{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:ZFKMB4Y5EXVXZF25FXCZFZH2HO","short_pith_number":"pith:ZFKMB4Y5","canonical_record":{"source":{"id":"2501.03790","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-01-07T13:54:47Z","cross_cats_sorted":[],"title_canon_sha256":"ff669bac728c213ddb3ab6a23bbc35c80dae5413ac533f44c78fb551e5cdc163","abstract_canon_sha256":"e23a4a1e5a0716eadcbd85beb4873efebcfbabc31c1718014bab08cd241e9680"},"schema_version":"1.0"},"canonical_sha256":"c954c0f31d25eb7c975d2dc592e4fa3b8227ca61f1b8794cc4b3c6ab2e8fc40f","source":{"kind":"arxiv","id":"2501.03790","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03790","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03790v1","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03790","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZFKMB4Y5EXVX","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZFKMB4Y5EXVXZF25","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZFKMB4Y5","created_at":"2026-07-05T09:57:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:ZFKMB4Y5EXVXZF25FXCZFZH2HO","target":"record","payload":{"canonical_record":{"source":{"id":"2501.03790","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-01-07T13:54:47Z","cross_cats_sorted":[],"title_canon_sha256":"ff669bac728c213ddb3ab6a23bbc35c80dae5413ac533f44c78fb551e5cdc163","abstract_canon_sha256":"e23a4a1e5a0716eadcbd85beb4873efebcfbabc31c1718014bab08cd241e9680"},"schema_version":"1.0"},"canonical_sha256":"c954c0f31d25eb7c975d2dc592e4fa3b8227ca61f1b8794cc4b3c6ab2e8fc40f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:59.579614Z","signature_b64":"c52rXMyKGfPN666jJHz5uuMr63aW9ZzIVsiJp7PIt2wXlnXaMoUgTkU5Cbmt2a+eIkXxR/rt2gMdWuNGJH/LAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c954c0f31d25eb7c975d2dc592e4fa3b8227ca61f1b8794cc4b3c6ab2e8fc40f","last_reissued_at":"2026-07-05T09:57:59.579124Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:59.579124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.03790","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":"2026-07-05T09:57:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FF8jk54l4OxVmWoBS2z7JAlunnkTZ/r5Hk6TB9+9gYBToDSDFLz1/AbyBE0wKvUIrOzr73pJPMKJtfneraJaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:10:43.325749Z"},"content_sha256":"db7dc9ee87e095e5c4c55390f742d22cf3a278f8545b26a6e6a0519c12ee76a9","schema_version":"1.0","event_id":"sha256:db7dc9ee87e095e5c4c55390f742d22cf3a278f8545b26a6e6a0519c12ee76a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:ZFKMB4Y5EXVXZF25FXCZFZH2HO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limits at infinity for functions in fractional Sobolev spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Angha Agarwal, Kaushik Mohanta, Pekka Koskela","submitted_at":"2025-01-07T13:54:47Z","abstract_excerpt":"We establish optimal results on limits at infinity for functions in fractional Sobolev spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03790","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/2501.03790/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":"2026-07-05T09:57:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hbln0IKqh146xkXtWuBuC2+V6T1ptmBhPG/xc9omAqsLDq33TiQkQ+0QbLw0PHzVIAg1J0W8fvb0gTRKLO0tDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:10:43.326241Z"},"content_sha256":"55c0d1a02618a746e0d47ee2fe659941bc74e20768663ba7c0222648a8b9468e","schema_version":"1.0","event_id":"sha256:55c0d1a02618a746e0d47ee2fe659941bc74e20768663ba7c0222648a8b9468e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZFKMB4Y5EXVXZF25FXCZFZH2HO/bundle.json","state_url":"https://pith.science/pith/ZFKMB4Y5EXVXZF25FXCZFZH2HO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZFKMB4Y5EXVXZF25FXCZFZH2HO/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":"2026-08-08T13:10:43Z","links":{"resolver":"https://pith.science/pith/ZFKMB4Y5EXVXZF25FXCZFZH2HO","bundle":"https://pith.science/pith/ZFKMB4Y5EXVXZF25FXCZFZH2HO/bundle.json","state":"https://pith.science/pith/ZFKMB4Y5EXVXZF25FXCZFZH2HO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZFKMB4Y5EXVXZF25FXCZFZH2HO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZFKMB4Y5EXVXZF25FXCZFZH2HO","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":"e23a4a1e5a0716eadcbd85beb4873efebcfbabc31c1718014bab08cd241e9680","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-01-07T13:54:47Z","title_canon_sha256":"ff669bac728c213ddb3ab6a23bbc35c80dae5413ac533f44c78fb551e5cdc163"},"schema_version":"1.0","source":{"id":"2501.03790","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03790","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03790v1","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03790","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"pith_short_12","alias_value":"ZFKMB4Y5EXVX","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZFKMB4Y5EXVXZF25","created_at":"2026-07-05T09:57:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZFKMB4Y5","created_at":"2026-07-05T09:57:59Z"}],"graph_snapshots":[{"event_id":"sha256:55c0d1a02618a746e0d47ee2fe659941bc74e20768663ba7c0222648a8b9468e","target":"graph","created_at":"2026-07-05T09:57:59Z","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/2501.03790/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish optimal results on limits at infinity for functions in fractional Sobolev spaces.","authors_text":"Angha Agarwal, Kaushik Mohanta, Pekka Koskela","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-01-07T13:54:47Z","title":"Limits at infinity for functions in fractional Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03790","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:db7dc9ee87e095e5c4c55390f742d22cf3a278f8545b26a6e6a0519c12ee76a9","target":"record","created_at":"2026-07-05T09:57:59Z","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":"e23a4a1e5a0716eadcbd85beb4873efebcfbabc31c1718014bab08cd241e9680","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-01-07T13:54:47Z","title_canon_sha256":"ff669bac728c213ddb3ab6a23bbc35c80dae5413ac533f44c78fb551e5cdc163"},"schema_version":"1.0","source":{"id":"2501.03790","kind":"arxiv","version":1}},"canonical_sha256":"c954c0f31d25eb7c975d2dc592e4fa3b8227ca61f1b8794cc4b3c6ab2e8fc40f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c954c0f31d25eb7c975d2dc592e4fa3b8227ca61f1b8794cc4b3c6ab2e8fc40f","first_computed_at":"2026-07-05T09:57:59.579124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:59.579124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c52rXMyKGfPN666jJHz5uuMr63aW9ZzIVsiJp7PIt2wXlnXaMoUgTkU5Cbmt2a+eIkXxR/rt2gMdWuNGJH/LAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:59.579614Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.03790","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db7dc9ee87e095e5c4c55390f742d22cf3a278f8545b26a6e6a0519c12ee76a9","sha256:55c0d1a02618a746e0d47ee2fe659941bc74e20768663ba7c0222648a8b9468e"],"state_sha256":"49b93b23a24e2cd8438ef62f74496fb109e656ad992397dc96954c71f0df001e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lo6gVnqMqF3xBmg8gzcLLTT/VBwXI8L1yj+IB6ww/GOg5xPzyOqaYd8isqw5mslEX3r0a/Y/5rgYkn3LPrOJAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T13:10:43.329861Z","bundle_sha256":"69b0c1a57b9bb09398ee8396eade5f56e34ba4e917849d614ecaff4464a0c9f8"}}