{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZO5RSTQ45WAHNJ653S5EKQN7NC","short_pith_number":"pith:ZO5RSTQ4","canonical_record":{"source":{"id":"1808.04202","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-13T13:37:26Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"ac75d5565c6e836d5d2fb0cc1ffdb824e73b66eafe924e888440b5020522c21e","abstract_canon_sha256":"6204cff6fe839f69359f38a9271b88cd0812f9580635731c12a4b4e08645c71e"},"schema_version":"1.0"},"canonical_sha256":"cbbb194e1ced8076a7dddcba4541bf68aa5c17b805f57d5481f2ffb31ef7f09c","source":{"kind":"arxiv","id":"1808.04202","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04202","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04202v2","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04202","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZO5RSTQ45WAH","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"pith_short_16","alias_value":"ZO5RSTQ45WAHNJ65","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"pith_short_8","alias_value":"ZO5RSTQ4","created_at":"2026-07-05T00:33:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZO5RSTQ45WAHNJ653S5EKQN7NC","target":"record","payload":{"canonical_record":{"source":{"id":"1808.04202","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-13T13:37:26Z","cross_cats_sorted":["math.MP","math.SP"],"title_canon_sha256":"ac75d5565c6e836d5d2fb0cc1ffdb824e73b66eafe924e888440b5020522c21e","abstract_canon_sha256":"6204cff6fe839f69359f38a9271b88cd0812f9580635731c12a4b4e08645c71e"},"schema_version":"1.0"},"canonical_sha256":"cbbb194e1ced8076a7dddcba4541bf68aa5c17b805f57d5481f2ffb31ef7f09c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:33:32.695193Z","signature_b64":"7/wOoS5NJJUecIRMQ6Vxa/xzSPYRSag+dDe280Y397N1TSXN3omL+SXmB5hxHGx/AE2fjQoF+M8PooIieuEsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbbb194e1ced8076a7dddcba4541bf68aa5c17b805f57d5481f2ffb31ef7f09c","last_reissued_at":"2026-07-05T00:33:32.694804Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:33:32.694804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.04202","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":"2026-07-05T00:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QHuo1nEWUnvl79sob3wZRy3lnzJbSoOpH29ucMKJnA0e6B29qCwP6NLCzYI+oAIBlf/KGM6WTBweNb0YPMzKCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:08:29.598220Z"},"content_sha256":"a883de6ae76e68fbf8ff68a78ee96679ad53d1ab7f9b1bf989e61a8f13294539","schema_version":"1.0","event_id":"sha256:a883de6ae76e68fbf8ff68a78ee96679ad53d1ab7f9b1bf989e61a8f13294539"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZO5RSTQ45WAHNJ653S5EKQN7NC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lower bounds for Dirichlet Laplacians and uncertainty principles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"G\\\"unter Stolz, Peter Stollmann","submitted_at":"2018-08-13T13:37:26Z","abstract_excerpt":"We prove lower bounds for the Dirichlet Laplacian on possibly unbounded domains in terms of natural geometric conditions. This is used to derive uncertainty principles for low energy functions of general elliptic second order divergence form operators with not necessarily continuous main part."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04202","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/1808.04202/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":"2026-07-05T00:33:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9P8lP0zQ5VHcrrMx/0fVZGEL2QH0ILRlpxUe8QEMVOuc8EKTY6Dtp1+b5zfwlAcFciH7MQ58yxc6fJ9zuo6EBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T22:08:29.598783Z"},"content_sha256":"7b56e36ac81d773922f55a98b34d11bbd4c65bcda6f782a8794215c331ae528b","schema_version":"1.0","event_id":"sha256:7b56e36ac81d773922f55a98b34d11bbd4c65bcda6f782a8794215c331ae528b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZO5RSTQ45WAHNJ653S5EKQN7NC/bundle.json","state_url":"https://pith.science/pith/ZO5RSTQ45WAHNJ653S5EKQN7NC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZO5RSTQ45WAHNJ653S5EKQN7NC/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":"2026-08-13T22:08:29Z","links":{"resolver":"https://pith.science/pith/ZO5RSTQ45WAHNJ653S5EKQN7NC","bundle":"https://pith.science/pith/ZO5RSTQ45WAHNJ653S5EKQN7NC/bundle.json","state":"https://pith.science/pith/ZO5RSTQ45WAHNJ653S5EKQN7NC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZO5RSTQ45WAHNJ653S5EKQN7NC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZO5RSTQ45WAHNJ653S5EKQN7NC","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":"6204cff6fe839f69359f38a9271b88cd0812f9580635731c12a4b4e08645c71e","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-13T13:37:26Z","title_canon_sha256":"ac75d5565c6e836d5d2fb0cc1ffdb824e73b66eafe924e888440b5020522c21e"},"schema_version":"1.0","source":{"id":"1808.04202","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04202","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04202v2","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04202","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZO5RSTQ45WAH","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"pith_short_16","alias_value":"ZO5RSTQ45WAHNJ65","created_at":"2026-07-05T00:33:32Z"},{"alias_kind":"pith_short_8","alias_value":"ZO5RSTQ4","created_at":"2026-07-05T00:33:32Z"}],"graph_snapshots":[{"event_id":"sha256:7b56e36ac81d773922f55a98b34d11bbd4c65bcda6f782a8794215c331ae528b","target":"graph","created_at":"2026-07-05T00:33:32Z","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/1808.04202/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove lower bounds for the Dirichlet Laplacian on possibly unbounded domains in terms of natural geometric conditions. This is used to derive uncertainty principles for low energy functions of general elliptic second order divergence form operators with not necessarily continuous main part.","authors_text":"G\\\"unter Stolz, Peter Stollmann","cross_cats":["math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-13T13:37:26Z","title":"Lower bounds for Dirichlet Laplacians and uncertainty principles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04202","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:a883de6ae76e68fbf8ff68a78ee96679ad53d1ab7f9b1bf989e61a8f13294539","target":"record","created_at":"2026-07-05T00:33:32Z","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":"6204cff6fe839f69359f38a9271b88cd0812f9580635731c12a4b4e08645c71e","cross_cats_sorted":["math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-08-13T13:37:26Z","title_canon_sha256":"ac75d5565c6e836d5d2fb0cc1ffdb824e73b66eafe924e888440b5020522c21e"},"schema_version":"1.0","source":{"id":"1808.04202","kind":"arxiv","version":2}},"canonical_sha256":"cbbb194e1ced8076a7dddcba4541bf68aa5c17b805f57d5481f2ffb31ef7f09c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbbb194e1ced8076a7dddcba4541bf68aa5c17b805f57d5481f2ffb31ef7f09c","first_computed_at":"2026-07-05T00:33:32.694804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:33:32.694804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7/wOoS5NJJUecIRMQ6Vxa/xzSPYRSag+dDe280Y397N1TSXN3omL+SXmB5hxHGx/AE2fjQoF+M8PooIieuEsCg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:33:32.695193Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.04202","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a883de6ae76e68fbf8ff68a78ee96679ad53d1ab7f9b1bf989e61a8f13294539","sha256:7b56e36ac81d773922f55a98b34d11bbd4c65bcda6f782a8794215c331ae528b"],"state_sha256":"8336758058a282737344b794e02aa4176125f2355a0a017318e95fc4883fb6b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WG82Hud2RFoKmUDG26XY4D6jLDHvVI2yfkvfTey8GlM2qO0hPI7tckW/X4wjeVX9Unm/D3yAOYjhg/UKNbyxAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T22:08:29.615732Z","bundle_sha256":"372d6db8952ae632b173b43d054095e97ce6c221f0265f15a7010f7a06ea5a17"}}