{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SW4AT5LUY6U2NYYH6A2AJMWPAU","short_pith_number":"pith:SW4AT5LU","canonical_record":{"source":{"id":"2607.11702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T15:33:35Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"14b1841cc5ccbde9c6145b43a4dc84fa9b6d2373786681353c28dee6cf89d9a6","abstract_canon_sha256":"f302b20d041296e8c43b7c6530002f13fd0f94bb56b12fd8c36a2ab3a080972d"},"schema_version":"1.0"},"canonical_sha256":"95b809f574c7a9a6e307f03404b2cf05060f96914e32d125051b2c9fda19726f","source":{"kind":"arxiv","id":"2607.11702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.11702","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"2607.11702v1","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.11702","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"SW4AT5LUY6U2","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"pith_short_16","alias_value":"SW4AT5LUY6U2NYYH","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"pith_short_8","alias_value":"SW4AT5LU","created_at":"2026-07-14T02:22:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SW4AT5LUY6U2NYYH6A2AJMWPAU","target":"record","payload":{"canonical_record":{"source":{"id":"2607.11702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T15:33:35Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"14b1841cc5ccbde9c6145b43a4dc84fa9b6d2373786681353c28dee6cf89d9a6","abstract_canon_sha256":"f302b20d041296e8c43b7c6530002f13fd0f94bb56b12fd8c36a2ab3a080972d"},"schema_version":"1.0"},"canonical_sha256":"95b809f574c7a9a6e307f03404b2cf05060f96914e32d125051b2c9fda19726f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-14T02:22:19.848779Z","signature_b64":"V8CcRKVEKQ662qbS1d7tjVVp9OeUUDRGJMy4A5e9smmsdONjHhbfBj1Vw+sp3MF4qe2RDW+1Lh3aJ/GjN4qWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"95b809f574c7a9a6e307f03404b2cf05060f96914e32d125051b2c9fda19726f","last_reissued_at":"2026-07-14T02:22:19.847968Z","signature_status":"signed_v1","first_computed_at":"2026-07-14T02:22:19.847968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.11702","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":"2026-07-14T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S8jm886V2mhdCML66MLr/2gKmjUKWJUzh7d4ge7AHYyV2BlPJN0TGFpH1UiE+Tg78fJTJNSVUFg9nASojDfCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T06:21:25.097738Z"},"content_sha256":"c7a73df0e482090ca11f8078c212ccfe197f6998c31993fcc07af7840badf19e","schema_version":"1.0","event_id":"sha256:c7a73df0e482090ca11f8078c212ccfe197f6998c31993fcc07af7840badf19e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SW4AT5LUY6U2NYYH6A2AJMWPAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform controllability for the wave equation with large potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AP","authors_text":"Arthur Yax (LMO)","submitted_at":"2026-07-13T15:33:35Z","abstract_excerpt":"This paper investigates the dependence of the control cost for a wave equation with respect to perturbation by a time-independent potential $\\lmbd V$ scaled by a large parameter $\\lmbd$ on a compact Riemannian manifold. We introduce the geometric control condition~\\eqref{GCC+}, a variant of the geometric control condition of Bardos--Lebeau--Rauch--Taylor, tailored to accommodate the influence of the potential $V$. We show that~\\eqref{GCC+} is necessary and sufficient for the existence of a uniform \\emph{observability cost} with respect to the large parameter $\\lmbd$. We provide geometric examp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11702","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.11702/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-14T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NmZQcAiG3D9RJVCc45ALzT7Jh5LW0DZ0hmtxs1EMfj9PN9M3J4nn+PgiUJNCRVKZdFofI1Z2osMxbvkGeCG4BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T06:21:25.100091Z"},"content_sha256":"1c584280447155787e0b7c9770b23be15428c47ea3092b38fcba4589ed589f0e","schema_version":"1.0","event_id":"sha256:1c584280447155787e0b7c9770b23be15428c47ea3092b38fcba4589ed589f0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SW4AT5LUY6U2NYYH6A2AJMWPAU/bundle.json","state