{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:I3SU7JKNJDM5H4PPUYJO4ZXMZ7","short_pith_number":"pith:I3SU7JKN","canonical_record":{"source":{"id":"0707.4470","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2007-07-30T19:38:41Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"a80074125ba4b1afdfc0aac5582cfdf3742128672295b0f2ab4979491432a839","abstract_canon_sha256":"1c7e481137027c3af5def4a71e34bb9cf3084a945ca866c5c38c6eb293b22ba0"},"schema_version":"1.0"},"canonical_sha256":"46e54fa54d48d9d3f1efa612ee66eccffef19604552f50b6d9561e962d3506e7","source":{"kind":"arxiv","id":"0707.4470","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.4470","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"arxiv_version","alias_value":"0707.4470v3","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.4470","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"pith_short_12","alias_value":"I3SU7JKNJDM5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"I3SU7JKNJDM5H4PP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"I3SU7JKN","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:I3SU7JKNJDM5H4PPUYJO4ZXMZ7","target":"record","payload":{"canonical_record":{"source":{"id":"0707.4470","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2007-07-30T19:38:41Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"a80074125ba4b1afdfc0aac5582cfdf3742128672295b0f2ab4979491432a839","abstract_canon_sha256":"1c7e481137027c3af5def4a71e34bb9cf3084a945ca866c5c38c6eb293b22ba0"},"schema_version":"1.0"},"canonical_sha256":"46e54fa54d48d9d3f1efa612ee66eccffef19604552f50b6d9561e962d3506e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:55.188555Z","signature_b64":"xVbmw8uUORvk3ojrfVR+9VqKcQuMBEs2mRwXwsbQPTCIqrco7ekUN9cw1S7zX7hpKiG9uyvqFKSM4zOrjew7Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46e54fa54d48d9d3f1efa612ee66eccffef19604552f50b6d9561e962d3506e7","last_reissued_at":"2026-05-18T01:27:55.187402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:55.187402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.4470","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3bzEg/EF1ZDVWqoXIbTE8ulw55z9ig0fUAF9nntAnSPECQbxWx+PyMLD2u5Fvr4dKTAgBqKQ2e5CKgy8jHkaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T17:15:09.843930Z"},"content_sha256":"fc280d77fdc1920b86144b9b74bd0799f3ea0fe2f37d56c8bbe44960df2030a5","schema_version":"1.0","event_id":"sha256:fc280d77fdc1920b86144b9b74bd0799f3ea0fe2f37d56c8bbe44960df2030a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:I3SU7JKNJDM5H4PPUYJO4ZXMZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Ari Stern, Jerrold E. Marsden, Mathieu Desbrun, Yiying Tong","submitted_at":"2007-07-30T19:38:41Z","abstract_excerpt":"In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of variational, multisymplectic numerical methods for solving Maxwell's equations that automatically preserve key symmetries and invariants.\n  In doing so, we demonstrate several new results, which apply both to some well-established numerical methods and to new methods introduced here. First, we show that Yee's finite-difference time-domain (FDTD) scheme, along with a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.4470","kind":"arxiv","version":3},"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":"2026-05-18T01:27:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H42YrMXmQt6eah/bxXQhd+oqq9YrWmzBmQccM1XGufDRgx6exOxfYGXAxfISJEKcExnKhScxt7zdft1GCHGvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T17:15:09.844663Z"},"content_sha256":"fb27b7de221cd2783c4ce634d61c6489ae85dd67ff6b2ff6953448f1fdf0cc92","schema_version":"1.0","event_id":"sha256:fb27b7de221cd2783c4ce634d61c6489ae85dd67ff6b2ff6953448f1fdf0cc92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3SU7JKNJDM5H4PPUYJO4ZXMZ7/bundle.json","state_url":"https://pith.science/pith/I3SU7JKNJDM5H4PPUYJO4ZXMZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3SU7JKNJDM5H4PPUYJO4ZXMZ7/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":"2026-05-23T17:15:09Z","links