AvMGA3n5bnYyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:21:55.045253Z"},"content_sha256":"eeafd4669c9b545dd7241bac49d69f107ffc941ea96994cde359f81a6efc8592","schema_version":"1.0","event_id":"sha256:eeafd4669c9b545dd7241bac49d69f107ffc941ea96994cde359f81a6efc8592"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZK7PJQ4PXAXG4IQMINBB46CWKV/bundle.json","state_url":"https://pith.science/pith/ZK7PJQ4PXAXG4IQMINBB46CWKV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZK7PJQ4PXAXG4IQMINBB46CWKV/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":"2026-06-21T13:21:55Z","links":{"resolver":"https://pith.science/pith/ZK7PJQ4PXAXG4IQMINBB46CWKV","bundle":"https://pith.science/pith/ZK7PJQ4PXAXG4IQMINBB46CWKV/bundle.json","state":"https://pith.science/pith/ZK7PJQ4PXAXG4IQMINBB46CWKV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZK7PJQ4PXAXG4IQMINBB46CWKV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZK7PJQ4PXAXG4IQMINBB46CWKV","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":"afcb9d62b93d25f5fffed893719adaf9e78bef55566c999ec53627a1b9a4a355","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T04:23:50Z","title_canon_sha256":"ac7254112b8198d0c3914f028dbba77e932cc2fd910336aa8567aa37fff39647"},"schema_version":"1.0","source":{"id":"1711.04418","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04418","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04418v3","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04418","created_at":"2026-05-18T00:10:11Z"},{"alias_kind":"pith_short_12","alias_value":"ZK7PJQ4PXAXG","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZK7PJQ4PXAXG4IQM","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZK7PJQ4P","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:eeafd4669c9b545dd7241bac49d69f107ffc941ea96994cde359f81a6efc8592","target":"graph","created_at":"2026-05-18T00:10:11Z","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 establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schr\\\"odinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the","authors_text":"Alessandro Michelangeli, Alessandro Olgiati, Raffaele Scandone","cross_cats":["math-ph","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T04:23:50Z","title":"The singular Hartree equation in fractional perturbed Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04418","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":"sha256:20dafb24cc2156d2ad0892f8c95ffbee3b023885fe7878d9b94aeed771e2da78","target":"record","created_at":"2026-05-18T00:10:11Z","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":"afcb9d62b93d25f5fffed893719adaf9e78bef55566c999ec53627a1b9a4a355","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-13T04:23:50Z","title_canon_sha256":"ac7254112b8198d0c3914f028dbba77e932cc2fd910336aa8567aa37fff39647"},"schema_version":"1.0","source":{"id":"1711.04418","kind":"arxiv","version":3}},"canonical_sha256":"cabef4c38fb82e6e220c43421e7856557a26c3cb988cbf4749db4c7fd6161768","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cabef4c38fb82e6e220c43421e7856557a26c3cb988cbf4749db4c7fd6161768","first_computed_at":"2026-05-18T00:10:11.101676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:11.101676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uXi4gBAKMqj2TEczQ5oV3fGwKth3ZQZDPQauuFaFv9/DlLYQPXBJhADnu9L6tRYKUV+iA9g+HXMy5DWvXCGXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:11.102378Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04418","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20dafb24cc2156d2ad0892f8c95ffbee3b023885fe7878d9b94aeed771e2da78","sha256:eeafd4669c9b545dd7241bac49d69f107ffc941ea96994cde359f81a6efc8592"],"state_sha256":"d811c3c7078bab28efd161d7016b5d51acef199ad7474a497c852288ec112f1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HQkijRgL7H8bTjWsUEiTp3wp/Qq/rvESpL6mM4HH2RPj5FC2V8ckYHhVVHo48g9ceVvcg/s0WTXQb+t9aUu5Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T13:21:55.047192Z","bundle_sha256":"0db3a0b1e34a61b3164042371b9b71c2b27469f378513504518480251a467ea5"}}