{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:KM34AC3H6JBUSG2TQWIOVTJUPN","short_pith_number":"pith:KM34AC3H","canonical_record":{"source":{"id":"1602.08649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-27T23:33:03Z","cross_cats_sorted":["math.MP","math.NA"],"title_canon_sha256":"75b4ff0c89c16fba7f10500f1921294ae10c29b9f528f7452b077bcfec0245bd","abstract_canon_sha256":"6fa111aee610c86d4373f5fc5f03a7aa2ba0a1246b288f5e437ffb3ad11ed913"},"schema_version":"1.0"},"canonical_sha256":"5337c00b67f243491b538590eacd347b4bef85abf7724179b8814fbc3584691c","source":{"kind":"arxiv","id":"1602.08649","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08649","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08649v2","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08649","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"KM34AC3H6JBU","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KM34AC3H6JBUSG2T","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KM34AC3H","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:KM34AC3H6JBUSG2TQWIOVTJUPN","target":"record","payload":{"canonical_record":{"source":{"id":"1602.08649","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-27T23:33:03Z","cross_cats_sorted":["math.MP","math.NA"],"title_canon_sha256":"75b4ff0c89c16fba7f10500f1921294ae10c29b9f528f7452b077bcfec0245bd","abstract_canon_sha256":"6fa111aee610c86d4373f5fc5f03a7aa2ba0a1246b288f5e437ffb3ad11ed913"},"schema_version":"1.0"},"canonical_sha256":"5337c00b67f243491b538590eacd347b4bef85abf7724179b8814fbc3584691c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:01.547838Z","signature_b64":"6BpNn/3IAx/zdmkAi799MXYsmVLAIcu9+t5dnzTIl3dUlyIQHnNXakroSadDJZ2P7/P/ziKnz9Xo8l7HtyWKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5337c00b67f243491b538590eacd347b4bef85abf7724179b8814fbc3584691c","last_reissued_at":"2026-05-18T00:44:01.547170Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:01.547170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.08649","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":"2026-05-18T00:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rKIZfkku6oXIP/fSlhnFmcx/FgoT8/2aU4ehoKoA8/WlvwDhdDRW3tCQOutHNr0y1hgL/DDW8QjRR36P9linDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:01:09.434346Z"},"content_sha256":"8b2b26258a3e9aea8da66846ff20a3a4ce5da0c7e7009da25d203020c91de35d","schema_version":"1.0","event_id":"sha256:8b2b26258a3e9aea8da66846ff20a3a4ce5da0c7e7009da25d203020c91de35d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:KM34AC3H6JBUSG2TQWIOVTJUPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiphase Allen-Cahn and Cahn-Hilliard Models and Their Discretizations with the Effect of Pairwise Surface Tensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Jinchao Xu, Shuonan Wu","submitted_at":"2016-02-27T23:33:03Z","abstract_excerpt":"In this paper, the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an $N$-component mixture are studied. For the general choice of phase variables, the unisolvent property of the coefficient matrix involved in the $N$-phase models based on the pairwise surface tensions is established. Moreover, the symmetric positive-definite property of the coefficient matrix on an $(N-1)$-dimensional hyperplane --- which is of fundamental importance to the well-posedness of the models --- can be proved equivalent to some physical condition for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08649","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":""},"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":"2026-05-18T00:44:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C9HvYFOaaFOYi/fg3nxXK8gu99WQKMHZlbR7KylZlS5Nro+Pte+TUktyHO72JJ7EXCyehFHCBwMcE/NoPM3gDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T14:01:09.434697Z"},"content_sha256":"9990b5f9267d4d8adddec1e8d951c8953bb0b1a9de032ca8b6a29b7460676e11","schema_version":"1.0","event_id":"sha256:9990b5f9267d4d8adddec1e8d951c8953bb0b1a9de032ca8b6a29b7460676e11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KM34AC3H6JBUSG2TQWIOVTJUPN/bundle.json","state_url":"https://pith.science/pith/KM