{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q2UCIFJ44NJSADHSIPBB7MNEWC","short_pith_number":"pith:Q2UCIFJ4","canonical_record":{"source":{"id":"1301.5447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-23T09:44:23Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ed803de607a8e4672178dfcf242465375cb38d6d2a29784ffa30fc5bebe0c78e","abstract_canon_sha256":"c9c42b9e983a678a90c95828d6d9289a591320a8a39a61750d56a86a216c2b6c"},"schema_version":"1.0"},"canonical_sha256":"86a824153ce353200cf243c21fb1a4b0b59763460202517a98c3b0db8f9dd2f3","source":{"kind":"arxiv","id":"1301.5447","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5447","created_at":"2026-05-18T03:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5447v2","created_at":"2026-05-18T03:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5447","created_at":"2026-05-18T03:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"Q2UCIFJ44NJS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q2UCIFJ44NJSADHS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q2UCIFJ4","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q2UCIFJ44NJSADHSIPBB7MNEWC","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5447","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-23T09:44:23Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"ed803de607a8e4672178dfcf242465375cb38d6d2a29784ffa30fc5bebe0c78e","abstract_canon_sha256":"c9c42b9e983a678a90c95828d6d9289a591320a8a39a61750d56a86a216c2b6c"},"schema_version":"1.0"},"canonical_sha256":"86a824153ce353200cf243c21fb1a4b0b59763460202517a98c3b0db8f9dd2f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:49.452627Z","signature_b64":"GtAN8G0t7+1lOX95SikjZEUfn0PqnelRNeMs2/KWALzQvxP1kr6hwdOPpjKXnBr87hd1oygwwgMRan3v/X0gCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86a824153ce353200cf243c21fb1a4b0b59763460202517a98c3b0db8f9dd2f3","last_reissued_at":"2026-05-18T03:33:49.451776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:49.451776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5447","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1nRN6t3/f3Z//oTf3hqs6CFM0fEqtvOodLgWNN6l4SupCqUzSRJix9wzITk/mnj71pIXo34Nzji9QhkGYDGODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:36:11.462788Z"},"content_sha256":"8de84e3060751d12a8635a15fad05aa1e007bf76c9471892569c1603c7890838","schema_version":"1.0","event_id":"sha256:8de84e3060751d12a8635a15fad05aa1e007bf76c9471892569c1603c7890838"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q2UCIFJ44NJSADHSIPBB7MNEWC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-dimensional degenerate diffusion operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Angela A. Albanese, Elisabetta M. Mangino","submitted_at":"2013-01-23T09:44:23Z","abstract_excerpt":"The aim of this paper is to present some results about generation, sectoriality and gradient estimates both for the semigroup and for the resolvent of suitable realizations of the operators [\\Ab u(x)=\\gamma xu\"(x) + b u'(x),] with constants $\\gamma >0$ and $b\\geq 0$, in the space $C([0,\\infty])$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5447","kind":"arxiv","version":2},"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":"2026-05-18T03:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DBD+UeeuarrWd7LDKNInANwlglyw9V8eEbHeZMOgFisJAD2j3MfkVy6B66KlPUcAzbrEs5NI57soSM0j2WYCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:36:11.463133Z"},"content_sha256":"52885852e991acd8973ec5676323e6a3c7a32d24815d47e5c562f5babfd883c1","schema_version":"1.0","event_id":"sha256:52885852e991acd8973ec5676323e6a3c7a32d24815d47e5c562f5babfd883c1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2UCIFJ44NJSADHSIPBB7MNEWC/bundle.json","state_url":"https://pith.science/pith/Q2UCIFJ44NJSADHSIPBB7MNEWC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2UCIFJ44NJSADHSIPBB7MNEWC/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":"2026-06-24T22:36:11Z","links":{"resolver":"https://pith.science/pith/Q2UCIFJ44NJSADHSIPBB7MNEWC","bundle":"https://pith.science/pith/Q2UCIFJ44NJSADHSIPBB7MNEWC/bundle.json","state":"https://pith.science/pith/Q2UCIFJ44NJSADHSIPBB7MNEWC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2UCIFJ44NJSADHSIPBB7MNEWC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q2UCIFJ44NJSADHSIPBB7MNEWC","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":"c9c42b9e983a678a90c95828d6d9289a591320a8a39a61750d56a86a216c2b6c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-23T09:44:23Z","title_canon_sha256":"ed803de607a8e4672178dfcf242465375cb38d6d2a29784ffa30fc5bebe0c78e"},"schema_version":"1.0","source":{"id":"1301.5447","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5447","created_at":"2026-05-18T03:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5447v2","created_at":"2026-05-18T03:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5447","created_at":"2026-05-18T03:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"Q2UCIFJ44NJS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q2UCIFJ44NJSADHS","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q2UCIFJ4","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:52885852e991acd8973ec5676323e6a3c7a32d24815d47e5c562f5babfd883c1","target":"graph","created_at":"2026-05-18T03:33:49Z","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":"The aim of this paper is to present some results about generation, sectoriality and gradient estimates both for the semigroup and for the resolvent of suitable realizations of the operators [\\Ab u(x)=\\gamma xu\"(x) + b u'(x),] with constants $\\gamma >0$ and $b\\geq 0$, in the space $C([0,\\infty])$","authors_text":"Angela A. Albanese, Elisabetta M. Mangino","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-23T09:44:23Z","title":"One-dimensional degenerate diffusion operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5447","kind":"arxiv","version":2},"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":"sha256:8de84e3060751d12a8635a15fad05aa1e007bf76c9471892569c1603c7890838","target":"record","created_at":"2026-05-18T03:33:49Z","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":"c9c42b9e983a678a90c95828d6d9289a591320a8a39a61750d56a86a216c2b6c","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-23T09:44:23Z","title_canon_sha256":"ed803de607a8e4672178dfcf242465375cb38d6d2a29784ffa30fc5bebe0c78e"},"schema_version":"1.0","source":{"id":"1301.5447","kind":"arxiv","version":2}},"canonical_sha256":"86a824153ce353200cf243c21fb1a4b0b59763460202517a98c3b0db8f9dd2f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86a824153ce353200cf243c21fb1a4b0b59763460202517a98c3b0db8f9dd2f3","first_computed_at":"2026-05-18T03:33:49.451776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:49.451776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GtAN8G0t7+1lOX95SikjZEUfn0PqnelRNeMs2/KWALzQvxP1kr6hwdOPpjKXnBr87hd1oygwwgMRan3v/X0gCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:49.452627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5447","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8de84e3060751d12a8635a15fad05aa1e007bf76c9471892569c1603c7890838","sha256:52885852e991acd8973ec5676323e6a3c7a32d24815d47e5c562f5babfd883c1"],"state_sha256":"eac372c09490687a0131350cad674e37ed884dc98d62706c97d74af287070b3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+44z5sStHOn5OH6K/6bk83NsVcnXVy1V+rzS/Qu3F/9jtWNemXKxSwxO2bnofcuk8aXy1i29Rm6F0ZebhlaRAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:36:11.465077Z","bundle_sha256":"513177d3ac9a7513760a15d74c1c7d104f4384a33bac66e04436bea91f289bee"}}