{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:MUOJCMAO6ZCBTUHRYRRGXNFQMR","short_pith_number":"pith:MUOJCMAO","canonical_record":{"source":{"id":"1010.5185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-25T16:53:02Z","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"title_canon_sha256":"e7b3bab9812a5d7d80853f2ecdd6dfa64bed5187d7f81405987a1d1aaab1be6a","abstract_canon_sha256":"ecb4779cbe085604732a6a9e04411d2417fe97ed22ede3aac4492f1188e41f2c"},"schema_version":"1.0"},"canonical_sha256":"651c91300ef64419d0f1c4626bb4b064716bb146cd4e23fa55c5f3b67d81f1cc","source":{"kind":"arxiv","id":"1010.5185","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5185","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5185v1","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5185","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"MUOJCMAO6ZCB","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MUOJCMAO6ZCBTUHR","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MUOJCMAO","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:MUOJCMAO6ZCBTUHRYRRGXNFQMR","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5185","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-25T16:53:02Z","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"title_canon_sha256":"e7b3bab9812a5d7d80853f2ecdd6dfa64bed5187d7f81405987a1d1aaab1be6a","abstract_canon_sha256":"ecb4779cbe085604732a6a9e04411d2417fe97ed22ede3aac4492f1188e41f2c"},"schema_version":"1.0"},"canonical_sha256":"651c91300ef64419d0f1c4626bb4b064716bb146cd4e23fa55c5f3b67d81f1cc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:58.797138Z","signature_b64":"AXOgsDlh9MSgkIiGbzqaFy0Rj6UoU4AFK18yMilwseNCf1ummHQUtNUzf06dR43sh1PiPynFE54lk8NNf/ibDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"651c91300ef64419d0f1c4626bb4b064716bb146cd4e23fa55c5f3b67d81f1cc","last_reissued_at":"2026-05-18T02:04:58.796626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:58.796626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5185","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":"2026-05-18T02:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+BNCiTHuP6s5+HQwY7Qfw1JJoE/jNKaN1oBFVIPmoh9bb+lrGePj4JKOS5lBrkc5+dONCtMFua2Y2tnYPWQQAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:27:42.381013Z"},"content_sha256":"878e18f5abf78d7a2767e9398bf85da39367eab72042aed354d82e38f76222cd","schema_version":"1.0","event_id":"sha256:878e18f5abf78d7a2767e9398bf85da39367eab72042aed354d82e38f76222cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:MUOJCMAO6ZCBTUHRYRRGXNFQMR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Fractionary Schr\\\"{o}dinger Equation, Green Functions and Ultradistributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. L. De Paoli, M. C. Rocca","submitted_at":"2010-10-25T16:53:02Z","abstract_excerpt":"In this work, we generalize previous results about the Fractionary Schr\\\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate the Green's function for a free particle in the general case, for an arbitrary order of the derivative index."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5185","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":"2026-05-18T02:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z45WZ2/VW0soZyaFQFx2dJ1b5on1g0wHXrH4QntOUp5mi9qyfB8jb5c6RSE8E61baToKXx7MHIDz0CR43bkHBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:27:42.381595Z"},"content_sha256":"60c530158e3020d0894a94932e3df5100ab01c62c27d21e2ede09a7a4b050649","schema_version":"1.0","event_id":"sha256:60c530158e3020d0894a94932e3df5100ab01c62c27d21e2ede09a7a4b050649"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MUOJCMAO6ZCBTUHRYRRGXNFQMR/bundle.json","state_url":"https://pith.science/pith/MUOJCMAO6ZCBTUHRYRRGXNFQMR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MUOJCMAO6ZCBTUHRYRRGXNFQMR/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":"2026-05-31T21:27:42Z","links":{"resolver":"https://pith.science/pith/MUOJCMAO6ZCBTUHRYRRGXNFQMR","bundle":"https://pith.science/pith/MUOJCMAO6ZCBTUHRYRRGXNFQMR/bundle.json","state":"https://pith.science/pith/MUOJCMAO6ZCBTUHRYRRGXNFQMR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MUOJCMAO6ZCBTUHRYRRGXNFQMR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MUOJCMAO6ZCBTUHRYRRGXNFQMR","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":"ecb4779cbe085604732a6a9e04411d2417fe97ed22ede3aac4492f1188e41f2c","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-25T16:53:02Z","title_canon_sha256":"e7b3bab9812a5d7d80853f2ecdd6dfa64bed5187d7f81405987a1d1aaab1be6a"},"schema_version":"1.0","source":{"id":"1010.5185","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5185","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5185v1","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5185","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"MUOJCMAO6ZCB","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MUOJCMAO6ZCBTUHR","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MUOJCMAO","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:60c530158e3020d0894a94932e3df5100ab01c62c27d21e2ede09a7a4b050649","target":"graph","created_at":"2026-05-18T02:04:58Z","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 this work, we generalize previous results about the Fractionary Schr\\\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate the Green's function for a free particle in the general case, for an arbitrary order of the derivative index.","authors_text":"A. L. De Paoli, M. C. Rocca","cross_cats":["hep-th","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-25T16:53:02Z","title":"The Fractionary Schr\\\"{o}dinger Equation, Green Functions and Ultradistributions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5185","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":"sha256:878e18f5abf78d7a2767e9398bf85da39367eab72042aed354d82e38f76222cd","target":"record","created_at":"2026-05-18T02:04:58Z","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":"ecb4779cbe085604732a6a9e04411d2417fe97ed22ede3aac4492f1188e41f2c","cross_cats_sorted":["hep-th","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-25T16:53:02Z","title_canon_sha256":"e7b3bab9812a5d7d80853f2ecdd6dfa64bed5187d7f81405987a1d1aaab1be6a"},"schema_version":"1.0","source":{"id":"1010.5185","kind":"arxiv","version":1}},"canonical_sha256":"651c91300ef64419d0f1c4626bb4b064716bb146cd4e23fa55c5f3b67d81f1cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"651c91300ef64419d0f1c4626bb4b064716bb146cd4e23fa55c5f3b67d81f1cc","first_computed_at":"2026-05-18T02:04:58.796626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:58.796626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AXOgsDlh9MSgkIiGbzqaFy0Rj6UoU4AFK18yMilwseNCf1ummHQUtNUzf06dR43sh1PiPynFE54lk8NNf/ibDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:58.797138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5185","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:878e18f5abf78d7a2767e9398bf85da39367eab72042aed354d82e38f76222cd","sha256:60c530158e3020d0894a94932e3df5100ab01c62c27d21e2ede09a7a4b050649"],"state_sha256":"a99c55c9cd909c9bcc4f6ffa4bfc5a25bea5430160c6883c66040c0c99bc6f1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v19wRAu7IrG4kjh8ysQZUBUiUqgthbj71kW8rfyu5CBtQiSvJZpbQ1dXtijmPvVXABq45f1agtUyx50nwIznDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:27:42.384446Z","bundle_sha256":"acbf6844b0030b4bbe8a56893d77e4d36c06079fddcb2dc0c515255c28f87e4c"}}