{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I2BCIT4MAXGHWM5AJKVRMK5JQE","short_pith_number":"pith:I2BCIT4M","canonical_record":{"source":{"id":"1610.08002","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-25T18:21:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fe6b86255bf14f2917a7faf36eea3b3c98fe058d46781bdb9d9a13253d6c3568","abstract_canon_sha256":"ec524b7742c80cce369e4b5959d180ca398711bb4a8171a5200c780e4a667545"},"schema_version":"1.0"},"canonical_sha256":"4682244f8c05cc7b33a04aab162ba9813cc04e398eda56b235e419ab0a2e4606","source":{"kind":"arxiv","id":"1610.08002","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08002","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08002v2","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08002","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"I2BCIT4MAXGH","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"pith_short_16","alias_value":"I2BCIT4MAXGHWM5A","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"pith_short_8","alias_value":"I2BCIT4M","created_at":"2026-06-04T18:10:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I2BCIT4MAXGHWM5AJKVRMK5JQE","target":"record","payload":{"canonical_record":{"source":{"id":"1610.08002","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-25T18:21:59Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"fe6b86255bf14f2917a7faf36eea3b3c98fe058d46781bdb9d9a13253d6c3568","abstract_canon_sha256":"ec524b7742c80cce369e4b5959d180ca398711bb4a8171a5200c780e4a667545"},"schema_version":"1.0"},"canonical_sha256":"4682244f8c05cc7b33a04aab162ba9813cc04e398eda56b235e419ab0a2e4606","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T18:10:08.438058Z","signature_b64":"9B0qq9NzTGKK5lhidfvxQlzx+ZusSft0ZMH9LKmEFGT1xQcrmeU5CZNDp2b0HcSvKKOAq9agJKI3z6bAs5FiCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4682244f8c05cc7b33a04aab162ba9813cc04e398eda56b235e419ab0a2e4606","last_reissued_at":"2026-06-04T18:10:08.437594Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T18:10:08.437594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.08002","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":"2026-06-04T18:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S3Q9bi7f2oSFr+KD2Pdp6eIf7wnmzHVXyi03gRAmFuocCmxlTnxv7lDSyd/qGaZf2xFnlI0n4UZ4ogKFJ6nGAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:24:15.518612Z"},"content_sha256":"862e31c8c090e47a4ba11acdec80c7afd55fcff47f9c35810a9caa1cff7596b6","schema_version":"1.0","event_id":"sha256:862e31c8c090e47a4ba11acdec80c7afd55fcff47f9c35810a9caa1cff7596b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I2BCIT4MAXGHWM5AJKVRMK5JQE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Andrea Moiola, Ilaria Perugia","submitted_at":"2016-10-25T18:21:59Z","abstract_excerpt":"We introduce a space-time Trefftz discontinuous Galerkin method for the first-order transient acoustic wave equations in arbitrary space dimensions, extending the one dimensional scheme of Kretzschmar et al. (2016, IMA J. Numer. Anal., 36, 1599-1635). Test and trial discrete functions are space-time piecewise polynomial solutions of the wave equations. We prove well-posedness and a priori error bounds in both skeleton-based and mesh-independent norms. The space-time formulation corresponds to an implicit time-stepping scheme, if posed on meshes partitioned in time slabs, or to an explicit sche"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08002","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/1610.08002/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":"2026-06-04T18:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YuxoTemW1iKNP/y22YwwEaCOTYRr85As7JvSjPCAe0nYdFzMThTilOlS2h+Xoy3AMXNdxEaPUU0fY4YjrhEVDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:24:15.518984Z"},"content_sha256":"daceef15675daeb289c0db214e3737c98b82eb407e76b6ee81748d0581101d95","schema_version":"1.0","event_id":"sha256:daceef15675daeb289c0db214e3737c98b82eb407e76b6ee81748d0581101d95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2BCIT4MAXGHWM5AJKVRMK5JQE/bundle.json","state_url":"https://pith.science/pith/I2BCIT4MAXGHWM5AJKVRMK5JQE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