{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:I4OJJ27ISKPZVCPT6LCXTPBHOS","short_pith_number":"pith:I4OJJ27I","canonical_record":{"source":{"id":"2508.17004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-23T12:22:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9a93e8dd5d0ed79dbdcd318880f2e3dffca8afc9fc3748337cf041091861f874","abstract_canon_sha256":"88be490a747fe20c280e847c3494a256f15a751da738f455fe2c64683d72f2e8"},"schema_version":"1.0"},"canonical_sha256":"471c94ebe8929f9a89f3f2c579bc277497fe0ebdcacb64c3d0985a268f3eaaf2","source":{"kind":"arxiv","id":"2508.17004","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17004","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17004v2","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17004","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"I4OJJ27ISKPZ","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"I4OJJ27ISKPZVCPT","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"I4OJJ27I","created_at":"2026-05-29T01:04:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:I4OJJ27ISKPZVCPT6LCXTPBHOS","target":"record","payload":{"canonical_record":{"source":{"id":"2508.17004","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-23T12:22:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"9a93e8dd5d0ed79dbdcd318880f2e3dffca8afc9fc3748337cf041091861f874","abstract_canon_sha256":"88be490a747fe20c280e847c3494a256f15a751da738f455fe2c64683d72f2e8"},"schema_version":"1.0"},"canonical_sha256":"471c94ebe8929f9a89f3f2c579bc277497fe0ebdcacb64c3d0985a268f3eaaf2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:04:55.336200Z","signature_b64":"pgHsoETF0YDpp6sEZUuH9483qjX9IbMyJEmCwwOdOdsHdgSJc13zRVGX24zxACV8nsYh33+lWDyEOTwQsXxPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"471c94ebe8929f9a89f3f2c579bc277497fe0ebdcacb64c3d0985a268f3eaaf2","last_reissued_at":"2026-05-29T01:04:55.335723Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:04:55.335723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.17004","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":"2026-05-29T01:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R6z+dUZDIqH5yZFGj7UKn3Hv2Xm14P1jEYc9x0okK6H0ngWVjX7WRR+3qcwUB2AN/HE54L4qYRVfzND+R63XDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:19:39.716073Z"},"content_sha256":"7e8477f77163a821655151e45c6130464c0c2218e205f90f7a5733535da1f40d","schema_version":"1.0","event_id":"sha256:7e8477f77163a821655151e45c6130464c0c2218e205f90f7a5733535da1f40d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:I4OJJ27ISKPZVCPT6LCXTPBHOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An implicit-explicit BDF-Galerkin scheme of second order for the nonlinear thermistor problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"A. Moradi, R. Altmann","submitted_at":"2025-08-23T12:22:40Z","abstract_excerpt":"This paper proposes and analyzes an implicit-explicit BDF-Galerkin scheme of second order for the time-dependent nonlinear thermistor problem. For this, we combine the second-order backward differentiation formula with special extrapolation terms for time discretization with standard finite elements for spatial discretization. Unconditionally superclose and superconvergent error estimates are established, relying on two key techniques. First, a time-discrete system is introduced to decompose the error function into its temporal and spatial components. Second, superclose error estimates between"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17004","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/2508.17004/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":"2026-05-29T01:04:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dievWQlg2XL0HYKE+FS29stZsuIHVGO+HDLK2Awd7jpkxNmG0juyzwNlK9xRAxUer7P3SC79bfEOHwBLXS7oAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T12:19:39.716459Z"},"content_sha256":"699078fcf87b7382a72cf1d1151015d0522506ae761c434f80a5ab716bb5947f","schema_version":"1.0","event_id":"sha256:699078fcf87b7382a72cf1d1151015d0522506ae761c434f80a5ab716bb5947f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I4OJJ27ISKPZVCPT6LCXTPBHOS/bundle.json","state_url":"https://pith.science/pith/I4OJJ27ISKPZVCPT6LCXTPBHOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