{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:4ELLC5LSVTMKBMUYJVY7S3OX74","short_pith_number":"pith:4ELLC5LS","canonical_record":{"source":{"id":"math/0503075","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2005-03-04T19:05:27Z","cross_cats_sorted":[],"title_canon_sha256":"dd5d1e0487228ed66deef3aa978a4ef140ad2ddf9862f3df3f02246bf7714068","abstract_canon_sha256":"eadb3dddf6901174dc0b3916e0cbb4aee738aeaaf7a8942b1880a0dcc9d969b8"},"schema_version":"1.0"},"canonical_sha256":"e116b17572acd8a0b2984d71f96dd7ff1c615fb0a109e20b5cee64da981bcd9c","source":{"kind":"arxiv","id":"math/0503075","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0503075","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0503075v1","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0503075","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"4ELLC5LSVTMK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"4ELLC5LSVTMKBMUY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"4ELLC5LS","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:4ELLC5LSVTMKBMUYJVY7S3OX74","target":"record","payload":{"canonical_record":{"source":{"id":"math/0503075","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2005-03-04T19:05:27Z","cross_cats_sorted":[],"title_canon_sha256":"dd5d1e0487228ed66deef3aa978a4ef140ad2ddf9862f3df3f02246bf7714068","abstract_canon_sha256":"eadb3dddf6901174dc0b3916e0cbb4aee738aeaaf7a8942b1880a0dcc9d969b8"},"schema_version":"1.0"},"canonical_sha256":"e116b17572acd8a0b2984d71f96dd7ff1c615fb0a109e20b5cee64da981bcd9c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:53.724640Z","signature_b64":"EXodQot7RsETT2FiLIitzOjDXWbAi+Zjutl8s+G8kwB9ymARvThxcouTSUf2CN524H19U0+Sa5uki+FpQSYCAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e116b17572acd8a0b2984d71f96dd7ff1c615fb0a109e20b5cee64da981bcd9c","last_reissued_at":"2026-05-18T01:17:53.724004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:53.724004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0503075","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wXLKCu4s6aNL93nP8o809z1817Bh6XqSN0FKzjaHopADtSf67CpIyBjpR04lqFRorH/VgcDJ0xSoYe0O3p73CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:16:32.058842Z"},"content_sha256":"62f3d7617fab15a69ca7c338f9548036f4c5479d56a48daad58e67aa4e1cc455","schema_version":"1.0","event_id":"sha256:62f3d7617fab15a69ca7c338f9548036f4c5479d56a48daad58e67aa4e1cc455"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:4ELLC5LSVTMKBMUYJVY7S3OX74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Slowing down and reflection of waves in truncated periodic media","license":"","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"B. Vainberg, S. Molchanov","submitted_at":"2005-03-04T19:05:27Z","abstract_excerpt":"We consider wave propagation and scattering governed by one dimensional Schrodinger operators with truncated periodic potentials. The propagation of wave packets with narrow frequency supports is studied. The goal is to describe potentials for which the group velocity (for periodic problem) is small and the transmission coefficient for the truncated potential is not too small, i.e. to find media where a slowing down of the wave packets coexists with a transparency."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503075","kind":"arxiv","version":1},"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":"2026-05-18T01:17:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/UIl6OpQRYQ7u97mbYa6rgGxhn3NvfZfl04+idBTB2DoKq56Rf+1/yq21d7jHu8QNgGrhdTsBkxgld/sXuyyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:16:32.059177Z"},"content_sha256":"5a01730bd749079496346e20c19213ae16990eed182f781543e95d8952dee002","schema_version":"1.0","event_id":"sha256:5a01730bd749079496346e20c19213ae16990eed182f781543e95d8952dee002"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4ELLC5LSVTMKBMUYJVY7S3OX74/bundle.json","state_url":"https://pith.science/pith/4ELLC5LSVTMKBMUYJVY7S3OX74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