_url":"https://pith.science/pith/SW4AT5LUY6U2NYYH6A2AJMWPAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SW4AT5LUY6U2NYYH6A2AJMWPAU/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":"2026-08-20T06:21:25Z","links":{"resolver":"https://pith.science/pith/SW4AT5LUY6U2NYYH6A2AJMWPAU","bundle":"https://pith.science/pith/SW4AT5LUY6U2NYYH6A2AJMWPAU/bundle.json","state":"https://pith.science/pith/SW4AT5LUY6U2NYYH6A2AJMWPAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SW4AT5LUY6U2NYYH6A2AJMWPAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SW4AT5LUY6U2NYYH6A2AJMWPAU","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":"f302b20d041296e8c43b7c6530002f13fd0f94bb56b12fd8c36a2ab3a080972d","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T15:33:35Z","title_canon_sha256":"14b1841cc5ccbde9c6145b43a4dc84fa9b6d2373786681353c28dee6cf89d9a6"},"schema_version":"1.0","source":{"id":"2607.11702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.11702","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"2607.11702v1","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.11702","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"SW4AT5LUY6U2","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"pith_short_16","alias_value":"SW4AT5LUY6U2NYYH","created_at":"2026-07-14T02:22:19Z"},{"alias_kind":"pith_short_8","alias_value":"SW4AT5LU","created_at":"2026-07-14T02:22:19Z"}],"graph_snapshots":[{"event_id":"sha256:1c584280447155787e0b7c9770b23be15428c47ea3092b38fcba4589ed589f0e","target":"graph","created_at":"2026-07-14T02:22:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.11702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the dependence of the control cost for a wave equation with respect to perturbation by a time-independent potential $\\lmbd V$ scaled by a large parameter $\\lmbd$ on a compact Riemannian manifold. We introduce the geometric control condition~\\eqref{GCC+}, a variant of the geometric control condition of Bardos--Lebeau--Rauch--Taylor, tailored to accommodate the influence of the potential $V$. We show that~\\eqref{GCC+} is necessary and sufficient for the existence of a uniform \\emph{observability cost} with respect to the large parameter $\\lmbd$. We provide geometric examp","authors_text":"Arthur Yax (LMO)","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T15:33:35Z","title":"Uniform controllability for the wave equation with large potential"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11702","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:c7a73df0e482090ca11f8078c212ccfe197f6998c31993fcc07af7840badf19e","target":"record","created_at":"2026-07-14T02:22:19Z","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":"f302b20d041296e8c43b7c6530002f13fd0f94bb56b12fd8c36a2ab3a080972d","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-13T15:33:35Z","title_canon_sha256":"14b1841cc5ccbde9c6145b43a4dc84fa9b6d2373786681353c28dee6cf89d9a6"},"schema_version":"1.0","source":{"id":"2607.11702","kind":"arxiv","version":1}},"canonical_sha256":"95b809f574c7a9a6e307f03404b2cf05060f96914e32d125051b2c9fda19726f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95b809f574c7a9a6e307f03404b2cf05060f96914e32d125051b2c9fda19726f","first_computed_at":"2026-07-14T02:22:19.847968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T02:22:19.847968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V8CcRKVEKQ662qbS1d7tjVVp9OeUUDRGJMy4A5e9smmsdONjHhbfBj1Vw+sp3MF4qe2RDW+1Lh3aJ/GjN4qWBQ==","signature_status":"signed_v1","signed_at":"2026-07-14T02:22:19.848779Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.11702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7a73df0e482090ca11f8078c212ccfe197f6998c31993fcc07af7840badf19e","sha256:1c584280447155787e0b7c9770b23be15428c47ea3092b38fcba4589ed589f0e"],"state_sha256":"9397fa5b70d01a662d5199c3dead08ab83b1a42544137181a40d7e69d541a1f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UKaQ5dnOxGKiJgmmDZfrOjKtdh3TlM80eID6lPgciFE8VwMnYHasOV0z4EQ40ohydbk59d3TOIDda30p+3bABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T06:21:25.106788Z","bundle_sha256":"a0e2d645f514625831353499035546b5cd2f7f5ec580363419b024b73aab7016"}}