{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3UJ4A7WARKGK434O5YD3OKW4VF","short_pith_number":"pith:3UJ4A7WA","canonical_record":{"source":{"id":"1608.01944","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-05T17:22:28Z","cross_cats_sorted":[],"title_canon_sha256":"efa93b36da627eee960852dc60c15bfb063c9dbef1b9437a646f1e9a47a828ae","abstract_canon_sha256":"dbb0c3040590b08aeaea0889838097a10c86ddd717d4c390dfe9317b6a625b31"},"schema_version":"1.0"},"canonical_sha256":"dd13c07ec08a8cae6f8eee07b72adca96e7c82fe382645c9332d7fe8fdbabd5e","source":{"kind":"arxiv","id":"1608.01944","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01944","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01944v2","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01944","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"3UJ4A7WARKGK","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3UJ4A7WARKGK434O","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3UJ4A7WA","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3UJ4A7WARKGK434O5YD3OKW4VF","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01944","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-05T17:22:28Z","cross_cats_sorted":[],"title_canon_sha256":"efa93b36da627eee960852dc60c15bfb063c9dbef1b9437a646f1e9a47a828ae","abstract_canon_sha256":"dbb0c3040590b08aeaea0889838097a10c86ddd717d4c390dfe9317b6a625b31"},"schema_version":"1.0"},"canonical_sha256":"dd13c07ec08a8cae6f8eee07b72adca96e7c82fe382645c9332d7fe8fdbabd5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:40.099449Z","signature_b64":"zoOXcg/r+qI00OaxO3l6Mn0E+2HHYiqmYV0eHvIlDGxKGz69ndTMiHjtXANv5fq1Ome1Hd23WSQzPvdbuRh1Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd13c07ec08a8cae6f8eee07b72adca96e7c82fe382645c9332d7fe8fdbabd5e","last_reissued_at":"2026-05-18T00:53:40.099055Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:40.099055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01944","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":"2026-05-18T00:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BMgfSZTzVEL8M3Ufs2u4y96ZV/gvp4eF2d9QEeH4M8UF7crSycBeBTHfNMqxxF8t5u9FScJqKePdBszqnU06Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:04:54.904436Z"},"content_sha256":"0d92f0b34d68e68ef6fb204680d93d040e6f29b11fcf5f098290773b1cd69237","schema_version":"1.0","event_id":"sha256:0d92f0b34d68e68ef6fb204680d93d040e6f29b11fcf5f098290773b1cd69237"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3UJ4A7WARKGK434O5YD3OKW4VF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weight-adjusted discontinuous Galerkin methods: wave propagation in heterogeneous media","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jesse Chan, Russell J. Hewett, T. Warburton","submitted_at":"2016-08-05T17:22:28Z","abstract_excerpt":"Time-domain discontinuous Galerkin (DG) methods for wave propagation require accounting for the inversion of dense elemental mass matrices, where each mass matrix is computed with respect to a parameter-weighted L2 inner product. In applications where the wavespeed varies spatially at a sub-element scale, these matrices are distinct over each element, necessitating additional storage. In this work, we propose a weight-adjusted DG (WADG) method which reduces storage costs by replacing the weighted L2 inner product with a weight-adjusted inner product. This equivalent inner product results in an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01944","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":""},"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":"2026-05-18T00:53:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2n9zpv11bzhR+/SYjJ6y5S9jfpcXg3dfnVpDTx/j51lfInY1CuJi6xkJanfwvjLDlrwPwggbW/7/biRazBROCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:04:54.904778Z"},"content_sha256":"91576eaa8b60e0e44d2d9567e73d828b37c18668d32995aa60d6d64fc9292813","schema_version":"1.0","event_id":"sha256:91576eaa8b60e0e44d2d9567e73d828b37c18668d32995aa60d6d64fc9292813"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3UJ4A7WARKGK434O5YD3OKW4VF/bundle.json","state_url":"https://pith