{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4L2ZA2ADUJ7JA22UWWAXPTYDD6","short_pith_number":"pith:4L2ZA2AD","canonical_record":{"source":{"id":"1307.1410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-04T17:00:07Z","cross_cats_sorted":[],"title_canon_sha256":"6fbac8206c1e233c7140eb01dd10f248e5ba361461b0a0aa638783d193101f34","abstract_canon_sha256":"88c05a3b5f4969a8de127697ee480df8d4ff608f2768dd08b0e08e6cd8fdf21c"},"schema_version":"1.0"},"canonical_sha256":"e2f5906803a27e906b54b58177cf031fbe2d633cbb3576e2d12b3aef7fc66538","source":{"kind":"arxiv","id":"1307.1410","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1410","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1410v1","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1410","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"pith_short_12","alias_value":"4L2ZA2ADUJ7J","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4L2ZA2ADUJ7JA22U","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4L2ZA2AD","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4L2ZA2ADUJ7JA22UWWAXPTYDD6","target":"record","payload":{"canonical_record":{"source":{"id":"1307.1410","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-04T17:00:07Z","cross_cats_sorted":[],"title_canon_sha256":"6fbac8206c1e233c7140eb01dd10f248e5ba361461b0a0aa638783d193101f34","abstract_canon_sha256":"88c05a3b5f4969a8de127697ee480df8d4ff608f2768dd08b0e08e6cd8fdf21c"},"schema_version":"1.0"},"canonical_sha256":"e2f5906803a27e906b54b58177cf031fbe2d633cbb3576e2d12b3aef7fc66538","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:13.774477Z","signature_b64":"ZOWSqB3Tv+9xcWbuWiQyKXaD0pB9pZtj9QRiDJyVPfSOAUpAZMNzNcIMy0ZSDPm+SvPdRi6KvuaVP0gZuu8hAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2f5906803a27e906b54b58177cf031fbe2d633cbb3576e2d12b3aef7fc66538","last_reissued_at":"2026-05-18T03:19:13.773758Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:13.773758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.1410","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":"2026-05-18T03:19:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hJKNQUejW4VxPZJTZXEYvBC2t+RVgu4LUPQkqd0p+4eisgizzH96oJb3SnCoN6JY8qj4z3C5JEjlArsvMPeuBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:42:42.046515Z"},"content_sha256":"d6210bb9d95bdd9ff139f397dfa79ee1c093d729c537493d96df55860adbb261","schema_version":"1.0","event_id":"sha256:d6210bb9d95bdd9ff139f397dfa79ee1c093d729c537493d96df55860adbb261"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4L2ZA2ADUJ7JA22UWWAXPTYDD6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A nonlocal two phase Stefan problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emmanuel Chasseigne (LMPT, FRDP), Silvia Sastre-Gomez","submitted_at":"2013-07-04T17:00:07Z","abstract_excerpt":"We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for sign-changing solutions of the equation, ut = J * v - v, v = {\\Gamma}(u), where the monotone graph is given by {\\Gamma}(s) = sign(s)(|s|-1)+ . We give general results of existence, uniqueness and comparison, in the spirit of [2]. Then we focus on the study of the asymptotic behaviour for sign-changing solutions, which present challenging difficulties due to the non-mo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1410","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":"2026-05-18T03:19:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pvzwAnQpWvYOj9ITQV+7sREnwSzRXZVS45FignZPSCShAJeM0L38n1Y0vsE9E5yiGseylD2QauB5GPS0sGHBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T21:42:42.046860Z"},"content_sha256":"5e0fd51aa292c959e0cc74eaecb482d7123234ded1ac25a8b468b0733ff658af","schema_version":"1.0","event_id":"sha256:5e0fd51aa292c959e0cc74eaecb482d7123234ded1ac25a8b468b0733ff658af"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4L2ZA2ADUJ7JA22UWWAXPTYDD6/bundle.json","state_url":"https://pith.science/pith/4L2ZA2