{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:ACUCZIHIPO2FNBB7MQBJP5MW7O","short_pith_number":"pith:ACUCZIHI","canonical_record":{"source":{"id":"2606.04488","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T06:13:50Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0efd353b1ce66c28296aba7460251a1d00cfba1ad5892959745f24b1aa50be93","abstract_canon_sha256":"469b3fb27df3867500e37c980fce8111af634c26e2bac46ea538889e90cc5345"},"schema_version":"1.0"},"canonical_sha256":"00a82ca0e87bb456843f640297f596fbb68c8d7900dcf0d5943327bc6ad5e6f9","source":{"kind":"arxiv","id":"2606.04488","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04488","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04488v1","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04488","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"pith_short_12","alias_value":"ACUCZIHIPO2F","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"pith_short_16","alias_value":"ACUCZIHIPO2FNBB7","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"pith_short_8","alias_value":"ACUCZIHI","created_at":"2026-06-04T01:09:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:ACUCZIHIPO2FNBB7MQBJP5MW7O","target":"record","payload":{"canonical_record":{"source":{"id":"2606.04488","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T06:13:50Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"0efd353b1ce66c28296aba7460251a1d00cfba1ad5892959745f24b1aa50be93","abstract_canon_sha256":"469b3fb27df3867500e37c980fce8111af634c26e2bac46ea538889e90cc5345"},"schema_version":"1.0"},"canonical_sha256":"00a82ca0e87bb456843f640297f596fbb68c8d7900dcf0d5943327bc6ad5e6f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:09:10.267199Z","signature_b64":"c6iVwtV2HNEM/YN9NCxiaK9+0E2rkqDGbR0mj48Pg0t6SKrt0G7qNlU56tesdW22bK/rDYvnZfVLK5JbcJKoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00a82ca0e87bb456843f640297f596fbb68c8d7900dcf0d5943327bc6ad5e6f9","last_reissued_at":"2026-06-04T01:09:10.266454Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:09:10.266454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.04488","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":"2026-06-04T01:09:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ElQDUZ3geCN1Jn24FmLPSbOjoPDsdiGb3TDEcYjezbRWNT9bbOpGr95wqJmDf5QfyQyEp9zcTApcfvOgbfjYAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:37:55.912128Z"},"content_sha256":"43e42d8fe5909925b711d9f9b8bef623417f3788965a7dda3204eb619f89318d","schema_version":"1.0","event_id":"sha256:43e42d8fe5909925b711d9f9b8bef623417f3788965a7dda3204eb619f89318d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:ACUCZIHIPO2FNBB7MQBJP5MW7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical analysis of the second-order time-dependent saddle point Maxwell system via a parameter-free discontinuous Galerkin method: The first optimal ${\\bf L}^{2}$-norm error estimates","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Achyuta Ranjan Dutta Mohapatra, Bhupen Deka","submitted_at":"2026-06-03T06:13:50Z","abstract_excerpt":"We present a novel parameter-free discontinuous Galerkin (dG) finite element method (FEM) for the time-dependent Maxwell system formulated as a saddle point problem. We establish the stability of the proposed semi-discrete problem and derive optimal error estimates in energy and \\( {\\bf L}^{2} \\) norms for the electric field variable, as well as in \\( L^{2} \\) norm for the potential function. To the best of our knowledge, this work provides the first optimal \\( {\\bf L}^{2} \\)-norm error analysis for the second-order time-dependent saddle point Maxwell equations using any variants of FEMs. Addi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04488","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.04488/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":"2026-06-04T01:09:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"glP+871gqgzi1c6WsQ+rXA93csUfX5zfcgntEtbQm+Ry4SE9Bn8D41ODPn/5M+M4LNLMBQTK/O1uzOeHDaKLBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T18:37:55.912827Z"},"content_sha256":"8c7bed6ac109e6aed25ba2923d9394006f2d78428b3ee897270dbad2085c3782","schema_version":"1.0","event_id":"sha256:8c7bed6ac109e6aed25ba2923d9394006f2d78428b3ee897270dbad2085c3782"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/bundle.json","state_url":