{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:SLQ3W7TX6JX2NH345AFUEDHATU","short_pith_number":"pith:SLQ3W7TX","canonical_record":{"source":{"id":"1710.03389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-10-10T03:48:10Z","cross_cats_sorted":["math.AP","math.MP","math.SP","physics.optics"],"title_canon_sha256":"6c79e78eabd0d3f303cafe6f2712c8fdcb6121b0ed0a321335d7590d13609e61","abstract_canon_sha256":"01041d1a8ef4a1c98f80d60197f938332f2a543747f5d623a3194eaac911ac2c"},"schema_version":"1.0"},"canonical_sha256":"92e1bb7e77f26fa69f7ce80b420ce09d27aa3fcf4836065243751100d58144ee","source":{"kind":"arxiv","id":"1710.03389","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03389","created_at":"2026-05-18T00:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03389v2","created_at":"2026-05-18T00:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03389","created_at":"2026-05-18T00:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"SLQ3W7TX6JX2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SLQ3W7TX6JX2NH34","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SLQ3W7TX","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:SLQ3W7TX6JX2NH345AFUEDHATU","target":"record","payload":{"canonical_record":{"source":{"id":"1710.03389","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-10-10T03:48:10Z","cross_cats_sorted":["math.AP","math.MP","math.SP","physics.optics"],"title_canon_sha256":"6c79e78eabd0d3f303cafe6f2712c8fdcb6121b0ed0a321335d7590d13609e61","abstract_canon_sha256":"01041d1a8ef4a1c98f80d60197f938332f2a543747f5d623a3194eaac911ac2c"},"schema_version":"1.0"},"canonical_sha256":"92e1bb7e77f26fa69f7ce80b420ce09d27aa3fcf4836065243751100d58144ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:00.146303Z","signature_b64":"9jEAwVRkDd96of7YSvQTNhP1XAJ1bDnr3+v16yKR+lDKkUnrEj43FGIvFJgcTIMwL60Wjr/sGXP1JZhQ4njlDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92e1bb7e77f26fa69f7ce80b420ce09d27aa3fcf4836065243751100d58144ee","last_reissued_at":"2026-05-18T00:01:00.145902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:00.145902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.03389","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":"2026-05-18T00:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1z2jqTKceEZU6DjQX6E6iK15xEWedlunVWWq4Qte6aVIi9YEDSh8v/6vRDMAuQ8xo8JvzxLoOdToLUP2oOdnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:56:45.265703Z"},"content_sha256":"8f0d4e7bc51712e991a6b1d6f555bbe76b2d74cf5d75b451fc367a834b8c4a1b","schema_version":"1.0","event_id":"sha256:8f0d4e7bc51712e991a6b1d6f555bbe76b2d74cf5d75b451fc367a834b8c4a1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:SLQ3W7TX6JX2NH345AFUEDHATU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic operators with honeycomb symmetry: Dirac points, Edge States and Applications to Photonic Graphene","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP","physics.optics"],"primary_cat":"math-ph","authors_text":"J. P. Lee-Thorp, M. I. Weinstein, Y. Zhu","submitted_at":"2017-10-10T03:48:10Z","abstract_excerpt":"Consider electromagnetic waves in two-dimensional {\\it honeycomb structured media}. The properties of transverse electric (TE) polarized waves are determined by the spectral properties of the elliptic operator $\\LA=-\\nabla_\\bx\\cdot A(\\bx) \\nabla_\\bx$, where $A(\\bx)$ is $\\Lambda_h-$ periodic ($\\Lambda_h$ denotes the equilateral triangular lattice), and such that with respect to some origin of coordinates, $A(\\bx)$ is $\\mathcal{P}\\mathcal{C}-$ invariant ($A(\\bx)=\\overline{A(-\\bx)}$) and $120^\\circ$ rotationally invariant ($A(R^*\\bx)=R^*A(\\bx)R$, where $R$ is a $120^\\circ$ rotation in the plane)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03389","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":"2026-05-18T00:01:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EVOkpeDUU/N4RwFCJh2O6CKLkz3eZAr+XK0x0VELTnTs1EavEKnuCPRVGsyn+tBNMsUwssPo/PUjL1vJLOuMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:56:45.266374Z"},"content_sha256":"b90fb2b06a49b737fced07578a9c8ff499b4f2421878bf96c8cb01f686ca851d","schema_version":"1.0","event_id":"sha256:b90fb2b06a49b737fced07578a9c8ff499b4f2421878bf96c8cb01f686ca851d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SLQ3W7TX6JX2NH345AFUEDHATU/bundle.json","state_url":"https://pith.science/pith/SLQ3W7TX6JX2NH345AFUEDHATU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SLQ3W7TX6JX2NH345AFUEDHATU/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":"2026-06-09T04:56:45Z","links":{"resolver":"https://pith.science/pith/SLQ3W7TX6JX2NH345AFUEDHATU","bundle":"https://pith.science/pith/SLQ3W7TX6JX2NH345AFUEDHATU/bundle.json","state":"https://pith.science/pith/SLQ3W7TX6JX2NH345AFUEDHATU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SLQ3W7TX6JX2NH345AFUEDHATU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:SLQ3W7TX6JX2NH345AFUEDHATU","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":"01041d1a8ef4a1c98f80d60197f938332f2a543747f5d623a3194eaac911ac2c","cross_cats_sorted":["math.AP","math.MP","math.SP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-10-10T03:48:10Z","title_canon_sha256":"6c79e78eabd0d3f303cafe6f2712c8fdcb6121b0ed0a321335d7590d13609e61"},"schema_version":"1.0","source":{"id":"1710.03389","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.03389","created_at":"2026-05-18T00:01:00Z"},{"alias_kind":"arxiv_version","alias_value":"1710.03389v2","created_at":"2026-05-18T00:01:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.03389","created_at":"2026-05-18T00:01:00Z"},{"alias_kind":"pith_short_12","alias_value":"SLQ3W7TX6JX2","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"SLQ3W7TX6JX2NH34","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"SLQ3W7TX","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:b90fb2b06a49b737fced07578a9c8ff499b4f2421878bf96c8cb01f686ca851d","target":"graph","created_at":"2026-05-18T00:01:00Z","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":"Consider electromagnetic waves in two-dimensional {\\it honeycomb structured media}. The properties of transverse electric (TE) polarized waves are determined by the spectral properties of the elliptic operator $\\LA=-\\nabla_\\bx\\cdot A(\\bx) \\nabla_\\bx$, where $A(\\bx)$ is $\\Lambda_h-$ periodic ($\\Lambda_h$ denotes the equilateral triangular lattice), and such that with respect to some origin of coordinates, $A(\\bx)$ is $\\mathcal{P}\\mathcal{C}-$ invariant ($A(\\bx)=\\overline{A(-\\bx)}$) and $120^\\circ$ rotationally invariant ($A(R^*\\bx)=R^*A(\\bx)R$, where $R$ is a $120^\\circ$ rotation in the plane).","authors_text":"J. P. Lee-Thorp, M. I. Weinstein, Y. Zhu","cross_cats":["math.AP","math.MP","math.SP","physics.optics"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-10-10T03:48:10Z","title":"Elliptic operators with honeycomb symmetry: Dirac points, Edge States and Applications to Photonic Graphene"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.03389","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":"sha256:8f0d4e7bc51712e991a6b1d6f555bbe76b2d74cf5d75b451fc367a834b8c4a1b","target":"record","created_at":"2026-05-18T00:01:00Z","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":"01041d1a8ef4a1c98f80d60197f938332f2a543747f5d623a3194eaac911ac2c","cross_cats_sorted":["math.AP","math.MP","math.SP","physics.optics"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-10-10T03:48:10Z","title_canon_sha256":"6c79e78eabd0d3f303cafe6f2712c8fdcb6121b0ed0a321335d7590d13609e61"},"schema_version":"1.0","source":{"id":"1710.03389","kind":"arxiv","version":2}},"canonical_sha256":"92e1bb7e77f26fa69f7ce80b420ce09d27aa3fcf4836065243751100d58144ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92e1bb7e77f26fa69f7ce80b420ce09d27aa3fcf4836065243751100d58144ee","first_computed_at":"2026-05-18T00:01:00.145902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:00.145902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9jEAwVRkDd96of7YSvQTNhP1XAJ1bDnr3+v16yKR+lDKkUnrEj43FGIvFJgcTIMwL60Wjr/sGXP1JZhQ4njlDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:00.146303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.03389","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f0d4e7bc51712e991a6b1d6f555bbe76b2d74cf5d75b451fc367a834b8c4a1b","sha256:b90fb2b06a49b737fced07578a9c8ff499b4f2421878bf96c8cb01f686ca851d"],"state_sha256":"5c6ee9475ac56ff11b9408ffbf95c2a92bdb3c75ef2fd374aaed49a09cc8be37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"exzKZTiF99ZA2OzfleEbSQuwj+ibGa74H03PScmk6r60/vfSP/DHUfU9lGKLuo8DBl5/2aIlr8DJFU/FZm60Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:56:45.270218Z","bundle_sha256":"34569275431581ba4111ac25f958490a1ea5905f3ec34f27725ebdd33a3a9df4"}}