{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:XL3Q6CMXEPM6ZOGFMW46DNTR7J","short_pith_number":"pith:XL3Q6CMX","canonical_record":{"source":{"id":"1305.6920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-29T19:56:02Z","cross_cats_sorted":[],"title_canon_sha256":"86be93d7be30aecf69733e69fb2e4f8c6cdef65c90fc66b10c3a290d02d55b30","abstract_canon_sha256":"67e9eb9185e663da66799ca0cc1cd41ebc2259a422896010947c7884bf80e638"},"schema_version":"1.0"},"canonical_sha256":"baf70f099723d9ecb8c565b9e1b671fa70ef5d1270dad6cb871cf6d2632a7962","source":{"kind":"arxiv","id":"1305.6920","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6920","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6920v1","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6920","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"XL3Q6CMXEPM6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XL3Q6CMXEPM6ZOGF","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XL3Q6CMX","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:XL3Q6CMXEPM6ZOGFMW46DNTR7J","target":"record","payload":{"canonical_record":{"source":{"id":"1305.6920","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-29T19:56:02Z","cross_cats_sorted":[],"title_canon_sha256":"86be93d7be30aecf69733e69fb2e4f8c6cdef65c90fc66b10c3a290d02d55b30","abstract_canon_sha256":"67e9eb9185e663da66799ca0cc1cd41ebc2259a422896010947c7884bf80e638"},"schema_version":"1.0"},"canonical_sha256":"baf70f099723d9ecb8c565b9e1b671fa70ef5d1270dad6cb871cf6d2632a7962","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.467215Z","signature_b64":"SkByI3be5iY9MjbNXzW7YqOr1V9QOWngnRNbnGzlgMAvY4Bx7EKNTufTSEb+I97zJH7KRZMuO6ti0TDTGDvdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"baf70f099723d9ecb8c565b9e1b671fa70ef5d1270dad6cb871cf6d2632a7962","last_reissued_at":"2026-05-17T23:53:17.466452Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.466452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.6920","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":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9u+MbdIXfePMPYtaHEAr/fQfHfnRgmaO4+Kk6adh7ZW+RMoM04wyBg2mwbEFCvISrxN4cfV//Scwda3nUjHcCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:57:33.659783Z"},"content_sha256":"bd3b884d61655370ad755a687f41660d84bb6f16bcf5445c39e51d80a9a66424","schema_version":"1.0","event_id":"sha256:bd3b884d61655370ad755a687f41660d84bb6f16bcf5445c39e51d80a9a66424"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:XL3Q6CMXEPM6ZOGFMW46DNTR7J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivation of a homogenized two-temperature model from the heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fran\\c{c}ois Golse, Laurent Desvillettes, Valeria Ricci","submitted_at":"2013-05-29T19:56:02Z","abstract_excerpt":"This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat: Coll\\`ege de France Seminar vol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138. Pit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6920","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":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V0S2+PdCzISFDkRN1EUmj0lUlB7ylwGnPETEs8JXfq2yg/9SRg1b/aDD0MdaClM3tZ1QUWgYt7Tz/B5G+oX6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:57:33.660498Z"},"content_sha256":"69cf55877f09a4719c39083eaf7a1dd6fb8ec40a80fcdf0faf5e04f8e6039d1e","schema_version":"1.0","event_id":"sha256:69cf55877f09a4719c39083eaf7a1dd6fb8ec40a80fcdf0faf5e04f8e6039d1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XL3Q6CMXEPM6ZOGFMW46DNTR7J/bundle.json","state_url":"https://pith.science/pith/XL3Q6CMXEPM6ZOGFMW46DNTR7J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XL3Q6CMXEPM6ZOGFMW46DNTR7J/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":"2026-05-29T14:57:33Z","links":{"resolver":"https://pith.science/pith/XL3Q6CMXEPM6ZOGFMW46DNTR7J","bundle":"https://pith.science/pith/XL3Q6CMXEPM6ZOGFMW46DNTR7J/bundle.json","state":"https://pith.science/pith/XL3Q6CMXEPM6ZOGFMW46DNTR7J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XL3Q6CMXEPM6ZOGFMW46DNTR7J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XL3Q6CMXEPM6ZOGFMW46DNTR7J","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":"67e9eb9185e663da66799ca0cc1cd41ebc2259a422896010947c7884bf80e638","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-29T19:56:02Z","title_canon_sha256":"86be93d7be30aecf69733e69fb2e4f8c6cdef65c90fc66b10c3a290d02d55b30"},"schema_version":"1.0","source":{"id":"1305.6920","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6920","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6920v1","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6920","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"XL3Q6CMXEPM6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XL3Q6CMXEPM6ZOGF","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XL3Q6CMX","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:69cf55877f09a4719c39083eaf7a1dd6fb8ec40a80fcdf0faf5e04f8e6039d1e","target":"graph","created_at":"2026-05-17T23:53:17Z","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":"This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat: Coll\\`ege de France Seminar vol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138. Pit","authors_text":"Fran\\c{c}ois Golse, Laurent Desvillettes, Valeria Ricci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-29T19:56:02Z","title":"Derivation of a homogenized two-temperature model from the heat equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6920","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:bd3b884d61655370ad755a687f41660d84bb6f16bcf5445c39e51d80a9a66424","target":"record","created_at":"2026-05-17T23:53:17Z","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":"67e9eb9185e663da66799ca0cc1cd41ebc2259a422896010947c7884bf80e638","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-29T19:56:02Z","title_canon_sha256":"86be93d7be30aecf69733e69fb2e4f8c6cdef65c90fc66b10c3a290d02d55b30"},"schema_version":"1.0","source":{"id":"1305.6920","kind":"arxiv","version":1}},"canonical_sha256":"baf70f099723d9ecb8c565b9e1b671fa70ef5d1270dad6cb871cf6d2632a7962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"baf70f099723d9ecb8c565b9e1b671fa70ef5d1270dad6cb871cf6d2632a7962","first_computed_at":"2026-05-17T23:53:17.466452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:17.466452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SkByI3be5iY9MjbNXzW7YqOr1V9QOWngnRNbnGzlgMAvY4Bx7EKNTufTSEb+I97zJH7KRZMuO6ti0TDTGDvdDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:17.467215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6920","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd3b884d61655370ad755a687f41660d84bb6f16bcf5445c39e51d80a9a66424","sha256:69cf55877f09a4719c39083eaf7a1dd6fb8ec40a80fcdf0faf5e04f8e6039d1e"],"state_sha256":"31e6cc018a175920704750b1c12b883bfb48275a63a14e35f71656b9a3b37541"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MLWnpe2ZiAUCLX3dVhHn/tWSSZIUNEx0xbaKTXgWmmE88fL3EHLzyTEh29hctsSxpDvIalIIvrnAzl5ZeXJTCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:57:33.664052Z","bundle_sha256":"a94a382542fe69913e43aad2a80b7033d76c9ab5fc85568e61a475f8c41b1498"}}