{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:23WELLVASFJ2QEUEUW4ODEA66O","short_pith_number":"pith:23WELLVA","canonical_record":{"source":{"id":"1204.4998","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-23T08:33:20Z","cross_cats_sorted":[],"title_canon_sha256":"a515ece14bf0042d2885f6d451666f17d6212c8a315cc6c9057decb8801dfb41","abstract_canon_sha256":"2b00bb6df509363c8af92c739600a4d0489ddb1570f554629bb327eee336f687"},"schema_version":"1.0"},"canonical_sha256":"d6ec45aea09153a81284a5b8e1901ef3b349f96a7247bcac8eb20ff5ea78c2c8","source":{"kind":"arxiv","id":"1204.4998","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4998","created_at":"2026-05-18T02:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4998v2","created_at":"2026-05-18T02:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4998","created_at":"2026-05-18T02:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"23WELLVASFJ2","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"23WELLVASFJ2QEUE","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"23WELLVA","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:23WELLVASFJ2QEUEUW4ODEA66O","target":"record","payload":{"canonical_record":{"source":{"id":"1204.4998","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-23T08:33:20Z","cross_cats_sorted":[],"title_canon_sha256":"a515ece14bf0042d2885f6d451666f17d6212c8a315cc6c9057decb8801dfb41","abstract_canon_sha256":"2b00bb6df509363c8af92c739600a4d0489ddb1570f554629bb327eee336f687"},"schema_version":"1.0"},"canonical_sha256":"d6ec45aea09153a81284a5b8e1901ef3b349f96a7247bcac8eb20ff5ea78c2c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:40.738150Z","signature_b64":"+LxYKnBW0UufW8crxej217qjibqUYmqHnVskWn9+BHlisZvWFUYVZK6DsrgjduDfqrvJPWHikCMIeo5pBsdNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d6ec45aea09153a81284a5b8e1901ef3b349f96a7247bcac8eb20ff5ea78c2c8","last_reissued_at":"2026-05-18T02:50:40.737533Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:40.737533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.4998","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":"2026-05-18T02:50:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+tN566xBlAar49blITguC6MJf6hbqXSykuu4oJKGFHd6wn99grF15vApLIyV9V9+notOmjoU8MCoTWNpvxdzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:51:08.629476Z"},"content_sha256":"4afc493acc17837f04b7a22b31cdadcd4ac5c7a98c55b86eb156895e3b26a295","schema_version":"1.0","event_id":"sha256:4afc493acc17837f04b7a22b31cdadcd4ac5c7a98c55b86eb156895e3b26a295"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:23WELLVASFJ2QEUEUW4ODEA66O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dispersive effects and high frequency behaviour for the Schr\\\"odinger equation in star-shaped networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felix Ali Mehmeti, Ka\\\"is Ammari, Serge Nicaise","submitted_at":"2012-04-23T08:33:20Z","abstract_excerpt":"We prove the time decay estimates $L^1({\\cal R}) \\rightarrow L^\\infty ({\\cal R}),$ where ${\\cal R}$ is an infinite star-shaped network, for the Schr\\\"odinger group $e^{it(- \\frac{d^2}{dx^2} + V)}$ for real-valued potentials $V$ satisfying some regularity and decay assumptions. Further we show that the solution for initial conditions with a lower cutoff frequency tends to the free solution, if the cutoff frequency tends to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4998","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":"2026-05-18T02:50:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZkrKTAC5Ycj5YB0FqiJ43joVzH3em16kyYIhNsqQm30cXzpWlK/mRR3l4NT8lPgYEkEkxRNI+47lTFiYtQxZDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:51:08.629823Z"},"content_sha256":"75891a3d71cfb928c20d95de0828668729039663336a2ca22aa80f1d1fca6935","schema_version":"1.0","event_id":"sha256:75891a3d71cfb928c20d95de0828668729039663336a2ca22aa80f1d1fca6935"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/23WELLVASFJ2QEUEUW4ODEA66O/bundle.json","state_url":"https://pith.science/pith/23WELLVASFJ2QEUEUW4ODEA66O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/23WELLVASFJ2QEUEUW4ODEA66O/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":"2026-06-23T16:51:08Z","links":{"resolver":"https://pith.science/pith/23WELLVASFJ2QEUEUW4ODEA66O","bundle":"https://pith.science/pith/23WELLVASFJ2QEUEUW4ODEA66O/bundle.json","state":"https://pith.science/pith/23WELLVASFJ2QEUEUW4ODEA66O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/23WELLVASFJ2QEUEUW4ODEA66O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:23WELLVASFJ2QEUEUW4ODEA66O","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":"2b00bb6df509363c8af92c739600a4d0489ddb1570f554629bb327eee336f687","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-23T08:33:20Z","title_canon_sha256":"a515ece14bf0042d2885f6d451666f17d6212c8a315cc6c9057decb8801dfb41"},"schema_version":"1.0","source":{"id":"1204.4998","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.4998","created_at":"2026-05-18T02:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"1204.4998v2","created_at":"2026-05-18T02:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.4998","created_at":"2026-05-18T02:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"23WELLVASFJ2","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"23WELLVASFJ2QEUE","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"23WELLVA","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:75891a3d71cfb928c20d95de0828668729039663336a2ca22aa80f1d1fca6935","target":"graph","created_at":"2026-05-18T02:50:40Z","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 prove the time decay estimates $L^1({\\cal R}) \\rightarrow L^\\infty ({\\cal R}),$ where ${\\cal R}$ is an infinite star-shaped network, for the Schr\\\"odinger group $e^{it(- \\frac{d^2}{dx^2} + V)}$ for real-valued potentials $V$ satisfying some regularity and decay assumptions. Further we show that the solution for initial conditions with a lower cutoff frequency tends to the free solution, if the cutoff frequency tends to infinity.","authors_text":"Felix Ali Mehmeti, Ka\\\"is Ammari, Serge Nicaise","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-23T08:33:20Z","title":"Dispersive effects and high frequency behaviour for the Schr\\\"odinger equation in star-shaped networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4998","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":"sha256:4afc493acc17837f04b7a22b31cdadcd4ac5c7a98c55b86eb156895e3b26a295","target":"record","created_at":"2026-05-18T02:50:40Z","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":"2b00bb6df509363c8af92c739600a4d0489ddb1570f554629bb327eee336f687","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-04-23T08:33:20Z","title_canon_sha256":"a515ece14bf0042d2885f6d451666f17d6212c8a315cc6c9057decb8801dfb41"},"schema_version":"1.0","source":{"id":"1204.4998","kind":"arxiv","version":2}},"canonical_sha256":"d6ec45aea09153a81284a5b8e1901ef3b349f96a7247bcac8eb20ff5ea78c2c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6ec45aea09153a81284a5b8e1901ef3b349f96a7247bcac8eb20ff5ea78c2c8","first_computed_at":"2026-05-18T02:50:40.737533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:40.737533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+LxYKnBW0UufW8crxej217qjibqUYmqHnVskWn9+BHlisZvWFUYVZK6DsrgjduDfqrvJPWHikCMIeo5pBsdNBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:40.738150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.4998","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4afc493acc17837f04b7a22b31cdadcd4ac5c7a98c55b86eb156895e3b26a295","sha256:75891a3d71cfb928c20d95de0828668729039663336a2ca22aa80f1d1fca6935"],"state_sha256":"c03ff6e306acdf8e2b0218489137a5e906603da0c0cf86e86946a1c0436bcd62"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61uakC9RiXyRLX6BlW6G2JTYxgvl/Ht4uUmddDEFVJWM6MRmPk33WAuic8TbA9adSBYEmvF0gm5zUO8SzQNNCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:51:08.631809Z","bundle_sha256":"7cc1f458012d91988e6465cf695535e369c13a1a4203d9c0b133eb56d30ff19d"}}