{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IOE3U22JZFDEIQ2WF3KTECZJPK","short_pith_number":"pith:IOE3U22J","canonical_record":{"source":{"id":"1604.02436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-04-08T19:34:01Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"ec19c57f18b1576df7f5db80dd8a00d95797d2d9ded8c98c8cb7a4d74df45a89","abstract_canon_sha256":"963ae610aaa5733308d1796198cf33b2e10736a7120001576fef3a2658ea79cb"},"schema_version":"1.0"},"canonical_sha256":"4389ba6b49c9464443562ed5320b297ab2f1d2028ef84bc4c21ccb852db81a2c","source":{"kind":"arxiv","id":"1604.02436","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02436","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02436v1","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02436","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"IOE3U22JZFDE","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IOE3U22JZFDEIQ2W","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IOE3U22J","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IOE3U22JZFDEIQ2WF3KTECZJPK","target":"record","payload":{"canonical_record":{"source":{"id":"1604.02436","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-04-08T19:34:01Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"ec19c57f18b1576df7f5db80dd8a00d95797d2d9ded8c98c8cb7a4d74df45a89","abstract_canon_sha256":"963ae610aaa5733308d1796198cf33b2e10736a7120001576fef3a2658ea79cb"},"schema_version":"1.0"},"canonical_sha256":"4389ba6b49c9464443562ed5320b297ab2f1d2028ef84bc4c21ccb852db81a2c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:10.772568Z","signature_b64":"ib7Ydho8DLXlAKCPq3zAw5KG6Lcj1KJZHgFxv6Um1NF0+itMIJeBeYWE520Xk8gcvue5EyQ/tZFnX72y0GVQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4389ba6b49c9464443562ed5320b297ab2f1d2028ef84bc4c21ccb852db81a2c","last_reissued_at":"2026-05-18T00:01:10.771871Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:10.771871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.02436","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":"2026-05-18T00:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h4HHLdH4c5hCz5jial1Y9ajbQN4IX5TIrtq9YdYkpMEYBQffOo17Ixq/3UMMRtumyIVm7jSLL945EnO9/xmlDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:12:44.940034Z"},"content_sha256":"e59830dca5d036e552b9d299c2986f3ef684d847cbd0df8e526de954000edb44","schema_version":"1.0","event_id":"sha256:e59830dca5d036e552b9d299c2986f3ef684d847cbd0df8e526de954000edb44"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IOE3U22JZFDEIQ2WF3KTECZJPK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schroedinger operators on exterior domains with Robin boundary conditions: heat kernel estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.SP","authors_text":"Delio Mugnolo, Hynek Kovarik","submitted_at":"2016-04-08T19:34:01Z","abstract_excerpt":"We study Schroedinger operators with Robin boundary conditions on exterior domains in $\\R^d$. We prove sharp point-wise estimates for the associated semi-groups which show, in particular, how the boundary conditions affect the time decay of the heat kernel in dimensions one and two. Applications to spectral estimates are discussed as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02436","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":""},"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":"2026-05-18T00:01:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPuxa4cCB/pAfbkFx8AHFupjs22QFf+P/GCjP4RDbdktU38L1yfja40F6RH2O3c22pJjX57SZ+QrongV1U1UDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:12:44.940386Z"},"content_sha256":"7669bb3a2ca76626e09eb2b0c481d18904b34c482a88f3e6d460d1d3cb17e707","schema_version":"1.0","event_id":"sha256:7669bb3a2ca76626e09eb2b0c481d18904b34c482a88f3e6d460d1d3cb17e707"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IOE3U22JZFDEIQ2WF3KTECZJPK/bundle.json","state_url":"https://pith.science/pith/IOE3U22JZFDEIQ2WF3KTECZJPK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IOE3U22JZFDEIQ2WF3KTECZJPK/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":"2026-06-02T07:12:44Z","links":{"resolver":"https://pith.science/pith/IOE3U22JZFDEIQ2WF3KTECZJPK","bundle":"https://pith.science/pith/IOE3U22JZFDEIQ2WF3KTECZJPK/bundle.json","state":"https://pith.science/pith/IOE3U22JZFDEIQ2WF3KTECZJPK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IOE3U22JZFDEIQ2WF3KTECZJPK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IOE3U22JZFDEIQ2WF3KTECZJPK","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":"963ae610aaa5733308d1796198cf33b2e10736a7120001576fef3a2658ea79cb","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-04-08T19:34:01Z","title_canon_sha256":"ec19c57f18b1576df7f5db80dd8a00d95797d2d9ded8c98c8cb7a4d74df45a89"},"schema_version":"1.0","source":{"id":"1604.02436","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.02436","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"arxiv_version","alias_value":"1604.02436v1","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.02436","created_at":"2026-05-18T00:01:10Z"},{"alias_kind":"pith_short_12","alias_value":"IOE3U22JZFDE","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IOE3U22JZFDEIQ2W","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IOE3U22J","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:7669bb3a2ca76626e09eb2b0c481d18904b34c482a88f3e6d460d1d3cb17e707","target":"graph","created_at":"2026-05-18T00:01:10Z","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 study Schroedinger operators with Robin boundary conditions on exterior domains in $\\R^d$. We prove sharp point-wise estimates for the associated semi-groups which show, in particular, how the boundary conditions affect the time decay of the heat kernel in dimensions one and two. Applications to spectral estimates are discussed as well.","authors_text":"Delio Mugnolo, Hynek Kovarik","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-04-08T19:34:01Z","title":"Schroedinger operators on exterior domains with Robin boundary conditions: heat kernel estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02436","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:e59830dca5d036e552b9d299c2986f3ef684d847cbd0df8e526de954000edb44","target":"record","created_at":"2026-05-18T00:01:10Z","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":"963ae610aaa5733308d1796198cf33b2e10736a7120001576fef3a2658ea79cb","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2016-04-08T19:34:01Z","title_canon_sha256":"ec19c57f18b1576df7f5db80dd8a00d95797d2d9ded8c98c8cb7a4d74df45a89"},"schema_version":"1.0","source":{"id":"1604.02436","kind":"arxiv","version":1}},"canonical_sha256":"4389ba6b49c9464443562ed5320b297ab2f1d2028ef84bc4c21ccb852db81a2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4389ba6b49c9464443562ed5320b297ab2f1d2028ef84bc4c21ccb852db81a2c","first_computed_at":"2026-05-18T00:01:10.771871Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:10.771871Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ib7Ydho8DLXlAKCPq3zAw5KG6Lcj1KJZHgFxv6Um1NF0+itMIJeBeYWE520Xk8gcvue5EyQ/tZFnX72y0GVQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:10.772568Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.02436","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e59830dca5d036e552b9d299c2986f3ef684d847cbd0df8e526de954000edb44","sha256:7669bb3a2ca76626e09eb2b0c481d18904b34c482a88f3e6d460d1d3cb17e707"],"state_sha256":"6430594d004a19ed11eae89117c93c37d4ac29fea8edc074531c806a62af9381"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9glaFN9xlzV0tH26ZSkK8C3B9q6ag5+Cayp/HyXvzpmfn+x2cQrENRjo+H8tR3FSXEuJtojRZat5wIksMqJBBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:12:44.942359Z","bundle_sha256":"237e857d2356ded85f26637ef3754a2dd60e9eced7146faca81104811689efd6"}}