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/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":"2026-06-11T18:37:55Z","links":{"resolver":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O","bundle":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/bundle.json","state":"https://pith.science/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ACUCZIHIPO2FNBB7MQBJP5MW7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ACUCZIHIPO2FNBB7MQBJP5MW7O","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":"469b3fb27df3867500e37c980fce8111af634c26e2bac46ea538889e90cc5345","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T06:13:50Z","title_canon_sha256":"0efd353b1ce66c28296aba7460251a1d00cfba1ad5892959745f24b1aa50be93"},"schema_version":"1.0","source":{"id":"2606.04488","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.04488","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"arxiv_version","alias_value":"2606.04488v1","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.04488","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"pith_short_12","alias_value":"ACUCZIHIPO2F","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"pith_short_16","alias_value":"ACUCZIHIPO2FNBB7","created_at":"2026-06-04T01:09:10Z"},{"alias_kind":"pith_short_8","alias_value":"ACUCZIHI","created_at":"2026-06-04T01:09:10Z"}],"graph_snapshots":[{"event_id":"sha256:8c7bed6ac109e6aed25ba2923d9394006f2d78428b3ee897270dbad2085c3782","target":"graph","created_at":"2026-06-04T01:09:10Z","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/2606.04488/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a novel parameter-free discontinuous Galerkin (dG) finite element method (FEM) for the time-dependent Maxwell system formulated as a saddle point problem. We establish the stability of the proposed semi-discrete problem and derive optimal error estimates in energy and \\( {\\bf L}^{2} \\) norms for the electric field variable, as well as in \\( L^{2} \\) norm for the potential function. To the best of our knowledge, this work provides the first optimal \\( {\\bf L}^{2} \\)-norm error analysis for the second-order time-dependent saddle point Maxwell equations using any variants of FEMs. Addi","authors_text":"Achyuta Ranjan Dutta Mohapatra, Bhupen Deka","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T06:13:50Z","title":"Numerical analysis of the second-order time-dependent saddle point Maxwell system via a parameter-free discontinuous Galerkin method: The first optimal ${\\bf L}^{2}$-norm error estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04488","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":"sha256:43e42d8fe5909925b711d9f9b8bef623417f3788965a7dda3204eb619f89318d","target":"record","created_at":"2026-06-04T01:09:10Z","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":"469b3fb27df3867500e37c980fce8111af634c26e2bac46ea538889e90cc5345","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NA","submitted_at":"2026-06-03T06:13:50Z","title_canon_sha256":"0efd353b1ce66c28296aba7460251a1d00cfba1ad5892959745f24b1aa50be93"},"schema_version":"1.0","source":{"id":"2606.04488","kind":"arxiv","version":1}},"canonical_sha256":"00a82ca0e87bb456843f640297f596fbb68c8d7900dcf0d5943327bc6ad5e6f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00a82ca0e87bb456843f640297f596fbb68c8d7900dcf0d5943327bc6ad5e6f9","first_computed_at":"2026-06-04T01:09:10.266454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T01:09:10.266454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c6iVwtV2HNEM/YN9NCxiaK9+0E2rkqDGbR0mj48Pg0t6SKrt0G7qNlU56tesdW22bK/rDYvnZfVLK5JbcJKoBA==","signature_status":"signed_v1","signed_at":"2026-06-04T01:09:10.267199Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.04488","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:43e42d8fe5909925b711d9f9b8bef623417f3788965a7dda3204eb619f89318d","sha256:8c7bed6ac109e6aed25ba2923d9394006f2d78428b3ee897270dbad2085c3782"],"state_sha256":"197539ccffcea1ddda1299da588163d40f1c8eb4132e60603147957122642526"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EnGG1oCkBi1Ti/YjEqavlMxJI8WgeALRuLHPUhbZmt8exXBivlobLRzfSe+jSyxLq0t1xFPIxi/ufkZGipNDAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T18:37:55.918772Z","bundle_sha256":"e11e6ed69796c913d68e194a9d61c78ca8074c0568ef3dcbcbf02163b1d912e0"}}