I4OJJ27ISKPZVCPT6LCXTPBHOS/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":"2026-06-29T12:19:39Z","links":{"resolver":"https://pith.science/pith/I4OJJ27ISKPZVCPT6LCXTPBHOS","bundle":"https://pith.science/pith/I4OJJ27ISKPZVCPT6LCXTPBHOS/bundle.json","state":"https://pith.science/pith/I4OJJ27ISKPZVCPT6LCXTPBHOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I4OJJ27ISKPZVCPT6LCXTPBHOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:I4OJJ27ISKPZVCPT6LCXTPBHOS","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":"88be490a747fe20c280e847c3494a256f15a751da738f455fe2c64683d72f2e8","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-23T12:22:40Z","title_canon_sha256":"9a93e8dd5d0ed79dbdcd318880f2e3dffca8afc9fc3748337cf041091861f874"},"schema_version":"1.0","source":{"id":"2508.17004","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.17004","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"arxiv_version","alias_value":"2508.17004v2","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.17004","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"pith_short_12","alias_value":"I4OJJ27ISKPZ","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"pith_short_16","alias_value":"I4OJJ27ISKPZVCPT","created_at":"2026-05-29T01:04:55Z"},{"alias_kind":"pith_short_8","alias_value":"I4OJJ27I","created_at":"2026-05-29T01:04:55Z"}],"graph_snapshots":[{"event_id":"sha256:699078fcf87b7382a72cf1d1151015d0522506ae761c434f80a5ab716bb5947f","target":"graph","created_at":"2026-05-29T01:04:55Z","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/2508.17004/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper proposes and analyzes an implicit-explicit BDF-Galerkin scheme of second order for the time-dependent nonlinear thermistor problem. For this, we combine the second-order backward differentiation formula with special extrapolation terms for time discretization with standard finite elements for spatial discretization. Unconditionally superclose and superconvergent error estimates are established, relying on two key techniques. First, a time-discrete system is introduced to decompose the error function into its temporal and spatial components. Second, superclose error estimates between","authors_text":"A. Moradi, R. Altmann","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-23T12:22:40Z","title":"An implicit-explicit BDF-Galerkin scheme of second order for the nonlinear thermistor problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.17004","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":"sha256:7e8477f77163a821655151e45c6130464c0c2218e205f90f7a5733535da1f40d","target":"record","created_at":"2026-05-29T01:04:55Z","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":"88be490a747fe20c280e847c3494a256f15a751da738f455fe2c64683d72f2e8","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-08-23T12:22:40Z","title_canon_sha256":"9a93e8dd5d0ed79dbdcd318880f2e3dffca8afc9fc3748337cf041091861f874"},"schema_version":"1.0","source":{"id":"2508.17004","kind":"arxiv","version":2}},"canonical_sha256":"471c94ebe8929f9a89f3f2c579bc277497fe0ebdcacb64c3d0985a268f3eaaf2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"471c94ebe8929f9a89f3f2c579bc277497fe0ebdcacb64c3d0985a268f3eaaf2","first_computed_at":"2026-05-29T01:04:55.335723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:04:55.335723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pgHsoETF0YDpp6sEZUuH9483qjX9IbMyJEmCwwOdOdsHdgSJc13zRVGX24zxACV8nsYh33+lWDyEOTwQsXxPAQ==","signature_status":"signed_v1","signed_at":"2026-05-29T01:04:55.336200Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.17004","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e8477f77163a821655151e45c6130464c0c2218e205f90f7a5733535da1f40d","sha256:699078fcf87b7382a72cf1d1151015d0522506ae761c434f80a5ab716bb5947f"],"state_sha256":"aea2615590d89c8dcee1e249751604ce7ceb4ab9efd03999b8476d263d2ee12a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BJTu7VqHJFFJ+/Hd4TO51iGPwwlvYjaE9s/srIkxrmQvkMV7fq9/n67g1KXjTxLWwGKD4UfSl0h8Dc/Olr6QDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T12:19:39.718402Z","bundle_sha256":"3b9dcae5b7cdca2d244e3587f7d710e6c6df71724a1ddb0f012952408391c8cb"}}