{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:AW3AP6VKUB2GSDOEL7EL6ASIXR","short_pith_number":"pith:AW3AP6VK","canonical_record":{"source":{"id":"2607.11036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T03:00:52Z","cross_cats_sorted":[],"title_canon_sha256":"c4531f4f0defea4b3587579373708998b5a637f55f261d8764748d1a061ab98f","abstract_canon_sha256":"25314788cb495c7a262160211d7ac0c1c5150a654a2020627238e1f9e9cffce9"},"schema_version":"1.0"},"canonical_sha256":"05b607faaaa074690dc45fc8bf0248bc45378f7c9b66794e14d6354f320f29f6","source":{"kind":"arxiv","id":"2607.11036","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.11036","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.11036v1","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.11036","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"AW3AP6VKUB2G","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"AW3AP6VKUB2GSDOE","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"AW3AP6VK","created_at":"2026-07-14T01:22:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:AW3AP6VKUB2GSDOEL7EL6ASIXR","target":"record","payload":{"canonical_record":{"source":{"id":"2607.11036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T03:00:52Z","cross_cats_sorted":[],"title_canon_sha256":"c4531f4f0defea4b3587579373708998b5a637f55f261d8764748d1a061ab98f","abstract_canon_sha256":"25314788cb495c7a262160211d7ac0c1c5150a654a2020627238e1f9e9cffce9"},"schema_version":"1.0"},"canonical_sha256":"05b607faaaa074690dc45fc8bf0248bc45378f7c9b66794e14d6354f320f29f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T01:22:12.781201Z","signature_b64":"YYWjasdSTqxXUa2bSWlg4yIaJibdt6HXqZdRphJBAD7GZjd97V6zEeAoIbNFSrCBydSKGnWJU+4G9kBarq2yBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05b607faaaa074690dc45fc8bf0248bc45378f7c9b66794e14d6354f320f29f6","last_reissued_at":"2026-07-14T01:22:12.780382Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T01:22:12.780382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.11036","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":"2026-07-14T01:22:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e40/WtiNuM8uDLCr9N8l1lBfaDChgy5EpMsIBrjA0Lrl0Y7cHSmhYFS3Cf5ns0+EjG3j6OXgkZpWIa9xCHH1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:57:14.103116Z"},"content_sha256":"1936c9761f2f07c9dbc07f3d0cbda8cec7a28c53f6ac80d49922d54c0f490096","schema_version":"1.0","event_id":"sha256:1936c9761f2f07c9dbc07f3d0cbda8cec7a28c53f6ac80d49922d54c0f490096"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:AW3AP6VKUB2GSDOEL7EL6ASIXR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogenization of a non-homogeneous incompressible heat-conducting fluid in perforated domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiaojiao Pan, Luqi Wang, Yong Lu","submitted_at":"2026-07-13T03:00:52Z","abstract_excerpt":"This paper provides the study of the homogenization of the 3D non-homogeneous incompressible heat-conducting fluid in perforated domains with holes of subcritical size, where the viscosity and the heat conductivity coefficient are assumed to depend on the temperature. The diameter of the holes is of order $\\varepsilon^{\\alpha} \\ (\\alpha>3)$, where $\\varepsilon > 0$ is a small parameter that measures the mutual distance between the holes. We prove that as $\\varepsilon\\to 0$, the limit behavior of velocity, density and temperature is governed by the original system in homogeneous domain without "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11036","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/2607.11036/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":"2026-07-14T01:22:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yEzJlkIK8S44AkG6uTWaPGW+37w8+TTOle+FWYmewdtfFOYYxebxHKst08abyEXOrcar80F6x2WV5Wexgc/VCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:57:14.103606Z"},"content_sha256":"63ceeed9290ac0dcb734406c8d2d137890a41c521b5420d9639fbe8f7450cdb0","schema_version":"1.0","event_id":"sha256:63ceeed9290ac0dcb734406c8d2d137890a41c521b5420d9639fbe8f7450cdb0"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:AW3AP6VKUB2GSDOEL7EL6ASIXR","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s00021-015-0200-2) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"E. Feireisl and Y. Lu,Homogenization of stationary Navier-Stokes equations in domains with tiny holes, J. Math. Fluid Mech., 17 (2) (2015), pp. 381–392, https://doi:10.1007/s00021-015- 0200-2","arxiv_id":"2607.11036","detector":"doi_compliance","evidence":{"ref_index":11,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s00021-015-","reconstructed_doi":"10.1007/s00021-015-0200-2"},"severity":"advisory","ref_index":11,"audited_at":"2026-07-29T12:32:51.052394Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s00021-015-0200-2","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"bb6119d557fdf42db90998788cee0fde5538864386629d4f48643de87b4dfeb8","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":13496,"payload_sha256":"94d6943857827e88d7145ea367506ac22b420ca4ce739c3f03da0558c433c0cd","signature_b64":null,"signing_key_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-29T12:36:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7hgnZmbM48PLYzNEcdh6w/aVvTGqR1Yy6aQSI5inB1zjb30z21WtkjggMmKu6Uw8Sea6mvm5Pfa0wJ8811/oCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:57:14.106444Z"},"content_sha256":"939eb5d05b175249ab1c15daa0d58d126013b775e721dcf9462c84f6605ab886","schema_version":"1.0","event_id":"sha256:939eb5d05b175249ab1c15daa0d58d126013b775e721dcf9462c84f6605ab886"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:AW3AP6VKUB2GSDOEL7EL6ASIXR","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s11425-025-2540-2) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"D. Basari´ c, F. Oschmann and J. Pan,Qualitative derivation of a density dependent incom- pressible Darcy law, Sci. China Math., 69 (2026), pp. 1–24, https://doi.org/10.1007/s11425- 025-2540-2","arxiv_id":"2607.11036","detector":"doi_compliance","evidence":{"ref_index":4,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s11425-","reconstructed_doi":"10.1007/s11425-025-2540-2"},"severity":"advisory","ref_index":4,"audited_at":"2026-07-29T12:32:51.052394Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s11425-025-2540-2","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"fbce5178e18e32d90fb9532facacaa008e64375ee742716dba9249e8afd811da","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":13495,"payload_sha256":"4605d9b1a6dfba48e358c374231fc261fa0fdb86a246caca2f8ddd59d124e7ae","signature_b64":null,"signing_key_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-29T12:36:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/JF15Wf/u5niuj1X2OucyE0tO6s6ozZqMreIaBRwgyGZ32+l9Upx/C0LVCjNY6hM3X4lhxnQTZWQCYQbxG/ZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:57:14.106820Z"},"content_sha256":"d2ba2f29c8c78dd79333539c07e4f1c08888ad0819ab291b39dd4ce59273136a","schema_version":"1.0","event_id":"sha256:d2ba2f29c8c78dd79333539c07e4f1c08888ad0819ab291b39dd4ce59273136a"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:AW3AP6VKUB2GSDOEL7EL6ASIXR","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s00021-022-00745-9.18) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"Y. Lu and P. Yang,Homogenization of Evolutionary Incompressible Navier-Stokes System in Perforated Domains, J. Math. Fluid Mech., 25 (2023), pp. 4–23, https://doi:10.1007/s00021- 022-00745-9. 18","arxiv_id":"2607.11036","detector":"doi_compliance","evidence":{"ref_index":28,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"Y. Lu and P. Yang,Homogenization of Evolutionary Incompressible Navier-Stokes System in Perforated Domains, J. Math. Fluid Mech., 25 (2023), pp. 4–23, https://doi:10.1007/s00021- 022-00745-9. 