{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:J5LTPEUEYUNTX3UMRXRXHRHVOZ","short_pith_number":"pith:J5LTPEUE","schema_version":"1.0","canonical_sha256":"4f57379284c51b3bee8c8de373c4f57652baf54af0f2adbfba289be3cb4b4701","source":{"kind":"arxiv","id":"2503.18864","version":2},"attestation_state":"computed","paper":{"title":"The Graph Geometric Control Condition","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Alessandro Duca, Ka\\\"is Ammari, K\\'evin Le Balc'h, Romain Joly","submitted_at":"2025-03-24T16:39:48Z","abstract_excerpt":"In this paper, we introduce a novel concept called the Graph Geometric Control Condition (GGCC). It turns out to be a simple, geometric rewriting of many of the frameworks in which the controllability of PDEs on graphs has been studied. We prove that (GGCC) is a necessary and sufficient condition for the exact controllability of the wave equation on metric graphs with internal controls and Dirichlet boundary conditions. We then investigate the internal exact controllability of the wave equation with mixed boundary conditions and the one of the Schr\\\"odinger equation, as well as the internal nu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2503.18864","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.OC","submitted_at":"2025-03-24T16:39:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"6c6d4ca567d3292d3a153b80dd067242f3bee186a8ac475b47df8958069f9d18","abstract_canon_sha256":"0a0e78ad851fb34a4f7c1891afe5b6bc8c77353efa8152dc5a5462670c310ad9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:42:27.805482Z","signature_b64":"7vlMRj+idRrw5Oh9Tqbp8l26vDG7/ym8veS3Nbze6iva1Q8qiponUL6bL04Ytic/HglPfRkHsDhYp9WaqL2bCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f57379284c51b3bee8c8de373c4f57652baf54af0f2adbfba289be3cb4b4701","last_reissued_at":"2026-07-05T11:42:27.804927Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:42:27.804927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Graph Geometric Control Condition","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"Alessandro Duca, Ka\\\"is Ammari, K\\'evin Le Balc'h, Romain Joly","submitted_at":"2025-03-24T16:39:48Z","abstract_excerpt":"In this paper, we introduce a novel concept called the Graph Geometric Control Condition (GGCC). It turns out to be a simple, geometric rewriting of many of the frameworks in which the controllability of PDEs on graphs has been studied. We prove that (GGCC) is a necessary and sufficient condition for the exact controllability of the wave equation on metric graphs with internal controls and Dirichlet boundary conditions. We then investigate the internal exact controllability of the wave equation with mixed boundary conditions and the one of the Schr\\\"odinger equation, as well as the internal nu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.18864","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.18864/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2503.18864","created_at":"2026-07-05T11:42:27.804994+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.18864v2","created_at":"2026-07-05T11:42:27.804994+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.18864","created_at":"2026-07-05T11:42:27.804994+00:00"},{"alias_kind":"pith_short_12","alias_value":"J5LTPEUEYUNT","created_at":"2026-07-05T11:42:27.804994+00:00"},{"alias_kind":"pith_short_16","alias_value":"J5LTPEUEYUNTX3UM","created_at":"2026-07-05T11:42:27.804994+00:00"},{"alias_kind":"pith_short_8","alias_value":"J5LTPEUE","created_at":"2026-07-05T11:42:27.804994+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2511.10358","citing_title":"Observable sets for Schr\\\"odinger equations on combinatorial graphs","ref_index":1,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J5LTPEUEYUNTX3UMRXRXHRHVOZ","json":"https://pith.science/pith/J5LTPEUEYUNTX3UMRXRXHRHVOZ.json","graph_json":"https://pith.science/api/pith-number/J5LTPEUEYUNTX3UMRXRXHRHVOZ/graph.json","events_json":"https://pith.science/api/pith-number/J5LTPEUEYUNTX3UMRXRXHRHVOZ/events.json","paper":"https://pith.science/paper/J5LTPEUE"},"agent_actions":{"view_html":"https://pith.science/pith/J5LTPEUEYUNTX3UMRXRXHRHVOZ","download_json":"https://pith.science/pith/J5LTPEUEYUNTX3UMRXRXHRHVOZ.json","view_paper":"https://pith.science/paper/J5LTPEUE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.18864&json=true","fetch_graph":"https://pith.science/api/pith-number/J5LTPEUEYUNTX3UMRXRXHRHVOZ/graph.json","fetch_events":"https://pith.science/api/pith-number/J5LTPEUEYUNTX3UMRXRXHRHVOZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J5LTPEUEYUNTX3UMRXRXHRHVOZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J5LTPEUEYUNTX3UMRXRXHRHVOZ/action/storage_attestation","attest_author":"https://pith.science/pith/J5LTPEUEYUNTX3UMRXRXHRHVOZ/action/author_attestation","sign_citation":"https://pith.science/pith/J5LTPEUEYUNTX3UMRXRXHRHVOZ/action/citation_signature","submit_replication":"https://pith.science/pith/J5LTPEUEYUNTX3UMRXRXHRHVOZ/action/replication_record"}},"created_at":"2026-07-05T11:42:27.804994+00:00","updated_at":"2026-07-05T11:42:27.804994+00:00"}