{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:EBHZZTSTBVUTSLEZS7CIRVOLQK","short_pith_number":"pith:EBHZZTST","canonical_record":{"source":{"id":"1302.4865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-20T10:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"2ec0acfb552f17908ae2b0535fd7404d1267c2e6bc2d51d4621b45ffe554f2a1","abstract_canon_sha256":"83698a0870be47a012d9ea19fc2e480852d65def1af9baea312d6261ff9d1280"},"schema_version":"1.0"},"canonical_sha256":"204f9cce530d69392c9997c488d5cb82a5a9301acc6f8ca127620ffacd4b3d4c","source":{"kind":"arxiv","id":"1302.4865","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4865","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4865v2","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4865","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"pith_short_12","alias_value":"EBHZZTSTBVUT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EBHZZTSTBVUTSLEZ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EBHZZTST","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:EBHZZTSTBVUTSLEZS7CIRVOLQK","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4865","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-20T10:42:17Z","cross_cats_sorted":[],"title_canon_sha256":"2ec0acfb552f17908ae2b0535fd7404d1267c2e6bc2d51d4621b45ffe554f2a1","abstract_canon_sha256":"83698a0870be47a012d9ea19fc2e480852d65def1af9baea312d6261ff9d1280"},"schema_version":"1.0"},"canonical_sha256":"204f9cce530d69392c9997c488d5cb82a5a9301acc6f8ca127620ffacd4b3d4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:39.201438Z","signature_b64":"nguczaZTvEsk2FOO0fGxTny/6rs2jqBUAf4wz7sUVxJtX73bvcwwLzzNZs54/S3IplKJT/9e4AZvDX/IU+HzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"204f9cce530d69392c9997c488d5cb82a5a9301acc6f8ca127620ffacd4b3d4c","last_reissued_at":"2026-05-18T03:14:39.200772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:39.200772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4865","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":"2026-05-18T03:14:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KzNjptBzCs9hOhLiYBy9dufnVRP+hCJIyyNp/TryvL5QG4AHUS/TBz/7xLmpwEo5+1qX0haqEYf4l/k/SgLQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:15:54.842851Z"},"content_sha256":"0d8c805eefd2e15af8b59df9c650b522ea2c001324d05d7dbcb09906b70a8b70","schema_version":"1.0","event_id":"sha256:0d8c805eefd2e15af8b59df9c650b522ea2c001324d05d7dbcb09906b70a8b70"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:EBHZZTSTBVUTSLEZS7CIRVOLQK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bloch-wave homogenization on large time scales and dispersive effective wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnes Lamacz, Ben Schweizer, Tomas Dohnal","submitted_at":"2013-02-20T10:42:17Z","abstract_excerpt":"We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\\R^n$, $n \\in \\{1, 2, 3\\}$. Standard homogenization theory provides, for the limit of a small periodicity length $\\eps>0$, an effective second order wave equation that describes solutions on time intervals $[0,T]$. In order to approximate solutions on large time intervals $[0,T\\eps^{-2}]$, one has to use a dispersive, higher order wave equation. In this work, we provide a well-posed, weakly dispersive effective equation, and an estimate for errors between the solution of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4865","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":"2026-05-18T03:14:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OSGWZMPTSi251qR6pNkYp/FtIjazp8rGZkUVoJO/x4A8W6h4+48LSa7Yj/fEBIXit/SyeD3OVWCQ5uO+XxEqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T14:15:54.843193Z"},"content_sha256":"c6ce8c71a14321b35e3553c5890b4effdd7d0e371bb7b174cea57f76a83a94d1","schema_version":"1.0","event_id":"sha256:c6ce8c71a14321b35e3553c5890b4effdd7d0e371bb7b174cea57f76a83a94d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EBHZZTSTBVUTSLEZS7CIRVOLQK/bundle.json","state_url":"https://pith.science/pith/EBHZZTSTBVUTSLEZS7CIRVOLQK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EBHZZTSTBVUTSLEZS7CIRVOLQK/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":"2026-06-20T14:15:54Z","links":{"resolver":"https://pith.science/pith/EBHZZTSTBVUTSLEZS7CIRVOLQK","bundle":"https://pith.science/pith/EBHZZTSTBVUTSLEZS7CIRVOLQK/bundle.json","state":"https://pith.science/pith/EBHZZTSTBVUTSLEZS7CIRVOLQK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EBHZZTSTBVUTSLEZS7CIRVOLQK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EBHZZTSTBVUTSLEZS7CIRVOLQK","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":"83698a0870be47a012d9ea19fc2e480852d65def1af9baea312d6261ff9d1280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-20T10:42:17Z","title_canon_sha256":"2ec0acfb552f17908ae2b0535fd7404d1267c2e6bc2d51d4621b45ffe554f2a1"},"schema_version":"1.0","source":{"id":"1302.4865","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4865","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4865v2","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4865","created_at":"2026-05-18T03:14:39Z"},{"alias_kind":"pith_short_12","alias_value":"EBHZZTSTBVUT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EBHZZTSTBVUTSLEZ","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EBHZZTST","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:c6ce8c71a14321b35e3553c5890b4effdd7d0e371bb7b174cea57f76a83a94d1","target":"graph","created_at":"2026-05-18T03:14:39Z","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 investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\\R^n$, $n \\in \\{1, 2, 3\\}$. Standard homogenization theory provides, for the limit of a small periodicity length $\\eps>0$, an effective second order wave equation that describes solutions on time intervals $[0,T]$. In order to approximate solutions on large time intervals $[0,T\\eps^{-2}]$, one has to use a dispersive, higher order wave equation. In this work, we provide a well-posed, weakly dispersive effective equation, and an estimate for errors between the solution of the","authors_text":"Agnes Lamacz, Ben Schweizer, Tomas Dohnal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-20T10:42:17Z","title":"Bloch-wave homogenization on large time scales and dispersive effective wave equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4865","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":"sha256:0d8c805eefd2e15af8b59df9c650b522ea2c001324d05d7dbcb09906b70a8b70","target":"record","created_at":"2026-05-18T03:14:39Z","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":"83698a0870be47a012d9ea19fc2e480852d65def1af9baea312d6261ff9d1280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-20T10:42:17Z","title_canon_sha256":"2ec0acfb552f17908ae2b0535fd7404d1267c2e6bc2d51d4621b45ffe554f2a1"},"schema_version":"1.0","source":{"id":"1302.4865","kind":"arxiv","version":2}},"canonical_sha256":"204f9cce530d69392c9997c488d5cb82a5a9301acc6f8ca127620ffacd4b3d4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"204f9cce530d69392c9997c488d5cb82a5a9301acc6f8ca127620ffacd4b3d4c","first_computed_at":"2026-05-18T03:14:39.200772Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:39.200772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nguczaZTvEsk2FOO0fGxTny/6rs2jqBUAf4wz7sUVxJtX73bvcwwLzzNZs54/S3IplKJT/9e4AZvDX/IU+HzDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:39.201438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4865","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d8c805eefd2e15af8b59df9c650b522ea2c001324d05d7dbcb09906b70a8b70","sha256:c6ce8c71a14321b35e3553c5890b4effdd7d0e371bb7b174cea57f76a83a94d1"],"state_sha256":"076199c9b550d5d3f35583731b5568d646485e1c0d82471575aa0873063c9404"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MMoWeWjv7kpHiMapEp1qX2jJ7b+mduDNsDX9oM9d9I3uwTUgPg9sb2nnjJRnPC4pXZ+ZawIF1MkGpG/YCeMtCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T14:15:54.845424Z","bundle_sha256":"dc3d1ca4fe89925386f68c58498e5ecdc23e4bb2ed5403c3a9dabd50c6ead6cc"}}