{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HSQCZPOAD7QMOVPI6LN7ZO7KIY","short_pith_number":"pith:HSQCZPOA","canonical_record":{"source":{"id":"2506.02305","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T22:48:08Z","cross_cats_sorted":[],"title_canon_sha256":"df38af2f87574b209eff325f1e302623d1c4fca6ae37b61e563e5e99b0bd1aef","abstract_canon_sha256":"12b19d9e838ad40178729baa5111fbe1aaa5ea55a5e3293bdf01b0d92e48524d"},"schema_version":"1.0"},"canonical_sha256":"3ca02cbdc01fe0c755e8f2dbfcbbea460f381297f8b6de290a5cefdac3c9e7f3","source":{"kind":"arxiv","id":"2506.02305","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02305","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02305v1","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02305","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"HSQCZPOAD7QM","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"pith_short_16","alias_value":"HSQCZPOAD7QMOVPI","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"pith_short_8","alias_value":"HSQCZPOA","created_at":"2026-07-05T11:14:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HSQCZPOAD7QMOVPI6LN7ZO7KIY","target":"record","payload":{"canonical_record":{"source":{"id":"2506.02305","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T22:48:08Z","cross_cats_sorted":[],"title_canon_sha256":"df38af2f87574b209eff325f1e302623d1c4fca6ae37b61e563e5e99b0bd1aef","abstract_canon_sha256":"12b19d9e838ad40178729baa5111fbe1aaa5ea55a5e3293bdf01b0d92e48524d"},"schema_version":"1.0"},"canonical_sha256":"3ca02cbdc01fe0c755e8f2dbfcbbea460f381297f8b6de290a5cefdac3c9e7f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:14:36.066779Z","signature_b64":"eTMDkhXfNDQfKYcSFmCPnJw97kClglMquSoM8koGBW/kUUzrMC3sLuKWv33hjDx9U7/xv6gJAqZRVjsHDRxkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ca02cbdc01fe0c755e8f2dbfcbbea460f381297f8b6de290a5cefdac3c9e7f3","last_reissued_at":"2026-07-05T11:14:36.066340Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:14:36.066340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.02305","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":"2026-07-05T11:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3YvlYGPM6kJVqvACSF9S0UB/sWZjavJtsZodl555JPmgMiGeKVjSi9XOVLzPZdvnqnmXyRvO0uNYlb0MmOCnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:31:55.473718Z"},"content_sha256":"1d8ff1feeaa9039a9fd87b9f8b3c56ad22ca44c5229d84ba668cecac5345b19f","schema_version":"1.0","event_id":"sha256:1d8ff1feeaa9039a9fd87b9f8b3c56ad22ca44c5229d84ba668cecac5345b19f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HSQCZPOAD7QMOVPI6LN7ZO7KIY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterization of positive superharmonic functions in a half-space","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Enzo Mitidieri, Lorenzo D'Ambrosio","submitted_at":"2025-06-02T22:48:08Z","abstract_excerpt":"We prove a representation formula for superharmonic functions on the half-space $\\mathbb{R}^N_+ := \\mathbb{R}^{N-1}\\times]0,+\\infty[$. As a consequence, we derive some comparison principles and various positivity results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02305","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.02305/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GxvT4DBIY4DzsApTYYQeXHnEVKqQAjfsHIMsjHVyvsZC00g5OnJx0Gqpesm7J3Fsa61M+hEtFxPvK00DOXueDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T23:31:55.474795Z"},"content_sha256":"5f9e419734270297416493090200eb1572ddf85f77817d1c9cc9b8c6f5e10aa3","schema_version":"1.0","event_id":"sha256:5f9e419734270297416493090200eb1572ddf85f77817d1c9cc9b8c6f5e10aa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HSQCZPOAD7QMOVPI6LN7ZO7KIY/bundle.json","state_url":"https://pith.science/pith/HSQCZPOAD7QMOVPI6LN7ZO7KIY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HSQCZPOAD7QMOVPI6LN7ZO7KIY/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":"2026-08-10T23:31:55Z","links":{"resolver":"https://pith.science/pith/HSQCZPOAD7QMOVPI6LN7ZO7KIY","bundle":"https://pith.science/pith/HSQCZPOAD7QMOVPI6LN7ZO7KIY/bundle.json","state":"https://pith.science/pith/HSQCZPOAD7QMOVPI6LN7ZO7KIY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HSQCZPOAD7QMOVPI6LN7ZO7KIY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HSQCZPOAD7QMOVPI6LN7ZO7KIY","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":"12b19d9e838ad40178729baa5111fbe1aaa5ea55a5e3293bdf01b0d92e48524d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T22:48:08Z","title_canon_sha256":"df38af2f87574b209eff325f1e302623d1c4fca6ae37b61e563e5e99b0bd1aef"},"schema_version":"1.0","source":{"id":"2506.02305","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02305","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02305v1","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02305","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"HSQCZPOAD7QM","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"pith_short_16","alias_value":"HSQCZPOAD7QMOVPI","created_at":"2026-07-05T11:14:36Z"},{"alias_kind":"pith_short_8","alias_value":"HSQCZPOA","created_at":"2026-07-05T11:14:36Z"}],"graph_snapshots":[{"event_id":"sha256:5f9e419734270297416493090200eb1572ddf85f77817d1c9cc9b8c6f5e10aa3","target":"graph","created_at":"2026-07-05T11:14:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.02305/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a representation formula for superharmonic functions on the half-space $\\mathbb{R}^N_+ := \\mathbb{R}^{N-1}\\times]0,+\\infty[$. As a consequence, we derive some comparison principles and various positivity results.","authors_text":"Enzo Mitidieri, Lorenzo D'Ambrosio","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T22:48:08Z","title":"Characterization of positive superharmonic functions in a half-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02305","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":"sha256:1d8ff1feeaa9039a9fd87b9f8b3c56ad22ca44c5229d84ba668cecac5345b19f","target":"record","created_at":"2026-07-05T11:14:36Z","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":"12b19d9e838ad40178729baa5111fbe1aaa5ea55a5e3293bdf01b0d92e48524d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-06-02T22:48:08Z","title_canon_sha256":"df38af2f87574b209eff325f1e302623d1c4fca6ae37b61e563e5e99b0bd1aef"},"schema_version":"1.0","source":{"id":"2506.02305","kind":"arxiv","version":1}},"canonical_sha256":"3ca02cbdc01fe0c755e8f2dbfcbbea460f381297f8b6de290a5cefdac3c9e7f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ca02cbdc01fe0c755e8f2dbfcbbea460f381297f8b6de290a5cefdac3c9e7f3","first_computed_at":"2026-07-05T11:14:36.066340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:14:36.066340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eTMDkhXfNDQfKYcSFmCPnJw97kClglMquSoM8koGBW/kUUzrMC3sLuKWv33hjDx9U7/xv6gJAqZRVjsHDRxkDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:14:36.066779Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02305","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d8ff1feeaa9039a9fd87b9f8b3c56ad22ca44c5229d84ba668cecac5345b19f","sha256:5f9e419734270297416493090200eb1572ddf85f77817d1c9cc9b8c6f5e10aa3"],"state_sha256":"47d4957c27a993d66e32cf42972ea4535eacec07329b9405b1f4b71fe41d84db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c5Ll/YO2FNUq+K7bnawILrLEHkQ/CavXa+bWR9OnN1vroFqIDkVkeLZpZ2a1lVlCgJTXvqNBgO5dvDYkQlORAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T23:31:55.481940Z","bundle_sha256":"7a0b78d6fe0a046411fb3a44ac40b11afb2d56ed62b90707fad7b659eb053ddc"}}