{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IA66M7MUM4EOYTU6HWHVRETRHS","short_pith_number":"pith:IA66M7MU","canonical_record":{"source":{"id":"1709.06345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-19T11:08:54Z","cross_cats_sorted":[],"title_canon_sha256":"2fb710a9f44a1748c52a4076a94efb6143d3af5749be32d9910c701814253ff1","abstract_canon_sha256":"db3978c4f928d87a25ce5e6bee78a8a3b837eb5fb7c054f68fa30223b2765892"},"schema_version":"1.0"},"canonical_sha256":"403de67d946708ec4e9e3d8f5892713c8d709675d7b5146ba8d2d07cd098f859","source":{"kind":"arxiv","id":"1709.06345","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06345","created_at":"2026-05-18T00:34:53Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06345v1","created_at":"2026-05-18T00:34:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06345","created_at":"2026-05-18T00:34:53Z"},{"alias_kind":"pith_short_12","alias_value":"IA66M7MUM4EO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IA66M7MUM4EOYTU6","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IA66M7MU","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IA66M7MUM4EOYTU6HWHVRETRHS","target":"record","payload":{"canonical_record":{"source":{"id":"1709.06345","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-19T11:08:54Z","cross_cats_sorted":[],"title_canon_sha256":"2fb710a9f44a1748c52a4076a94efb6143d3af5749be32d9910c701814253ff1","abstract_canon_sha256":"db3978c4f928d87a25ce5e6bee78a8a3b837eb5fb7c054f68fa30223b2765892"},"schema_version":"1.0"},"canonical_sha256":"403de67d946708ec4e9e3d8f5892713c8d709675d7b5146ba8d2d07cd098f859","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:53.467803Z","signature_b64":"53anYRQlLO6TY+N9G83ANIIbCJ7k9z/D4LfL1bAiF7/mEXsP+tAevG6wnFau0F/vMjJH2dUPRPkhnpXRWTfeCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"403de67d946708ec4e9e3d8f5892713c8d709675d7b5146ba8d2d07cd098f859","last_reissued_at":"2026-05-18T00:34:53.467124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:53.467124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.06345","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":"2026-05-18T00:34:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mucwYHqlZWzTv5PnLH0Qg4tJH7Twd5fTxpbtOCo6w19T/V72Q1WiEvF7A+GfAHjkjx0/orbCcHkdnMaBzxXIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:16:15.933956Z"},"content_sha256":"459c6f0647bec713effa2bf878de7aa2dffd77d5cb740bfe7cf8ab3e1a4c019f","schema_version":"1.0","event_id":"sha256:459c6f0647bec713effa2bf878de7aa2dffd77d5cb740bfe7cf8ab3e1a4c019f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IA66M7MUM4EOYTU6HWHVRETRHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trapped modes in thin and infinite ladder like domains. Part 1 : existence results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"B\\'erang\\`ere Delourme, Elizaveta Vasilevskaya, Patrick Joly (POEMS), Sonia Fliss (POEMS)","submitted_at":"2017-09-19T11:08:54Z","abstract_excerpt":"The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is a ladder like domain, namely a thin periodic structure (the thickness being characterized by a small parameter $\\epsilon > 0$) whose limit (as $\\epsilon$ tends to 0) is a periodic graph. The localized perturbation consists in changing the geometry of the reference medium by modifying the thickness of one rung of the ladder. Considering the scalar Helmholtz equation with Neumann boundary conditions in this do"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06345","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":"2026-05-18T00:34:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BOqeWxv3nVl6KNJErL/bA4m3xyFHVgQru5ddr8Y4tYGmV1dY2H8iAiAjZiwyfkoozIYAYkdOa7CJty77KoftAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T17:16:15.934302Z"},"content_sha256":"dd44bbddd0bedfd82946e16c21bcadab7b0ede26fe2ab321132cb0490a717748","schema_version":"1.0","event_id":"sha256:dd44bbddd0bedfd82946e16c21bcadab7b0ede26fe2ab321132cb0490a717748"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IA66M7MUM4EOYTU6HWHVRETRHS/bundle.json","state_url":"https://pith.science/pith/IA66M7MUM4EOYTU6HWHVRETRHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