ADUJ7JA22UWWAXPTYDD6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4L2ZA2ADUJ7JA22UWWAXPTYDD6/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":"2026-06-04T21:42:42Z","links":{"resolver":"https://pith.science/pith/4L2ZA2ADUJ7JA22UWWAXPTYDD6","bundle":"https://pith.science/pith/4L2ZA2ADUJ7JA22UWWAXPTYDD6/bundle.json","state":"https://pith.science/pith/4L2ZA2ADUJ7JA22UWWAXPTYDD6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4L2ZA2ADUJ7JA22UWWAXPTYDD6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4L2ZA2ADUJ7JA22UWWAXPTYDD6","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":"88c05a3b5f4969a8de127697ee480df8d4ff608f2768dd08b0e08e6cd8fdf21c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-04T17:00:07Z","title_canon_sha256":"6fbac8206c1e233c7140eb01dd10f248e5ba361461b0a0aa638783d193101f34"},"schema_version":"1.0","source":{"id":"1307.1410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.1410","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"arxiv_version","alias_value":"1307.1410v1","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.1410","created_at":"2026-05-18T03:19:13Z"},{"alias_kind":"pith_short_12","alias_value":"4L2ZA2ADUJ7J","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4L2ZA2ADUJ7JA22U","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4L2ZA2AD","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:5e0fd51aa292c959e0cc74eaecb482d7123234ded1ac25a8b468b0733ff658af","target":"graph","created_at":"2026-05-18T03:19:13Z","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":"We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for sign-changing solutions of the equation, ut = J * v - v, v = {\\Gamma}(u), where the monotone graph is given by {\\Gamma}(s) = sign(s)(|s|-1)+ . We give general results of existence, uniqueness and comparison, in the spirit of [2]. Then we focus on the study of the asymptotic behaviour for sign-changing solutions, which present challenging difficulties due to the non-mo","authors_text":"Emmanuel Chasseigne (LMPT, FRDP), Silvia Sastre-Gomez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-04T17:00:07Z","title":"A nonlocal two phase Stefan problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.1410","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:d6210bb9d95bdd9ff139f397dfa79ee1c093d729c537493d96df55860adbb261","target":"record","created_at":"2026-05-18T03:19:13Z","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":"88c05a3b5f4969a8de127697ee480df8d4ff608f2768dd08b0e08e6cd8fdf21c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-07-04T17:00:07Z","title_canon_sha256":"6fbac8206c1e233c7140eb01dd10f248e5ba361461b0a0aa638783d193101f34"},"schema_version":"1.0","source":{"id":"1307.1410","kind":"arxiv","version":1}},"canonical_sha256":"e2f5906803a27e906b54b58177cf031fbe2d633cbb3576e2d12b3aef7fc66538","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2f5906803a27e906b54b58177cf031fbe2d633cbb3576e2d12b3aef7fc66538","first_computed_at":"2026-05-18T03:19:13.773758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:13.773758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZOWSqB3Tv+9xcWbuWiQyKXaD0pB9pZtj9QRiDJyVPfSOAUpAZMNzNcIMy0ZSDPm+SvPdRi6KvuaVP0gZuu8hAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:13.774477Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.1410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6210bb9d95bdd9ff139f397dfa79ee1c093d729c537493d96df55860adbb261","sha256:5e0fd51aa292c959e0cc74eaecb482d7123234ded1ac25a8b468b0733ff658af"],"state_sha256":"39748ad354247212f190ec47c034215118e106929866e2bc11b16d3b5874c8dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t7FTaxedINkdOymVzqdquAd79dE09q/NDhm/vJ7F4Qqy+8xTSgm6IYtnkJWHCkbAGTtiQmMZzTizIBjVksctBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T21:42:42.048822Z","bundle_sha256":"9d770ecf4d4afcfcf0384e268f19fbd32197f5e9b1d8293c61d147d3f5a5c681"}}