{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LJORFXPFHBP5EGG3JBCIKGEZD6","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":"81b6979cf923b29acad046ffb16746956c783c18ad6c94a91af01a0128e07b6f","cross_cats_sorted":["cs.IT","math.DG","math.DS","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-22T01:26:27Z","title_canon_sha256":"05d13105832f49e4d7028e7904eee85282f63d2db5452ad47ee07b1252f0747b"},"schema_version":"1.0","source":{"id":"1207.5191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5191","created_at":"2026-05-18T03:50:24Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5191v1","created_at":"2026-05-18T03:50:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5191","created_at":"2026-05-18T03:50:24Z"},{"alias_kind":"pith_short_12","alias_value":"LJORFXPFHBP5","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LJORFXPFHBP5EGG3","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LJORFXPF","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:361cd20087e996c29715909865b383bf194feb54715fdafd767323b45ebd5da6","target":"graph","created_at":"2026-05-18T03:50:24Z","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":"In this paper, we study the schrodinger equation and wave equation with the Dirichlet boundary condition on a connected finite graph. The explicit expressions for solutions are given and the energy conservations are derived. Applications to the corresponding nonlinear problems are indicated.","authors_text":"Li Ma, X. Y. Wang","cross_cats":["cs.IT","math.DG","math.DS","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-22T01:26:27Z","title":"Schrodinger equation and wave equation on finite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5191","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:f4860da6520006ebb13c7ee15e2b212ee1b38c0bb6fc030b910ba2a43d66c1d9","target":"record","created_at":"2026-05-18T03:50:24Z","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":"81b6979cf923b29acad046ffb16746956c783c18ad6c94a91af01a0128e07b6f","cross_cats_sorted":["cs.IT","math.DG","math.DS","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-22T01:26:27Z","title_canon_sha256":"05d13105832f49e4d7028e7904eee85282f63d2db5452ad47ee07b1252f0747b"},"schema_version":"1.0","source":{"id":"1207.5191","kind":"arxiv","version":1}},"canonical_sha256":"5a5d12dde5385fd218db48448518991f8f083921ff42ef37f6a1fd02044956c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a5d12dde5385fd218db48448518991f8f083921ff42ef37f6a1fd02044956c5","first_computed_at":"2026-05-18T03:50:24.212213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:24.212213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fr3cZfAVerhon9lU2tpfZ+tQ66x/zOFJayhw7yQix4DdXMI6s8i3u+9fZf4cxgH4X2tOVyHx90HJKnJUFuzgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:24.213006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4860da6520006ebb13c7ee15e2b212ee1b38c0bb6fc030b910ba2a43d66c1d9","sha256:361cd20087e996c29715909865b383bf194feb54715fdafd767323b45ebd5da6"],"state_sha256":"a85fe046b9e3245b572f3db2dccc7aac42ec7993ba9b017539d7ab13f0c1172d"}