{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DNO2LED66GWNKCOZ4HPXA4BAAW","short_pith_number":"pith:DNO2LED6","canonical_record":{"source":{"id":"1411.3039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-12T01:33:00Z","cross_cats_sorted":[],"title_canon_sha256":"1c2d64b871427bfee1025c4a82b362effa3ce955d2edcb546de0cd2b715d2d21","abstract_canon_sha256":"f7b7dbbffc695bf81d0a315a64ecd73afbbcfabae083b6c4b590bbeaf15c5e58"},"schema_version":"1.0"},"canonical_sha256":"1b5da5907ef1acd509d9e1df7070200588ea09320c8e23330f28b783bb9b2a7f","source":{"kind":"arxiv","id":"1411.3039","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3039","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3039v1","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3039","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"DNO2LED66GWN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DNO2LED66GWNKCOZ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DNO2LED6","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DNO2LED66GWNKCOZ4HPXA4BAAW","target":"record","payload":{"canonical_record":{"source":{"id":"1411.3039","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-12T01:33:00Z","cross_cats_sorted":[],"title_canon_sha256":"1c2d64b871427bfee1025c4a82b362effa3ce955d2edcb546de0cd2b715d2d21","abstract_canon_sha256":"f7b7dbbffc695bf81d0a315a64ecd73afbbcfabae083b6c4b590bbeaf15c5e58"},"schema_version":"1.0"},"canonical_sha256":"1b5da5907ef1acd509d9e1df7070200588ea09320c8e23330f28b783bb9b2a7f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:51.088268Z","signature_b64":"ggQIub5nHSmT9uI0BlROYoxLrq0IqXR4hbYZ9kQO8OKAUll9+YaVVesrHMecS1gO1y1iDTZSOrPgGdLv9/wbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b5da5907ef1acd509d9e1df7070200588ea09320c8e23330f28b783bb9b2a7f","last_reissued_at":"2026-05-18T02:37:51.087560Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:51.087560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.3039","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":"2026-05-18T02:37:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MVBtyGiUqqw6YGWuMPUEOKrewhTGSMlsu45QTgp7s8ok7oTP++nOF1bfMbjPt9GW8oJqD2JnkevYM/k43b2TCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:04:42.000028Z"},"content_sha256":"d89b774ffc10c92ec7ba39dd72d48199b98cb5e4b1d8b0de62d55685af5025ef","schema_version":"1.0","event_id":"sha256:d89b774ffc10c92ec7ba39dd72d48199b98cb5e4b1d8b0de62d55685af5025ef"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DNO2LED66GWNKCOZ4HPXA4BAAW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Homogenization of the Stefan problem, with application to maple sap exudation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Isabell Graf, John M. Stockie","submitted_at":"2014-11-12T01:33:00Z","abstract_excerpt":"The technique of periodic homogenization with two-scale convergence is applied to the analysis of a two-phase Stefan-type problem that arises in the study of a periodic array of melting ice bars. For this \"reduced model\" we prove results on existence, uniqueness and convergence of the two-scale limit solution in the weak form, which requires solving a macroscale problem for the global temperature field and a reference cell problem at each point in space which captures the underlying phase change process occurring on the microscale. We state a corresponding strong formulation of the limit probl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3039","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":"2026-05-18T02:37:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aRWwFxvQR1E97zUmEjCaVw6TlINKFQUGNyhEm4DUPefdak+rSrkVqUzpaOcWxouNZm+/6ZxQqAppWIWutUmQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:04:42.000392Z"},"content_sha256":"4036e2f931f6b06b6c3059a00e6c88520ce041178128053336729e7c20a83ae9","schema_version":"1.0","event_id":"sha256:4036e2f931f6b06b6c3059a00e6c88520ce041178128053336729e7c20a83ae9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNO2LED66GWNKCOZ4HPXA4BAAW/bundle.json","state_url":"https://pith.science/pith/DNO2LED66GWNKCOZ4HPXA4BAAW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNO2LED66GWNKCOZ4HPXA4BAAW/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":"2026-06-23T20:04:42Z","links":{"resolver":"https://pith.science/pith/DNO2LED66GWNKCOZ4HPXA4BAAW","bundle":"https://pith.science/pith/DNO2LED66GWNKCOZ4HPXA4BAAW/bundle.json","state":"https://pith.science/pith/DNO2LED66GWNKCOZ4HPXA4BAAW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNO2LED66GWNKCOZ4HPXA4BAAW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DNO2LED66GWNKCOZ4HPXA4BAAW","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":"f7b7dbbffc695bf81d0a315a64ecd73afbbcfabae083b6c4b590bbeaf15c5e58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-12T01:33:00Z","title_canon_sha256":"1c2d64b871427bfee1025c4a82b362effa3ce955d2edcb546de0cd2b715d2d21"},"schema_version":"1.0","source":{"id":"1411.3039","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3039","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3039v1","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3039","created_at":"2026-05-18T02:37:51Z"},{"alias_kind":"pith_short_12","alias_value":"DNO2LED66GWN","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DNO2LED66GWNKCOZ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DNO2LED6","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:4036e2f931f6b06b6c3059a00e6c88520ce041178128053336729e7c20a83ae9","target":"graph","created_at":"2026-05-18T02:37:51Z","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":"The technique of periodic homogenization with two-scale convergence is applied to the analysis of a two-phase Stefan-type problem that arises in the study of a periodic array of melting ice bars. For this \"reduced model\" we prove results on existence, uniqueness and convergence of the two-scale limit solution in the weak form, which requires solving a macroscale problem for the global temperature field and a reference cell problem at each point in space which captures the underlying phase change process occurring on the microscale. We state a corresponding strong formulation of the limit probl","authors_text":"Isabell Graf, John M. Stockie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-12T01:33:00Z","title":"Homogenization of the Stefan problem, with application to maple sap exudation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3039","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:d89b774ffc10c92ec7ba39dd72d48199b98cb5e4b1d8b0de62d55685af5025ef","target":"record","created_at":"2026-05-18T02:37:51Z","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":"f7b7dbbffc695bf81d0a315a64ecd73afbbcfabae083b6c4b590bbeaf15c5e58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-12T01:33:00Z","title_canon_sha256":"1c2d64b871427bfee1025c4a82b362effa3ce955d2edcb546de0cd2b715d2d21"},"schema_version":"1.0","source":{"id":"1411.3039","kind":"arxiv","version":1}},"canonical_sha256":"1b5da5907ef1acd509d9e1df7070200588ea09320c8e23330f28b783bb9b2a7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b5da5907ef1acd509d9e1df7070200588ea09320c8e23330f28b783bb9b2a7f","first_computed_at":"2026-05-18T02:37:51.087560Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:51.087560Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ggQIub5nHSmT9uI0BlROYoxLrq0IqXR4hbYZ9kQO8OKAUll9+YaVVesrHMecS1gO1y1iDTZSOrPgGdLv9/wbBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:51.088268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3039","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d89b774ffc10c92ec7ba39dd72d48199b98cb5e4b1d8b0de62d55685af5025ef","sha256:4036e2f931f6b06b6c3059a00e6c88520ce041178128053336729e7c20a83ae9"],"state_sha256":"b4e480e44e03d6a9fe83f19c00106ac222a05f94479bc7a648ec7036ea4d96ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GcA6fP+hZYp0Af0C58Lfw0ZY6tD74wEjDFDJf4Ie6vXMG++txVyhB+PXX4IfKLu5PE0EMgEXsw08fucrBLXXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T20:04:42.002296Z","bundle_sha256":"fe4237e0e74f4dca32941717608d9d03dcd29d7973af4b05777b647a39183036"}}