18","reconstructed_doi":"10.1007/s00021-022-00745-9.18"},"severity":"advisory","ref_index":28,"audited_at":"2026-07-14T07:38:16.746550Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s00021-022-00745-9.18","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"53fbc51dfa9e4edfac095879cd3414a0777348cde3932358dc093434ea539edc","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":13173,"payload_sha256":"0a559d65ffa35f744e14a64d2f672b0d3d19b2a11dc5456d30d1f285d9029f1d","signature_b64":"Y00RLEGkzcqJYpM+WRqDIu4n2aF1kXSZz59RgmcLrIJnCeyXaJrTeS4C4zuDRPdddVGEKz76IeGNPAZwxBcQBg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-14T07:40:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tIduy3IUzQS7Sm+WwoRwARDPLvVQvMDp08YuGMcVjhIDKa4Mr4nDl485zhFmAdO+CyILJ/PaZ0VkuCdVT4XbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:57:14.107220Z"},"content_sha256":"df9083c7011182c202bf638251f62363c29fbdc8a823cc8c4eb706da2d99ce9a","schema_version":"1.0","event_id":"sha256:df9083c7011182c202bf638251f62363c29fbdc8a823cc8c4eb706da2d99ce9a"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:AW3AP6VKUB2GSDOEL7EL6ASIXR","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s00229-015-0778-y.17) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"E. Feireisl, Y. Namlyeyeva and ˇS. Neˇ casov´ a,Homogenization of the evolutionary Navier-Stokes system, Manuscripta Math., 149 (1–2) (2016), pp. 251–274, https://doi:10.1007/s00229-015- 0778-y. 17","arxiv_id":"2607.11036","detector":"doi_compliance","evidence":{"ref_index":13,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"E. Feireisl, Y. Namlyeyeva and ˇS. Neˇ casov´ a,Homogenization of the evolutionary Navier-Stokes system, Manuscripta Math., 149 (1–2) (2016), pp. 251–274, https://doi:10.1007/s00229-015- 0778-y. 17","reconstructed_doi":"10.1007/s00229-015-0778-y.17"},"severity":"advisory","ref_index":13,"audited_at":"2026-07-14T07:38:16.746550Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s00229-015-0778-y.17","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"27c0bb64978ad190504787f5d30a6fb76e9f3865370f7470f6217afea305cef7","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.0.0","detected_arxiv_id":null,"integrity_event_id":13172,"payload_sha256":"5b5680f750d9cfa023fc203ff5d2e26cc1228d35acbdeb2f60522cb4ac76fcb2","signature_b64":"f+jkKx6UNlnqCI1PTW3id1r9+rIiU7gc6RdJg4HF8KFT+cVvZgXShVWtYI/7gh0Ez2RvkuT2P1NAG08p9WRRCg==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-14T07:40:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"58GME913fB6hgoYDISm3mVidW5xhhsXJb9K65EjbgEua6r2+6BtBH+xgSxtsS9E/EYSoLhYxGK2OH8TD1izeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:57:14.107584Z"},"content_sha256":"7dc38af383592498b439616cc3d0bd8c22a42039d870b05b92972f85464c93f4","schema_version":"1.0","event_id":"sha256:7dc38af383592498b439616cc3d0bd8c22a42039d870b05b92972f85464c93f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AW3AP6VKUB2GSDOEL7EL6ASIXR/bundle.json","state_url":"https://pith.science/pith/AW3AP6VKUB2GSDOEL7EL6ASIXR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AW3AP6VKUB2GSDOEL7EL6ASIXR/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":"2026-08-04T09:57:14Z","links":{"resolver":"https://pith.science/pith/AW3AP6VKUB2GSDOEL7EL6ASIXR","bundle":"https://pith.science/pith/AW3AP6VKUB2GSDOEL7EL6ASIXR/bundle.json","state":"https://pith.science/pith/AW3AP6VKUB2GSDOEL7EL6ASIXR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AW3AP6VKUB2GSDOEL7EL6ASIXR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AW3AP6VKUB2GSDOEL7EL6ASIXR","merge_version":"pith-open-graph-merge-v1","event_count":6,"valid_event_count":6,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"25314788cb495c7a262160211d7ac0c1c5150a654a2020627238e1f9e9cffce