{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:IP4S7TG4XZAL5H7KBQ32MN5HEP","short_pith_number":"pith:IP4S7TG4","canonical_record":{"source":{"id":"2304.01527","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-04T04:37:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c0edb0f644dbdfe4b78cc9c6ebf1fb0cb64ccdeeace2eaaddd5640efe3107692","abstract_canon_sha256":"7f77e235936719d6fefedf72451d0e6a57916f27ddf21e716a78b6890a5b68af"},"schema_version":"1.0"},"canonical_sha256":"43f92fccdcbe40be9fea0c37a637a723ed2c3e2fcaaad8025161b57d7bdc9a28","source":{"kind":"arxiv","id":"2304.01527","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.01527","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"arxiv_version","alias_value":"2304.01527v2","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.01527","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"pith_short_12","alias_value":"IP4S7TG4XZAL","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"pith_short_16","alias_value":"IP4S7TG4XZAL5H7K","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"pith_short_8","alias_value":"IP4S7TG4","created_at":"2026-07-05T08:47:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:IP4S7TG4XZAL5H7KBQ32MN5HEP","target":"record","payload":{"canonical_record":{"source":{"id":"2304.01527","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-04T04:37:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c0edb0f644dbdfe4b78cc9c6ebf1fb0cb64ccdeeace2eaaddd5640efe3107692","abstract_canon_sha256":"7f77e235936719d6fefedf72451d0e6a57916f27ddf21e716a78b6890a5b68af"},"schema_version":"1.0"},"canonical_sha256":"43f92fccdcbe40be9fea0c37a637a723ed2c3e2fcaaad8025161b57d7bdc9a28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:47:05.737067Z","signature_b64":"w9KVK96bXPA4+qbpv3uiPG/ACFagyjZeUmkLNdB20FmtjAe0abuhmQgWWqzOBzaikx3y+rPSSjuVauJ/egCHBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43f92fccdcbe40be9fea0c37a637a723ed2c3e2fcaaad8025161b57d7bdc9a28","last_reissued_at":"2026-07-05T08:47:05.736655Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:47:05.736655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.01527","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":"2026-07-05T08:47:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3UEoPGJav0q9mzivFw4FjJdQz2O2+jLWWoAN5k03/rXfK/oOZCleFGokUaiQSZuGNWHhqr7dt+h4D9pM3BnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T10:53:47.085962Z"},"content_sha256":"af750f8567061e7591f231c93233f030802e6684b0c0058085bd0885096d07d2","schema_version":"1.0","event_id":"sha256:af750f8567061e7591f231c93233f030802e6684b0c0058085bd0885096d07d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:IP4S7TG4XZAL5H7KBQ32MN5HEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A micro-scale diffused interface model with Flory-Huggins logarithmic potential in a porous medium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Hari Shankar Mahato, Nitu Lakhmara","submitted_at":"2023-04-04T04:37:54Z","abstract_excerpt":"A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface tension term with the evolutionary Stokes equation at the pore scale. An evolving diffused interface of finite thickness, depending on the scale parameter $\\varepsilon$ separates the fluids. The model is studied in a bounded domain $\\Omega$ with a sufficiently smooth boundary $\\partial \\Omega$ in $\\mathbb{R}^d$ for $ d = 2 $, $3$. At first, we investigate the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.01527","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2304.01527/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":"2026-07-05T08:47:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wsF1cnD+f2ofPDAGhpP1gf/zDNY7MbYviLP3dhHKEv2LXu6z0TFweXBBWKBjF5RvVm3zN2v4ikttSZnsZqcuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T10:53:47.086634Z"},"content_sha256":"69a05463cae91bddb46884e01f96bfa6b3ec19b6d79f1616edc82f16313a6d11","schema_version":"1.0","event_id":"sha256:69a05463cae91bddb46884e01f96bfa6b3ec19b6d79f1616edc82f16313a6d11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IP4S7TG4XZAL5H7KBQ32MN5HEP/bundle.json","state_url":"https://pith.science/pith/IP4S7TG4XZAL5H7KBQ32MN5HEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