{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:XDTK3UUV2M3UKUW6ZYFZEK7KDZ","short_pith_number":"pith:XDTK3UUV","canonical_record":{"source":{"id":"1111.1140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-04T14:32:53Z","cross_cats_sorted":[],"title_canon_sha256":"7c7063187f275320aa1ec4f0c70b46d098e48ed70c8abd6f3d75d22a4306e12c","abstract_canon_sha256":"193316cd033518c5231b5534633b0e484de7a4331cb3b6e42593c560422a5a75"},"schema_version":"1.0"},"canonical_sha256":"b8e6add295d3374552dece0b922bea1e55fd51cc0408175565368a80fcee1161","source":{"kind":"arxiv","id":"1111.1140","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1140","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1140v1","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1140","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"pith_short_12","alias_value":"XDTK3UUV2M3U","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XDTK3UUV2M3UKUW6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XDTK3UUV","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:XDTK3UUV2M3UKUW6ZYFZEK7KDZ","target":"record","payload":{"canonical_record":{"source":{"id":"1111.1140","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-04T14:32:53Z","cross_cats_sorted":[],"title_canon_sha256":"7c7063187f275320aa1ec4f0c70b46d098e48ed70c8abd6f3d75d22a4306e12c","abstract_canon_sha256":"193316cd033518c5231b5534633b0e484de7a4331cb3b6e42593c560422a5a75"},"schema_version":"1.0"},"canonical_sha256":"b8e6add295d3374552dece0b922bea1e55fd51cc0408175565368a80fcee1161","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:09:35.650497Z","signature_b64":"TspONu66pVo4vD+/ky8LgRkFDAUr3htFhVllohAD8y3EglG4tSk1yvbK3Bxvkg2PUyqYKA7yUUTaHkZWV1UXBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8e6add295d3374552dece0b922bea1e55fd51cc0408175565368a80fcee1161","last_reissued_at":"2026-05-18T04:09:35.650053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:09:35.650053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.1140","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":"2026-05-18T04:09:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8WM9wUrABSZrIlJtxY+Vb9XU/pa/P0iuZwvSkxUACGVXLxwz0QGVoy7B1R7NcxvtVUioLdZpbW/04wHU1yChDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:50:36.531787Z"},"content_sha256":"195e8092646ab350ee5225dc04a35c2c6b5f995e3a2bb2a2f387063294413619","schema_version":"1.0","event_id":"sha256:195e8092646ab350ee5225dc04a35c2c6b5f995e3a2bb2a2f387063294413619"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:XDTK3UUV2M3UKUW6ZYFZEK7KDZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy flow above the threshold of tunnel effect","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felix Ali Mehmeti, Robert Haller-Dintelmann, Virginie R\\'egnier","submitted_at":"2011-11-04T14:32:53Z","abstract_excerpt":"We consider the Klein-Gordon equation on two half-axes connected at their origins. We add a potential that is constant but different on each branch. In a previous paper, we studied the L-infinity-time decay via H\\\"ormander's version of the stationary phase method. Here we apply these results to show that for initial conditions in an energy band above the threshold of the tunnel effect a fixed portion of the energy propagates between group lines. Further we consider the situation that the potential difference tends to infinity while the energy band of the initial condition is shifted upwards su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1140","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":"2026-05-18T04:09:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n5gK97fjLb3j2pxpmXJfZDZGxolQ1KPhxVE/Ke+34CnB6BpqaGA8oR3geZp1oMw/N40AS1HRri6R9uEtQXZCDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T14:50:36.532137Z"},"content_sha256":"1bc443d3f1f57f06c77aae13d7480ea3b0d170dd54c4da0d24c1eb5bc2ae2fb6","schema_version":"1.0","event_id":"sha256:1bc443d3f1f57f06c77aae13d7480ea3b0d170dd54c4da0d24c1eb5bc2ae2fb6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XDTK3UUV2M3UKUW6ZYFZEK7KDZ/bundle.json","state_url":"https://pith.science/pith/XDTK3UUV2