{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:T7OMP2C53RBEMVNQQTPOZKRXGD","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":"4e0e3768078c556ccf41123b80524fedac54c644b96935bd267f8c4fdb48a568","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2009-01-01T17:57:24Z","title_canon_sha256":"bb1daa51a11d4deb005e27d956628aaeeb2820dff394cbb003ef02de92476c85"},"schema_version":"1.0","source":{"id":"0901.0187","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.0187","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"0901.0187v4","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.0187","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"T7OMP2C53RBE","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"T7OMP2C53RBEMVNQ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"T7OMP2C5","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:38bfd65751c3f3890b9fdc0322cc0ff869b3507f12682e66b8b3d0d5a70b5393","target":"graph","created_at":"2026-05-18T02:15:03Z","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":"We study the linear phenomenological Maxwell's equations in the presence of a polarizable and magnetizable medium (magnetodielectric). For a dispersive, non-absorptive, medium with equal electric and magnetic permeabilities, the latter can assume the value -1 (+1 is their vacuum value) for a discrete set of frequencies, i.e., for these frequencies the medium behaves as a negative index material (NIM). We show that such systems have a well-defined time evolution. In particular the fields remain square integrable (and the electromagnetic energy finite) if this is the case at some initial time. N","authors_text":"A. Tip, B. Gralak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2009-01-01T17:57:24Z","title":"Macroscopic Maxwell's equations and negative index materials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.0187","kind":"arxiv","version":4},"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":"sha256:268a0adaebdcb795113fc4a27d8c791f91ba4f95c5c306ccecd46ef58db438bb","target":"record","created_at":"2026-05-18T02:15:03Z","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":"4e0e3768078c556ccf41123b80524fedac54c644b96935bd267f8c4fdb48a568","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.optics","submitted_at":"2009-01-01T17:57:24Z","title_canon_sha256":"bb1daa51a11d4deb005e27d956628aaeeb2820dff394cbb003ef02de92476c85"},"schema_version":"1.0","source":{"id":"0901.0187","kind":"arxiv","version":4}},"canonical_sha256":"9fdcc7e85ddc424655b084deecaa3730f9fdf6f651a53c930a9927eea5225990","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fdcc7e85ddc424655b084deecaa3730f9fdf6f651a53c930a9927eea5225990","first_computed_at":"2026-05-18T02:15:03.525839Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:03.525839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MnVkyNIgUcpH3dJgSY+0snGXaQXedQ6Qf97sCrwSgaRmyg5X7zIm5X5s+2F04v4nYY/gVYNG3pYlGECrOh1EBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:03.526223Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.0187","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:268a0adaebdcb795113fc4a27d8c791f91ba4f95c5c306ccecd46ef58db438bb","sha256:38bfd65751c3f3890b9fdc0322cc0ff869b3507f12682e66b8b3d0d5a70b5393"],"state_sha256":"ac80022fd6890c2c16dc5562b0bb1967cf0b2bcd0fa2eadcb8f048055d9316bf"}