IP4S7TG4XZAL5H7KBQ32MN5HEP/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":"2026-07-12T10:53:47Z","links":{"resolver":"https://pith.science/pith/IP4S7TG4XZAL5H7KBQ32MN5HEP","bundle":"https://pith.science/pith/IP4S7TG4XZAL5H7KBQ32MN5HEP/bundle.json","state":"https://pith.science/pith/IP4S7TG4XZAL5H7KBQ32MN5HEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IP4S7TG4XZAL5H7KBQ32MN5HEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:IP4S7TG4XZAL5H7KBQ32MN5HEP","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":"7f77e235936719d6fefedf72451d0e6a57916f27ddf21e716a78b6890a5b68af","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-04T04:37:54Z","title_canon_sha256":"c0edb0f644dbdfe4b78cc9c6ebf1fb0cb64ccdeeace2eaaddd5640efe3107692"},"schema_version":"1.0","source":{"id":"2304.01527","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.01527","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"arxiv_version","alias_value":"2304.01527v2","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.01527","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"pith_short_12","alias_value":"IP4S7TG4XZAL","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"pith_short_16","alias_value":"IP4S7TG4XZAL5H7K","created_at":"2026-07-05T08:47:05Z"},{"alias_kind":"pith_short_8","alias_value":"IP4S7TG4","created_at":"2026-07-05T08:47:05Z"}],"graph_snapshots":[{"event_id":"sha256:69a05463cae91bddb46884e01f96bfa6b3ec19b6d79f1616edc82f16313a6d11","target":"graph","created_at":"2026-07-05T08:47:05Z","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/2304.01527/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A diffused interface model describing the evolution of two conterminous incompressible fluids in a porous medium is discussed. The system consists of the Cahn-Hilliard equation with Flory-Huggins logarithmic potential, coupled via surface tension term with the evolutionary Stokes equation at the pore scale. An evolving diffused interface of finite thickness, depending on the scale parameter $\\varepsilon$ separates the fluids. The model is studied in a bounded domain $\\Omega$ with a sufficiently smooth boundary $\\partial \\Omega$ in $\\mathbb{R}^d$ for $ d = 2 $, $3$. At first, we investigate the","authors_text":"Hari Shankar Mahato, Nitu Lakhmara","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-04T04:37:54Z","title":"A micro-scale diffused interface model with Flory-Huggins logarithmic potential in a porous medium"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.01527","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:af750f8567061e7591f231c93233f030802e6684b0c0058085bd0885096d07d2","target":"record","created_at":"2026-07-05T08:47:05Z","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":"7f77e235936719d6fefedf72451d0e6a57916f27ddf21e716a78b6890a5b68af","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2023-04-04T04:37:54Z","title_canon_sha256":"c0edb0f644dbdfe4b78cc9c6ebf1fb0cb64ccdeeace2eaaddd5640efe3107692"},"schema_version":"1.0","source":{"id":"2304.01527","kind":"arxiv","version":2}},"canonical_sha256":"43f92fccdcbe40be9fea0c37a637a723ed2c3e2fcaaad8025161b57d7bdc9a28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43f92fccdcbe40be9fea0c37a637a723ed2c3e2fcaaad8025161b57d7bdc9a28","first_computed_at":"2026-07-05T08:47:05.736655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:47:05.736655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w9KVK96bXPA4+qbpv3uiPG/ACFagyjZeUmkLNdB20FmtjAe0abuhmQgWWqzOBzaikx3y+rPSSjuVauJ/egCHBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:47:05.737067Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.01527","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af750f8567061e7591f231c93233f030802e6684b0c0058085bd0885096d07d2","sha256:69a05463cae91bddb46884e01f96bfa6b3ec19b6d79f1616edc82f16313a6d11"],"state_sha256":"eb510caad31f1cac20dad2329e5419efcc07198176ad484e598e4edd14b25419"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/1upo0vwCXyXnujZJBo8zlpJUrMXKPWFCPquqA8l7VCGFksQlgQv08Cu+0GG7gHPxyv0DHJpnMTegDSk+AWpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T10:53:47.090759Z","bundle_sha256":"c1a126ebc7da8fb8791e86ef1a496ffb12bdc75ccca454c7fff67d069fccd186"}}