2BCIT4MAXGHWM5AJKVRMK5JQE/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":"2026-06-29T15:24:15Z","links":{"resolver":"https://pith.science/pith/I2BCIT4MAXGHWM5AJKVRMK5JQE","bundle":"https://pith.science/pith/I2BCIT4MAXGHWM5AJKVRMK5JQE/bundle.json","state":"https://pith.science/pith/I2BCIT4MAXGHWM5AJKVRMK5JQE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2BCIT4MAXGHWM5AJKVRMK5JQE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I2BCIT4MAXGHWM5AJKVRMK5JQE","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":"ec524b7742c80cce369e4b5959d180ca398711bb4a8171a5200c780e4a667545","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-25T18:21:59Z","title_canon_sha256":"fe6b86255bf14f2917a7faf36eea3b3c98fe058d46781bdb9d9a13253d6c3568"},"schema_version":"1.0","source":{"id":"1610.08002","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.08002","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"1610.08002v2","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08002","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"I2BCIT4MAXGH","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"pith_short_16","alias_value":"I2BCIT4MAXGHWM5A","created_at":"2026-06-04T18:10:08Z"},{"alias_kind":"pith_short_8","alias_value":"I2BCIT4M","created_at":"2026-06-04T18:10:08Z"}],"graph_snapshots":[{"event_id":"sha256:daceef15675daeb289c0db214e3737c98b82eb407e76b6ee81748d0581101d95","target":"graph","created_at":"2026-06-04T18:10:08Z","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/1610.08002/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a space-time Trefftz discontinuous Galerkin method for the first-order transient acoustic wave equations in arbitrary space dimensions, extending the one dimensional scheme of Kretzschmar et al. (2016, IMA J. Numer. Anal., 36, 1599-1635). Test and trial discrete functions are space-time piecewise polynomial solutions of the wave equations. We prove well-posedness and a priori error bounds in both skeleton-based and mesh-independent norms. The space-time formulation corresponds to an implicit time-stepping scheme, if posed on meshes partitioned in time slabs, or to an explicit sche","authors_text":"Andrea Moiola, Ilaria Perugia","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-25T18:21:59Z","title":"A space-time Trefftz discontinuous Galerkin method for the acoustic wave equation in first-order formulation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08002","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":"sha256:862e31c8c090e47a4ba11acdec80c7afd55fcff47f9c35810a9caa1cff7596b6","target":"record","created_at":"2026-06-04T18:10:08Z","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":"ec524b7742c80cce369e4b5959d180ca398711bb4a8171a5200c780e4a667545","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-10-25T18:21:59Z","title_canon_sha256":"fe6b86255bf14f2917a7faf36eea3b3c98fe058d46781bdb9d9a13253d6c3568"},"schema_version":"1.0","source":{"id":"1610.08002","kind":"arxiv","version":2}},"canonical_sha256":"4682244f8c05cc7b33a04aab162ba9813cc04e398eda56b235e419ab0a2e4606","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4682244f8c05cc7b33a04aab162ba9813cc04e398eda56b235e419ab0a2e4606","first_computed_at":"2026-06-04T18:10:08.437594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-04T18:10:08.437594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9B0qq9NzTGKK5lhidfvxQlzx+ZusSft0ZMH9LKmEFGT1xQcrmeU5CZNDp2b0HcSvKKOAq9agJKI3z6bAs5FiCw==","signature_status":"signed_v1","signed_at":"2026-06-04T18:10:08.438058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.08002","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:862e31c8c090e47a4ba11acdec80c7afd55fcff47f9c35810a9caa1cff7596b6","sha256:daceef15675daeb289c0db214e3737c98b82eb407e76b6ee81748d0581101d95"],"state_sha256":"22779361ab2a3df6beaf5c5fa92b0bbcb191358a069256adc0ae9e5a53d21fa8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qfT8tqBN6T+ZNn7iml8gBZKxEffohepDD56fXbXWuvsb8LfoDRt88qPl6Zr/PpH+vYQfDV7oODUdcof4rJ4xBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T15:24:15.520903Z","bundle_sha256":"7ccc46ebd2c2f9acce9201953146b78b8a9c252b5933bcab982673841716b573"}}