{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:2GU67FHGPVPIEZRKRAPJP5736L","short_pith_number":"pith:2GU67FHG","canonical_record":{"source":{"id":"2601.02540","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-05T20:26:56Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8b980bf8523014fcba4b8b7d8cf858673a33e0c8af1ab7fc2143ee478d4dc59b","abstract_canon_sha256":"23859f5ff0c0da9404c91bf41447beed4043f07f46e0470318e5fb676ef12802"},"schema_version":"1.0"},"canonical_sha256":"d1a9ef94e67d5e82662a881e97f7fbf2de68be8c5a118595696c2780c85295e2","source":{"kind":"arxiv","id":"2601.02540","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.02540","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"2601.02540v2","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.02540","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"2GU67FHGPVPI","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"pith_short_16","alias_value":"2GU67FHGPVPIEZRK","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"pith_short_8","alias_value":"2GU67FHG","created_at":"2026-05-27T02:05:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:2GU67FHGPVPIEZRKRAPJP5736L","target":"record","payload":{"canonical_record":{"source":{"id":"2601.02540","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-05T20:26:56Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"8b980bf8523014fcba4b8b7d8cf858673a33e0c8af1ab7fc2143ee478d4dc59b","abstract_canon_sha256":"23859f5ff0c0da9404c91bf41447beed4043f07f46e0470318e5fb676ef12802"},"schema_version":"1.0"},"canonical_sha256":"d1a9ef94e67d5e82662a881e97f7fbf2de68be8c5a118595696c2780c85295e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T02:05:10.117448Z","signature_b64":"SLi1qb/9hZPw/7UhmCI7j+Z+9nC9uSc7sLfGZMspL4JZOAN6fr4fpJRaNFWZeQn9zTlTs8RghEz9TOoRMOJhBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1a9ef94e67d5e82662a881e97f7fbf2de68be8c5a118595696c2780c85295e2","last_reissued_at":"2026-05-27T02:05:10.116375Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T02:05:10.116375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.02540","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":"2026-05-27T02:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TxKumtOpeMfMMLG/VgL/1lHE+HX2LrCNCA6HKEukPIAYXaIv3fAmvIUiFUZkwG976phQbDUS8VkBRsAY2IlzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:12:48.197006Z"},"content_sha256":"803022a4c725802e66bead53a8e3d3f886aa0fa09ed89445575337ba06469fcc","schema_version":"1.0","event_id":"sha256:803022a4c725802e66bead53a8e3d3f886aa0fa09ed89445575337ba06469fcc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:2GU67FHGPVPIEZRKRAPJP5736L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Collin Wittenstein, Hendrik Ranocha, Mario Ricchiuto, Vincent Marks","submitted_at":"2026-01-05T20:26:56Z","abstract_excerpt":"We develop energy-conserving numerical methods for a two-dimensional hyperbolic approximation of the Serre-Green-Naghdi equations with variable bathymetry and either periodic or reflecting boundary conditions. The hyperbolic formulation avoids the costly inversion of an elliptic operator present in the classical model. Our schemes combine split forms with summation-by-parts (SBP) operators to construct semi-discretizations that conserve the total water mass and the total energy. We provide analytical proofs of these conservation properties and also verify them numerically. While the framework "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.02540","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/2601.02540/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":"2026-05-27T02:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cvSZuRt4m0fi8FJRVvkp/SwvtMTvmAIn11YntWDNmqW2h0Pl27IwJSgtD9BCR6amL9Wy5b3OjN3FU3rztQnPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:12:48.197388Z"},"content_sha256":"70c0fae820cea39a2afd66efd4a803e9011ab66962dd861d1c60fc3e6f52a050","schema_version":"1.0","event_id":"sha256:70c0fae820cea39a2afd66efd4a803e9011ab66962dd861d1c60fc3e6f52a050"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2GU67FHGPVPIEZRKRAPJP5736L/bundle.json","state_url":"https://pith.science/pith/2GU67FHGPVPIEZRKRAPJP5736L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