IA66M7MUM4EOYTU6HWHVRETRHS/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":"2026-06-03T17:16:15Z","links":{"resolver":"https://pith.science/pith/IA66M7MUM4EOYTU6HWHVRETRHS","bundle":"https://pith.science/pith/IA66M7MUM4EOYTU6HWHVRETRHS/bundle.json","state":"https://pith.science/pith/IA66M7MUM4EOYTU6HWHVRETRHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IA66M7MUM4EOYTU6HWHVRETRHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IA66M7MUM4EOYTU6HWHVRETRHS","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":"db3978c4f928d87a25ce5e6bee78a8a3b837eb5fb7c054f68fa30223b2765892","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-19T11:08:54Z","title_canon_sha256":"2fb710a9f44a1748c52a4076a94efb6143d3af5749be32d9910c701814253ff1"},"schema_version":"1.0","source":{"id":"1709.06345","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06345","created_at":"2026-05-18T00:34:53Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06345v1","created_at":"2026-05-18T00:34:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06345","created_at":"2026-05-18T00:34:53Z"},{"alias_kind":"pith_short_12","alias_value":"IA66M7MUM4EO","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IA66M7MUM4EOYTU6","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IA66M7MU","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:dd44bbddd0bedfd82946e16c21bcadab7b0ede26fe2ab321132cb0490a717748","target":"graph","created_at":"2026-05-18T00:34:53Z","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":"The present paper deals with the wave propagation in a particular two dimensional structure, obtained from a localized perturbation of a reference periodic medium. This reference medium is a ladder like domain, namely a thin periodic structure (the thickness being characterized by a small parameter $\\epsilon > 0$) whose limit (as $\\epsilon$ tends to 0) is a periodic graph. The localized perturbation consists in changing the geometry of the reference medium by modifying the thickness of one rung of the ladder. Considering the scalar Helmholtz equation with Neumann boundary conditions in this do","authors_text":"B\\'erang\\`ere Delourme, Elizaveta Vasilevskaya, Patrick Joly (POEMS), Sonia Fliss (POEMS)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-19T11:08:54Z","title":"Trapped modes in thin and infinite ladder like domains. Part 1 : existence results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06345","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":"sha256:459c6f0647bec713effa2bf878de7aa2dffd77d5cb740bfe7cf8ab3e1a4c019f","target":"record","created_at":"2026-05-18T00:34:53Z","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":"db3978c4f928d87a25ce5e6bee78a8a3b837eb5fb7c054f68fa30223b2765892","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-19T11:08:54Z","title_canon_sha256":"2fb710a9f44a1748c52a4076a94efb6143d3af5749be32d9910c701814253ff1"},"schema_version":"1.0","source":{"id":"1709.06345","kind":"arxiv","version":1}},"canonical_sha256":"403de67d946708ec4e9e3d8f5892713c8d709675d7b5146ba8d2d07cd098f859","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"403de67d946708ec4e9e3d8f5892713c8d709675d7b5146ba8d2d07cd098f859","first_computed_at":"2026-05-18T00:34:53.467124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:53.467124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"53anYRQlLO6TY+N9G83ANIIbCJ7k9z/D4LfL1bAiF7/mEXsP+tAevG6wnFau0F/vMjJH2dUPRPkhnpXRWTfeCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:53.467803Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06345","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:459c6f0647bec713effa2bf878de7aa2dffd77d5cb740bfe7cf8ab3e1a4c019f","sha256:dd44bbddd0bedfd82946e16c21bcadab7b0ede26fe2ab321132cb0490a717748"],"state_sha256":"99df6738b9523eede96e915e750de8a2677f5e7773157cf41c9ab8f23a15af3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LQ2aJ6apiEyHVwCRHAkdRTsgB45mPMVkg1tnA24tdfK6BydnbTsIubaU7C6A1ktOF5TpX/UZfShdNAKUZWMBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T17:16:15.936268Z","bundle_sha256":"4b01421d78f40a4af94898169a3bacaf8d6807ca480c41e38eacb1bfe60d9c94"}}