":{"resolver":"https://pith.science/pith/I3SU7JKNJDM5H4PPUYJO4ZXMZ7","bundle":"https://pith.science/pith/I3SU7JKNJDM5H4PPUYJO4ZXMZ7/bundle.json","state":"https://pith.science/pith/I3SU7JKNJDM5H4PPUYJO4ZXMZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3SU7JKNJDM5H4PPUYJO4ZXMZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:I3SU7JKNJDM5H4PPUYJO4ZXMZ7","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":"1c7e481137027c3af5def4a71e34bb9cf3084a945ca866c5c38c6eb293b22ba0","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2007-07-30T19:38:41Z","title_canon_sha256":"a80074125ba4b1afdfc0aac5582cfdf3742128672295b0f2ab4979491432a839"},"schema_version":"1.0","source":{"id":"0707.4470","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.4470","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"arxiv_version","alias_value":"0707.4470v3","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.4470","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"pith_short_12","alias_value":"I3SU7JKNJDM5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"I3SU7JKNJDM5H4PP","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"I3SU7JKN","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:fb27b7de221cd2783c4ce634d61c6489ae85dd67ff6b2ff6953448f1fdf0cc92","target":"graph","created_at":"2026-05-18T01:27:55Z","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":"In this paper, we develop a structure-preserving discretization of the Lagrangian framework for electromagnetism, combining techniques from variational integrators and discrete differential forms. This leads to a general family of variational, multisymplectic numerical methods for solving Maxwell's equations that automatically preserve key symmetries and invariants.\n  In doing so, we demonstrate several new results, which apply both to some well-established numerical methods and to new methods introduced here. First, we show that Yee's finite-difference time-domain (FDTD) scheme, along with a ","authors_text":"Ari Stern, Jerrold E. Marsden, Mathieu Desbrun, Yiying Tong","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2007-07-30T19:38:41Z","title":"Geometric Computational Electrodynamics with Variational Integrators and Discrete Differential Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.4470","kind":"arxiv","version":3},"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:fc280d77fdc1920b86144b9b74bd0799f3ea0fe2f37d56c8bbe44960df2030a5","target":"record","created_at":"2026-05-18T01:27:55Z","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":"1c7e481137027c3af5def4a71e34bb9cf3084a945ca866c5c38c6eb293b22ba0","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2007-07-30T19:38:41Z","title_canon_sha256":"a80074125ba4b1afdfc0aac5582cfdf3742128672295b0f2ab4979491432a839"},"schema_version":"1.0","source":{"id":"0707.4470","kind":"arxiv","version":3}},"canonical_sha256":"46e54fa54d48d9d3f1efa612ee66eccffef19604552f50b6d9561e962d3506e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46e54fa54d48d9d3f1efa612ee66eccffef19604552f50b6d9561e962d3506e7","first_computed_at":"2026-05-18T01:27:55.187402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:55.187402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xVbmw8uUORvk3ojrfVR+9VqKcQuMBEs2mRwXwsbQPTCIqrco7ekUN9cw1S7zX7hpKiG9uyvqFKSM4zOrjew7Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:55.188555Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.4470","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc280d77fdc1920b86144b9b74bd0799f3ea0fe2f37d56c8bbe44960df2030a5","sha256:fb27b7de221cd2783c4ce634d61c6489ae85dd67ff6b2ff6953448f1fdf0cc92"],"state_sha256":"180b79a37870b2293e5c7312ce2eb0ea6d08f3b9403ed92b396095fb87a5ac96"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z8ZBGTvgC7VHwcloqwNr+XDH3xnkVhksJ06gaPpoiqZOipvKmwc2V9x8MIGbjF7nD3sALM35vv8XVGxvYKwWCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T17:15:09.847424Z","bundle_sha256":"3d1d813b44706f31baa33081df27133c87c284f50f955964cad9c137beb4fcfc"}}