4ELLC5LSVTMKBMUYJVY7S3OX74/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":"2026-06-03T17:16:32Z","links":{"resolver":"https://pith.science/pith/4ELLC5LSVTMKBMUYJVY7S3OX74","bundle":"https://pith.science/pith/4ELLC5LSVTMKBMUYJVY7S3OX74/bundle.json","state":"https://pith.science/pith/4ELLC5LSVTMKBMUYJVY7S3OX74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4ELLC5LSVTMKBMUYJVY7S3OX74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:4ELLC5LSVTMKBMUYJVY7S3OX74","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":"eadb3dddf6901174dc0b3916e0cbb4aee738aeaaf7a8942b1880a0dcc9d969b8","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2005-03-04T19:05:27Z","title_canon_sha256":"dd5d1e0487228ed66deef3aa978a4ef140ad2ddf9862f3df3f02246bf7714068"},"schema_version":"1.0","source":{"id":"math/0503075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0503075","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0503075v1","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0503075","created_at":"2026-05-18T01:17:53Z"},{"alias_kind":"pith_short_12","alias_value":"4ELLC5LSVTMK","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"4ELLC5LSVTMKBMUY","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"4ELLC5LS","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:5a01730bd749079496346e20c19213ae16990eed182f781543e95d8952dee002","target":"graph","created_at":"2026-05-18T01:17:53Z","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 consider wave propagation and scattering governed by one dimensional Schrodinger operators with truncated periodic potentials. The propagation of wave packets with narrow frequency supports is studied. The goal is to describe potentials for which the group velocity (for periodic problem) is small and the transmission coefficient for the truncated potential is not too small, i.e. to find media where a slowing down of the wave packets coexists with a transparency.","authors_text":"B. Vainberg, S. Molchanov","cross_cats":[],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2005-03-04T19:05:27Z","title":"Slowing down and reflection of waves in truncated periodic media"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0503075","kind":"arxiv","version":1},"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":"sha256:62f3d7617fab15a69ca7c338f9548036f4c5479d56a48daad58e67aa4e1cc455","target":"record","created_at":"2026-05-18T01:17:53Z","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":"eadb3dddf6901174dc0b3916e0cbb4aee738aeaaf7a8942b1880a0dcc9d969b8","cross_cats_sorted":[],"license":"","primary_cat":"math.CA","submitted_at":"2005-03-04T19:05:27Z","title_canon_sha256":"dd5d1e0487228ed66deef3aa978a4ef140ad2ddf9862f3df3f02246bf7714068"},"schema_version":"1.0","source":{"id":"math/0503075","kind":"arxiv","version":1}},"canonical_sha256":"e116b17572acd8a0b2984d71f96dd7ff1c615fb0a109e20b5cee64da981bcd9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e116b17572acd8a0b2984d71f96dd7ff1c615fb0a109e20b5cee64da981bcd9c","first_computed_at":"2026-05-18T01:17:53.724004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:53.724004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EXodQot7RsETT2FiLIitzOjDXWbAi+Zjutl8s+G8kwB9ymARvThxcouTSUf2CN524H19U0+Sa5uki+FpQSYCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:53.724640Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0503075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62f3d7617fab15a69ca7c338f9548036f4c5479d56a48daad58e67aa4e1cc455","sha256:5a01730bd749079496346e20c19213ae16990eed182f781543e95d8952dee002"],"state_sha256":"4d7e7e2ae93733f34a204ce4799654051ca5a35ee5ffa372b7bcdd94233bd8b8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7CPZzlh09EYxGKxEarREPQ66h6xHnBOgCsOzx20kNh+s0N3hJuvsouqmjhmZX+qitoJXdbbGmmI22yVBrRqoDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:16:32.061130Z","bundle_sha256":"ff67aa776f376ce7fcfc777d4b9600bdec5e04bfebb37646539ae29a21aad4a7"}}