.science/pith/3UJ4A7WARKGK434O5YD3OKW4VF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3UJ4A7WARKGK434O5YD3OKW4VF/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":"2026-06-02T14:04:54Z","links":{"resolver":"https://pith.science/pith/3UJ4A7WARKGK434O5YD3OKW4VF","bundle":"https://pith.science/pith/3UJ4A7WARKGK434O5YD3OKW4VF/bundle.json","state":"https://pith.science/pith/3UJ4A7WARKGK434O5YD3OKW4VF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3UJ4A7WARKGK434O5YD3OKW4VF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3UJ4A7WARKGK434O5YD3OKW4VF","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":"dbb0c3040590b08aeaea0889838097a10c86ddd717d4c390dfe9317b6a625b31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-05T17:22:28Z","title_canon_sha256":"efa93b36da627eee960852dc60c15bfb063c9dbef1b9437a646f1e9a47a828ae"},"schema_version":"1.0","source":{"id":"1608.01944","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01944","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01944v2","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01944","created_at":"2026-05-18T00:53:40Z"},{"alias_kind":"pith_short_12","alias_value":"3UJ4A7WARKGK","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"3UJ4A7WARKGK434O","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"3UJ4A7WA","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:91576eaa8b60e0e44d2d9567e73d828b37c18668d32995aa60d6d64fc9292813","target":"graph","created_at":"2026-05-18T00:53:40Z","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":"Time-domain discontinuous Galerkin (DG) methods for wave propagation require accounting for the inversion of dense elemental mass matrices, where each mass matrix is computed with respect to a parameter-weighted L2 inner product. In applications where the wavespeed varies spatially at a sub-element scale, these matrices are distinct over each element, necessitating additional storage. In this work, we propose a weight-adjusted DG (WADG) method which reduces storage costs by replacing the weighted L2 inner product with a weight-adjusted inner product. This equivalent inner product results in an","authors_text":"Jesse Chan, Russell J. Hewett, T. Warburton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-05T17:22:28Z","title":"Weight-adjusted discontinuous Galerkin methods: wave propagation in heterogeneous media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01944","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":"sha256:0d92f0b34d68e68ef6fb204680d93d040e6f29b11fcf5f098290773b1cd69237","target":"record","created_at":"2026-05-18T00:53:40Z","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":"dbb0c3040590b08aeaea0889838097a10c86ddd717d4c390dfe9317b6a625b31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-08-05T17:22:28Z","title_canon_sha256":"efa93b36da627eee960852dc60c15bfb063c9dbef1b9437a646f1e9a47a828ae"},"schema_version":"1.0","source":{"id":"1608.01944","kind":"arxiv","version":2}},"canonical_sha256":"dd13c07ec08a8cae6f8eee07b72adca96e7c82fe382645c9332d7fe8fdbabd5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd13c07ec08a8cae6f8eee07b72adca96e7c82fe382645c9332d7fe8fdbabd5e","first_computed_at":"2026-05-18T00:53:40.099055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:40.099055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zoOXcg/r+qI00OaxO3l6Mn0E+2HHYiqmYV0eHvIlDGxKGz69ndTMiHjtXANv5fq1Ome1Hd23WSQzPvdbuRh1Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:40.099449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01944","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d92f0b34d68e68ef6fb204680d93d040e6f29b11fcf5f098290773b1cd69237","sha256:91576eaa8b60e0e44d2d9567e73d828b37c18668d32995aa60d6d64fc9292813"],"state_sha256":"4e938581fbafd9d761b83880927e5ffd7bea36b7a063c5394b841319216022a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HdrDfZkt1uHu1Fskm9b3U71yvWmEef0SO48LzMzDv4I4R32QSAqwwnFaF6W6lhqRHWZpUPQniMHE9yOHA3nIAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:04:54.906717Z","bundle_sha256":"34a1daf501e7ef54b7a4b3d12e5d5bf2d3ee1cda6b09464160f98896e21a0576"}}