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T03:00:52Z","title_canon_sha256":"c4531f4f0defea4b3587579373708998b5a637f55f261d8764748d1a061ab98f"},"schema_version":"1.0","source":{"id":"2607.11036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.11036","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"2607.11036v1","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.11036","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"AW3AP6VKUB2G","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"AW3AP6VKUB2GSDOE","created_at":"2026-07-14T01:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"AW3AP6VK","created_at":"2026-07-14T01:22:12Z"}],"graph_snapshots":[{"event_id":"sha256:63ceeed9290ac0dcb734406c8d2d137890a41c521b5420d9639fbe8f7450cdb0","target":"graph","created_at":"2026-07-14T01:22:12Z","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/2607.11036/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper provides the study of the homogenization of the 3D non-homogeneous incompressible heat-conducting fluid in perforated domains with holes of subcritical size, where the viscosity and the heat conductivity coefficient are assumed to depend on the temperature. The diameter of the holes is of order $\\varepsilon^{\\alpha} \\ (\\alpha>3)$, where $\\varepsilon > 0$ is a small parameter that measures the mutual distance between the holes. We prove that as $\\varepsilon\\to 0$, the limit behavior of velocity, density and temperature is governed by the original system in homogeneous domain without ","authors_text":"Jiaojiao Pan, Luqi Wang, Yong Lu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T03:00:52Z","title":"Homogenization of a non-homogeneous incompressible heat-conducting fluid in perforated domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11036","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":"sha256:1936c9761f2f07c9dbc07f3d0cbda8cec7a28c53f6ac80d49922d54c0f490096","target":"record","created_at":"2026-07-14T01:22:12Z","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":"25314788cb495c7a262160211d7ac0c1c5150a654a2020627238e1f9e9cffce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T03:00:52Z","title_canon_sha256":"c4531f4f0defea4b3587579373708998b5a637f55f261d8764748d1a061ab98f"},"schema_version":"1.0","source":{"id":"2607.11036","kind":"arxiv","version":1}},"canonical_sha256":"05b607faaaa074690dc45fc8bf0248bc45378f7c9b66794e14d6354f320f29f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05b607faaaa074690dc45fc8bf0248bc45378f7c9b66794e14d6354f320f29f6","first_computed_at":"2026-07-14T01:22:12.780382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:22:12.780382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YYWjasdSTqxXUa2bSWlg4yIaJibdt6HXqZdRphJBAD7GZjd97V6zEeAoIbNFSrCBydSKGnWJU+4G9kBarq2yBQ==","signature_status":"signed_v1","signed_at":"2026-07-14T01:22:12.781201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.11036","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:7dc38af383592498b439616cc3d0bd8c22a42039d870b05b92972f85464c93f4","sha256:939eb5d05b175249ab1c15daa0d58d126013b775e721dcf9462c84f6605ab886","sha256:d2ba2f29c8c78dd79333539c07e4f1c08888ad0819ab291b39dd4ce59273136a","sha256:df9083c7011182c202bf638251f62363c29fbdc8a823cc8c4eb706da2d99ce9a"]}],"invalid_events":[],"applied_event_ids":["sha256:1936c9761f2f07c9dbc07f3d0cbda8cec7a28c53f6ac80d49922d54c0f490096","sha256:63ceeed9290ac0dcb734406c8d2d137890a41c521b5420d9639fbe8f7450cdb0"],"state_sha256":"d0af8900dcfadcd91aa1328aee5612b6f1ac866403d1c4417752408f0bf132d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nOVg9yLV0VQetSp46rUVJU20TNn99n0KftvlHVbkQ9lHkREk2pdrTCullDsvCfM19NV9CbBmAT9peW49KMg+Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:57:14.110890Z","bundle_sha256":"0493e87645175fbb82417bd6c1649bd81df9e5d721c97b10ac2d4d81715d2beb"}}