{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3LFRARZZTXV44WP5O62AER3XE2","short_pith_number":"pith:3LFRARZZ","canonical_record":{"source":{"id":"1507.02484","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-09T12:38:36Z","cross_cats_sorted":[],"title_canon_sha256":"dc55de33b06cbf3594078f3b3e72ff6fedd4742060a262316fd1183e6c2ff3c0","abstract_canon_sha256":"39809d80c53f6a307b9f36b207e33f35bef6818ecd601b937235714ec3934e02"},"schema_version":"1.0"},"canonical_sha256":"dacb1047399debce59fd77b4024777269c9fd866955bcbc22c79a0fddffcac0e","source":{"kind":"arxiv","id":"1507.02484","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02484","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02484v5","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02484","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"3LFRARZZTXV4","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3LFRARZZTXV44WP5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3LFRARZZ","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3LFRARZZTXV44WP5O62AER3XE2","target":"record","payload":{"canonical_record":{"source":{"id":"1507.02484","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-09T12:38:36Z","cross_cats_sorted":[],"title_canon_sha256":"dc55de33b06cbf3594078f3b3e72ff6fedd4742060a262316fd1183e6c2ff3c0","abstract_canon_sha256":"39809d80c53f6a307b9f36b207e33f35bef6818ecd601b937235714ec3934e02"},"schema_version":"1.0"},"canonical_sha256":"dacb1047399debce59fd77b4024777269c9fd866955bcbc22c79a0fddffcac0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:29.308540Z","signature_b64":"6W5urxnLGyrdhG9cTDuOIrrmaajm+Q3k7i7nbVtN2Tv35EjRAJ1XPRgWTsN2qTmVlc5slYMF7V1Hv5l1BjjPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dacb1047399debce59fd77b4024777269c9fd866955bcbc22c79a0fddffcac0e","last_reissued_at":"2026-05-18T00:14:29.307793Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:29.307793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.02484","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1WiYRFefH15z8f5th80QQrZx+iYPz2YZDz04snuIE7+UBQglDD3i6POOeGh3rjZNV37MkJiQA2facTsvG5uMBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:16:12.089785Z"},"content_sha256":"c87c07b8c1c52676db11b13d8fefe3d8613520f0669949e7f16c847ddeb1a208","schema_version":"1.0","event_id":"sha256:c87c07b8c1c52676db11b13d8fefe3d8613520f0669949e7f16c847ddeb1a208"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3LFRARZZTXV44WP5O62AER3XE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive Energy Preserving Methods for Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Brynjulf Owren, S{\\o}lve Eidnes, Torbj{\\o}rn Ringholm","submitted_at":"2015-07-09T12:38:36Z","abstract_excerpt":"A method for constructing first integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The method can be used with both finite difference and partition of unity approaches, thereby also including finite element approaches. The schemes are then extended to accommodate $r$-, $h$- and $p$-adaptivity. The method is applied to the Korteweg-de Vries equation and the Sine-Gordon equation and results from numerical experiments are presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02484","kind":"arxiv","version":5},"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":"2026-05-18T00:14:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SS8SBGppdg70nZGaWlqI6Y/jebAT5Tcnkra8m4XVPLGJS0K+4sVpxUWy9A8xRiWpa1kq91wtI9RWNhwjrXytAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T03:16:12.090131Z"},"content_sha256":"b4090052f3ab1cb040faccf012c1db0c6c4ddc01479c940d0b500b1ff79f2987","schema_version":"1.0","event_id":"sha256:b4090052f3ab1cb040faccf012c1db0c6c4ddc01479c940d0b500b1ff79f2987"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3LFRARZZTXV44WP5O62AER3XE2/bundle.json","state_url":"https://pith.science/pith/3LFRARZZTXV44WP5O62AER3XE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3LFRARZZTXV44WP5O62AER3XE2/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":"2026-06-02T03:16:12Z","links":{"resolver":"https://pith.science/pith/3LFRARZZTXV44WP5O62AER3XE2","bundle":"https://pith.science/pith/3LFRARZZTXV44WP5O62AER3XE2/bundle.json","state":"https://pith.science/pith/3LFRARZZTXV44WP5O62AER3XE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3LFRARZZTXV44WP5O62AER3XE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3LFRARZZTXV44WP5O62AER3XE2","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":"39809d80c53f6a307b9f36b207e33f35bef6818ecd601b937235714ec3934e02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-09T12:38:36Z","title_canon_sha256":"dc55de33b06cbf3594078f3b3e72ff6fedd4742060a262316fd1183e6c2ff3c0"},"schema_version":"1.0","source":{"id":"1507.02484","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02484","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02484v5","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02484","created_at":"2026-05-18T00:14:29Z"},{"alias_kind":"pith_short_12","alias_value":"3LFRARZZTXV4","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3LFRARZZTXV44WP5","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3LFRARZZ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:b4090052f3ab1cb040faccf012c1db0c6c4ddc01479c940d0b500b1ff79f2987","target":"graph","created_at":"2026-05-18T00:14:29Z","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":"A method for constructing first integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The method can be used with both finite difference and partition of unity approaches, thereby also including finite element approaches. The schemes are then extended to accommodate $r$-, $h$- and $p$-adaptivity. The method is applied to the Korteweg-de Vries equation and the Sine-Gordon equation and results from numerical experiments are presented.","authors_text":"Brynjulf Owren, S{\\o}lve Eidnes, Torbj{\\o}rn Ringholm","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-09T12:38:36Z","title":"Adaptive Energy Preserving Methods for Partial Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02484","kind":"arxiv","version":5},"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:c87c07b8c1c52676db11b13d8fefe3d8613520f0669949e7f16c847ddeb1a208","target":"record","created_at":"2026-05-18T00:14:29Z","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":"39809d80c53f6a307b9f36b207e33f35bef6818ecd601b937235714ec3934e02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-09T12:38:36Z","title_canon_sha256":"dc55de33b06cbf3594078f3b3e72ff6fedd4742060a262316fd1183e6c2ff3c0"},"schema_version":"1.0","source":{"id":"1507.02484","kind":"arxiv","version":5}},"canonical_sha256":"dacb1047399debce59fd77b4024777269c9fd866955bcbc22c79a0fddffcac0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dacb1047399debce59fd77b4024777269c9fd866955bcbc22c79a0fddffcac0e","first_computed_at":"2026-05-18T00:14:29.307793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:29.307793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6W5urxnLGyrdhG9cTDuOIrrmaajm+Q3k7i7nbVtN2Tv35EjRAJ1XPRgWTsN2qTmVlc5slYMF7V1Hv5l1BjjPAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:29.308540Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02484","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c87c07b8c1c52676db11b13d8fefe3d8613520f0669949e7f16c847ddeb1a208","sha256:b4090052f3ab1cb040faccf012c1db0c6c4ddc01479c940d0b500b1ff79f2987"],"state_sha256":"dc4eed00ec67441d4ce024a42d61356d0d43b191af19e19c7eb21b58a2b45e9b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"75YpsiuiJX/yAdbLgEkMC8i7maYOzc7SBm8E+lQv3vBkvQFxaNyECpeiwP7sNi22WxiQ+J+eCeWklkJXcD0pAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T03:16:12.092129Z","bundle_sha256":"069ae8621ad08566b9a4fec2a08ed3af6bc767a8a1c8d870fc84d3789705663b"}}