34AC3H6JBUSG2TQWIOVTJUPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KM34AC3H6JBUSG2TQWIOVTJUPN/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":"2026-06-27T14:01:09Z","links":{"resolver":"https://pith.science/pith/KM34AC3H6JBUSG2TQWIOVTJUPN","bundle":"https://pith.science/pith/KM34AC3H6JBUSG2TQWIOVTJUPN/bundle.json","state":"https://pith.science/pith/KM34AC3H6JBUSG2TQWIOVTJUPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KM34AC3H6JBUSG2TQWIOVTJUPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KM34AC3H6JBUSG2TQWIOVTJUPN","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":"6fa111aee610c86d4373f5fc5f03a7aa2ba0a1246b288f5e437ffb3ad11ed913","cross_cats_sorted":["math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-27T23:33:03Z","title_canon_sha256":"75b4ff0c89c16fba7f10500f1921294ae10c29b9f528f7452b077bcfec0245bd"},"schema_version":"1.0","source":{"id":"1602.08649","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08649","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08649v2","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08649","created_at":"2026-05-18T00:44:01Z"},{"alias_kind":"pith_short_12","alias_value":"KM34AC3H6JBU","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"KM34AC3H6JBUSG2T","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"KM34AC3H","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:9990b5f9267d4d8adddec1e8d951c8953bb0b1a9de032ca8b6a29b7460676e11","target":"graph","created_at":"2026-05-18T00:44:01Z","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":"In this paper, the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an $N$-component mixture are studied. For the general choice of phase variables, the unisolvent property of the coefficient matrix involved in the $N$-phase models based on the pairwise surface tensions is established. Moreover, the symmetric positive-definite property of the coefficient matrix on an $(N-1)$-dimensional hyperplane --- which is of fundamental importance to the well-posedness of the models --- can be proved equivalent to some physical condition for ","authors_text":"Jinchao Xu, Shuonan Wu","cross_cats":["math.MP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-27T23:33:03Z","title":"Multiphase Allen-Cahn and Cahn-Hilliard Models and Their Discretizations with the Effect of Pairwise Surface Tensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08649","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":"sha256:8b2b26258a3e9aea8da66846ff20a3a4ce5da0c7e7009da25d203020c91de35d","target":"record","created_at":"2026-05-18T00:44:01Z","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":"6fa111aee610c86d4373f5fc5f03a7aa2ba0a1246b288f5e437ffb3ad11ed913","cross_cats_sorted":["math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-02-27T23:33:03Z","title_canon_sha256":"75b4ff0c89c16fba7f10500f1921294ae10c29b9f528f7452b077bcfec0245bd"},"schema_version":"1.0","source":{"id":"1602.08649","kind":"arxiv","version":2}},"canonical_sha256":"5337c00b67f243491b538590eacd347b4bef85abf7724179b8814fbc3584691c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5337c00b67f243491b538590eacd347b4bef85abf7724179b8814fbc3584691c","first_computed_at":"2026-05-18T00:44:01.547170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:01.547170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6BpNn/3IAx/zdmkAi799MXYsmVLAIcu9+t5dnzTIl3dUlyIQHnNXakroSadDJZ2P7/P/ziKnz9Xo8l7HtyWKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:01.547838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08649","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b2b26258a3e9aea8da66846ff20a3a4ce5da0c7e7009da25d203020c91de35d","sha256:9990b5f9267d4d8adddec1e8d951c8953bb0b1a9de032ca8b6a29b7460676e11"],"state_sha256":"0c5987710d316fe0a9f44d29426f59854e85ce5e19d4f35ed1c0ba8ec6978f10"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+q1u+Zc/TrlVSi8Fbdi74glB80QGM7myDOcnBgrv3j4M/oPF4kSgLzu2acgbA2IkXrsIjU0qeETRLAZJuubwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T14:01:09.436666Z","bundle_sha256":"e337ea8c2532e3ea561d4fc62312b8654051896a3bdf238fd292d045bb8a3f9c"}}