M3UKUW6ZYFZEK7KDZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XDTK3UUV2M3UKUW6ZYFZEK7KDZ/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":"2026-06-04T14:50:36Z","links":{"resolver":"https://pith.science/pith/XDTK3UUV2M3UKUW6ZYFZEK7KDZ","bundle":"https://pith.science/pith/XDTK3UUV2M3UKUW6ZYFZEK7KDZ/bundle.json","state":"https://pith.science/pith/XDTK3UUV2M3UKUW6ZYFZEK7KDZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XDTK3UUV2M3UKUW6ZYFZEK7KDZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:XDTK3UUV2M3UKUW6ZYFZEK7KDZ","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":"193316cd033518c5231b5534633b0e484de7a4331cb3b6e42593c560422a5a75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-04T14:32:53Z","title_canon_sha256":"7c7063187f275320aa1ec4f0c70b46d098e48ed70c8abd6f3d75d22a4306e12c"},"schema_version":"1.0","source":{"id":"1111.1140","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.1140","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"arxiv_version","alias_value":"1111.1140v1","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.1140","created_at":"2026-05-18T04:09:35Z"},{"alias_kind":"pith_short_12","alias_value":"XDTK3UUV2M3U","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"XDTK3UUV2M3UKUW6","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"XDTK3UUV","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:1bc443d3f1f57f06c77aae13d7480ea3b0d170dd54c4da0d24c1eb5bc2ae2fb6","target":"graph","created_at":"2026-05-18T04:09:35Z","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 the Klein-Gordon equation on two half-axes connected at their origins. We add a potential that is constant but different on each branch. In a previous paper, we studied the L-infinity-time decay via H\\\"ormander's version of the stationary phase method. Here we apply these results to show that for initial conditions in an energy band above the threshold of the tunnel effect a fixed portion of the energy propagates between group lines. Further we consider the situation that the potential difference tends to infinity while the energy band of the initial condition is shifted upwards su","authors_text":"Felix Ali Mehmeti, Robert Haller-Dintelmann, Virginie R\\'egnier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-04T14:32:53Z","title":"Energy flow above the threshold of tunnel effect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1140","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":"sha256:195e8092646ab350ee5225dc04a35c2c6b5f995e3a2bb2a2f387063294413619","target":"record","created_at":"2026-05-18T04:09:35Z","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":"193316cd033518c5231b5534633b0e484de7a4331cb3b6e42593c560422a5a75","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-11-04T14:32:53Z","title_canon_sha256":"7c7063187f275320aa1ec4f0c70b46d098e48ed70c8abd6f3d75d22a4306e12c"},"schema_version":"1.0","source":{"id":"1111.1140","kind":"arxiv","version":1}},"canonical_sha256":"b8e6add295d3374552dece0b922bea1e55fd51cc0408175565368a80fcee1161","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8e6add295d3374552dece0b922bea1e55fd51cc0408175565368a80fcee1161","first_computed_at":"2026-05-18T04:09:35.650053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:35.650053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TspONu66pVo4vD+/ky8LgRkFDAUr3htFhVllohAD8y3EglG4tSk1yvbK3Bxvkg2PUyqYKA7yUUTaHkZWV1UXBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:35.650497Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.1140","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:195e8092646ab350ee5225dc04a35c2c6b5f995e3a2bb2a2f387063294413619","sha256:1bc443d3f1f57f06c77aae13d7480ea3b0d170dd54c4da0d24c1eb5bc2ae2fb6"],"state_sha256":"6708c5fcc0b3e9d2a4aa88f5324b4955c3915f752b73b3a1cb4a3f401d751ead"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lcdu2P+gKunJFzo5hCedxN7zQIPBgYoQk8MMp0AiMkbZeqUDaSmC8j3l/N+OcTXhbC0IaYeyuZhCyR4YkjALCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T14:50:36.534082Z","bundle_sha256":"cd80cf6a46681ce9745fceb8c28255b5cfef1430087dd81c1748e2bfe10dc7bb"}}