2GU67FHGPVPIEZRKRAPJP5736L/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":"2026-06-27T12:12:48Z","links":{"resolver":"https://pith.science/pith/2GU67FHGPVPIEZRKRAPJP5736L","bundle":"https://pith.science/pith/2GU67FHGPVPIEZRKRAPJP5736L/bundle.json","state":"https://pith.science/pith/2GU67FHGPVPIEZRKRAPJP5736L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2GU67FHGPVPIEZRKRAPJP5736L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2GU67FHGPVPIEZRKRAPJP5736L","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":"23859f5ff0c0da9404c91bf41447beed4043f07f46e0470318e5fb676ef12802","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-05T20:26:56Z","title_canon_sha256":"8b980bf8523014fcba4b8b7d8cf858673a33e0c8af1ab7fc2143ee478d4dc59b"},"schema_version":"1.0","source":{"id":"2601.02540","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.02540","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"2601.02540v2","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.02540","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"2GU67FHGPVPI","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"pith_short_16","alias_value":"2GU67FHGPVPIEZRK","created_at":"2026-05-27T02:05:10Z"},{"alias_kind":"pith_short_8","alias_value":"2GU67FHG","created_at":"2026-05-27T02:05:10Z"}],"graph_snapshots":[{"event_id":"sha256:70c0fae820cea39a2afd66efd4a803e9011ab66962dd861d1c60fc3e6f52a050","target":"graph","created_at":"2026-05-27T02:05:10Z","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/2601.02540/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop energy-conserving numerical methods for a two-dimensional hyperbolic approximation of the Serre-Green-Naghdi equations with variable bathymetry and either periodic or reflecting boundary conditions. The hyperbolic formulation avoids the costly inversion of an elliptic operator present in the classical model. Our schemes combine split forms with summation-by-parts (SBP) operators to construct semi-discretizations that conserve the total water mass and the total energy. We provide analytical proofs of these conservation properties and also verify them numerically. While the framework ","authors_text":"Collin Wittenstein, Hendrik Ranocha, Mario Ricchiuto, Vincent Marks","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-05T20:26:56Z","title":"GPU-Accelerated Energy-Conserving Methods for the Two-Dimensional Hyperbolized Serre-Green-Naghdi Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.02540","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":"sha256:803022a4c725802e66bead53a8e3d3f886aa0fa09ed89445575337ba06469fcc","target":"record","created_at":"2026-05-27T02:05:10Z","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":"23859f5ff0c0da9404c91bf41447beed4043f07f46e0470318e5fb676ef12802","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-01-05T20:26:56Z","title_canon_sha256":"8b980bf8523014fcba4b8b7d8cf858673a33e0c8af1ab7fc2143ee478d4dc59b"},"schema_version":"1.0","source":{"id":"2601.02540","kind":"arxiv","version":2}},"canonical_sha256":"d1a9ef94e67d5e82662a881e97f7fbf2de68be8c5a118595696c2780c85295e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1a9ef94e67d5e82662a881e97f7fbf2de68be8c5a118595696c2780c85295e2","first_computed_at":"2026-05-27T02:05:10.116375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:05:10.116375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SLi1qb/9hZPw/7UhmCI7j+Z+9nC9uSc7sLfGZMspL4JZOAN6fr4fpJRaNFWZeQn9zTlTs8RghEz9TOoRMOJhBQ==","signature_status":"signed_v1","signed_at":"2026-05-27T02:05:10.117448Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.02540","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:803022a4c725802e66bead53a8e3d3f886aa0fa09ed89445575337ba06469fcc","sha256:70c0fae820cea39a2afd66efd4a803e9011ab66962dd861d1c60fc3e6f52a050"],"state_sha256":"2eefd34489adcba5b13730d87cb52d36d46d39b01df94a98fcd315a09dc50e89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/4jQGqMoCHM5uHM7TnPipr71K4nVfuuZe+Ezjw3irblxJRGKn8p6bQod/oT7x/r28gfKMT8qWPT5Kro/CxzSDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:12:48.199343Z","bundle_sha256":"f788fc4c369850ef0c789d0ab052ba12590edea657d99e596e26af2cb82443ac"}}