{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:NXNAPPQAAYJJ74GTQE4SOLNUBK","short_pith_number":"pith:NXNAPPQA","canonical_record":{"source":{"id":"1607.07051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-24T14:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"d339a687be233edd2ece07f5e5f2d0f859aa930d0fa9dcc0ddb6386b54e4c31e","abstract_canon_sha256":"009ab876821245ae23645f81ef9db3e869fec43989ed93f4be42225efe13fc52"},"schema_version":"1.0"},"canonical_sha256":"6dda07be0006129ff0d38139272db40a99324ee9d53128b32e361a25a4c3bc1c","source":{"kind":"arxiv","id":"1607.07051","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07051","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07051v1","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07051","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"NXNAPPQAAYJJ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NXNAPPQAAYJJ74GT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NXNAPPQA","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:NXNAPPQAAYJJ74GTQE4SOLNUBK","target":"record","payload":{"canonical_record":{"source":{"id":"1607.07051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-24T14:57:44Z","cross_cats_sorted":[],"title_canon_sha256":"d339a687be233edd2ece07f5e5f2d0f859aa930d0fa9dcc0ddb6386b54e4c31e","abstract_canon_sha256":"009ab876821245ae23645f81ef9db3e869fec43989ed93f4be42225efe13fc52"},"schema_version":"1.0"},"canonical_sha256":"6dda07be0006129ff0d38139272db40a99324ee9d53128b32e361a25a4c3bc1c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:35.031925Z","signature_b64":"/L4whNoTUpvwD8Rmu4Lg5xNrzlP8nobhbziUqsalCcjR398fV6k5q+f2ZfUBJiMhbc0w++nHUl1KEpYY7waCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dda07be0006129ff0d38139272db40a99324ee9d53128b32e361a25a4c3bc1c","last_reissued_at":"2026-05-18T01:10:35.031281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:35.031281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.07051","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":"2026-05-18T01:10:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C70lMgAuFEOaVRxZYCa6XtJhqH5DgXxMel06Iw7pV1ECMiOmVdqM1+9Y46Ui+skXre/MWIcEiWiqe5qJZBPnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:31:52.799251Z"},"content_sha256":"f45af24000ed24dbf485b79d317fbbbfb34a41d5a9d19025fffa9c2f44be1b66","schema_version":"1.0","event_id":"sha256:f45af24000ed24dbf485b79d317fbbbfb34a41d5a9d19025fffa9c2f44be1b66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:NXNAPPQAAYJJ74GTQE4SOLNUBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of stationary turbulent flows with variable positive vortex intensity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Francesca De Marchis, Tonia Ricciardi","submitted_at":"2016-07-24T14:57:44Z","abstract_excerpt":"We prove the existence of stationary turbulent flows with arbitrary positive vortex circulation on non simply connected domains. Our construction yields solutions for all real values of the inverse temperature with the exception of a quantized set, for which blow-up phenomena may occur. Our results complete the analysis initiated in [J. Diff. Equ. 260 (2016), 339-369]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07051","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":"2026-05-18T01:10:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"338e3yVPkRlT5TmB5THwNts0DMDYUUlZEBHis73NZBjz2Mc2cfTP0oy55S/rzCuB60gI8u1rLJ3GPVvrEt2yDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:31:52.799746Z"},"content_sha256":"b2812439f6f27ce3c9274a313ca84d8eb3e8c37618715b7b3e0cddfa2ea6c7f4","schema_version":"1.0","event_id":"sha256:b2812439f6f27ce3c9274a313ca84d8eb3e8c37618715b7b3e0cddfa2ea6c7f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NXNAPPQAAYJJ74GTQE4SOLNUBK/bundle.json","state_url":"https://pith.science/pith/NXNAPPQAAYJJ74GTQE4SOLNUBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NXNAPPQAAYJJ74GTQE4SOLNUBK/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":"2026-06-25T21:31:52Z","links":{"resolver":"https://pith.science/pith/NXNAPPQAAYJJ74GTQE4SOLNUBK","bundle":"https://pith.science/pith/NXNAPPQAAYJJ74GTQE4SOLNUBK/bundle.json","state":"https://pith.science/pith/NXNAPPQAAYJJ74GTQE4SOLNUBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NXNAPPQAAYJJ74GTQE4SOLNUBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NXNAPPQAAYJJ74GTQE4SOLNUBK","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":"009ab876821245ae23645f81ef9db3e869fec43989ed93f4be42225efe13fc52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-24T14:57:44Z","title_canon_sha256":"d339a687be233edd2ece07f5e5f2d0f859aa930d0fa9dcc0ddb6386b54e4c31e"},"schema_version":"1.0","source":{"id":"1607.07051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07051","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07051v1","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07051","created_at":"2026-05-18T01:10:35Z"},{"alias_kind":"pith_short_12","alias_value":"NXNAPPQAAYJJ","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NXNAPPQAAYJJ74GT","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NXNAPPQA","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:b2812439f6f27ce3c9274a313ca84d8eb3e8c37618715b7b3e0cddfa2ea6c7f4","target":"graph","created_at":"2026-05-18T01:10:35Z","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 prove the existence of stationary turbulent flows with arbitrary positive vortex circulation on non simply connected domains. Our construction yields solutions for all real values of the inverse temperature with the exception of a quantized set, for which blow-up phenomena may occur. Our results complete the analysis initiated in [J. Diff. Equ. 260 (2016), 339-369].","authors_text":"Francesca De Marchis, Tonia Ricciardi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-24T14:57:44Z","title":"Existence of stationary turbulent flows with variable positive vortex intensity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07051","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:f45af24000ed24dbf485b79d317fbbbfb34a41d5a9d19025fffa9c2f44be1b66","target":"record","created_at":"2026-05-18T01:10:35Z","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":"009ab876821245ae23645f81ef9db3e869fec43989ed93f4be42225efe13fc52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-24T14:57:44Z","title_canon_sha256":"d339a687be233edd2ece07f5e5f2d0f859aa930d0fa9dcc0ddb6386b54e4c31e"},"schema_version":"1.0","source":{"id":"1607.07051","kind":"arxiv","version":1}},"canonical_sha256":"6dda07be0006129ff0d38139272db40a99324ee9d53128b32e361a25a4c3bc1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dda07be0006129ff0d38139272db40a99324ee9d53128b32e361a25a4c3bc1c","first_computed_at":"2026-05-18T01:10:35.031281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:35.031281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/L4whNoTUpvwD8Rmu4Lg5xNrzlP8nobhbziUqsalCcjR398fV6k5q+f2ZfUBJiMhbc0w++nHUl1KEpYY7waCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:35.031925Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f45af24000ed24dbf485b79d317fbbbfb34a41d5a9d19025fffa9c2f44be1b66","sha256:b2812439f6f27ce3c9274a313ca84d8eb3e8c37618715b7b3e0cddfa2ea6c7f4"],"state_sha256":"821e43c8f2f9a48e3cb82d8266eff41192755e1aa65e1a40796b2ff1adeeab2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4Qry1BbcQcn77FoXbIkcvJkuoVB1MKl58YklVIfx/iGKU3GmD8cFvOpvIg4skcVb49O5qKWAiSoKgkWxg4GDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T21:31:52.802295Z","bundle_sha256":"0623f308f2a1206f61067bc6aae1d270552679e3c09eb61ffbf08a86dde0ab3a"}}