{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FS2Q2WRYBZXLP6LPMO3UN5X4WR","short_pith_number":"pith:FS2Q2WRY","canonical_record":{"source":{"id":"1101.1806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-10T13:22:37Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"294a805fa2db514a1196141ddc42fdb283df04799456be038650aa1d55f7410d","abstract_canon_sha256":"66882ddf4a9b19304262b0e2dd355d885a0e704c6ec6b38155dd88da0e145066"},"schema_version":"1.0"},"canonical_sha256":"2cb50d5a380e6eb7f96f63b746f6fcb45f92c2692d8de1af588fc3a1b07f8306","source":{"kind":"arxiv","id":"1101.1806","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1806","created_at":"2026-05-18T03:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1806v1","created_at":"2026-05-18T03:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1806","created_at":"2026-05-18T03:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"FS2Q2WRYBZXL","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FS2Q2WRYBZXLP6LP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FS2Q2WRY","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FS2Q2WRYBZXLP6LPMO3UN5X4WR","target":"record","payload":{"canonical_record":{"source":{"id":"1101.1806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-10T13:22:37Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"294a805fa2db514a1196141ddc42fdb283df04799456be038650aa1d55f7410d","abstract_canon_sha256":"66882ddf4a9b19304262b0e2dd355d885a0e704c6ec6b38155dd88da0e145066"},"schema_version":"1.0"},"canonical_sha256":"2cb50d5a380e6eb7f96f63b746f6fcb45f92c2692d8de1af588fc3a1b07f8306","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:14.983101Z","signature_b64":"Q4ynOOmN30vMO1ruLVlGpVp51t9vMI99spJ7Uqkchp8sU/MBlqZGxn7V6KXj0IA7CPQ/K51cBm3ah5kLJsXrDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2cb50d5a380e6eb7f96f63b746f6fcb45f92c2692d8de1af588fc3a1b07f8306","last_reissued_at":"2026-05-18T03:17:14.982513Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:14.982513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.1806","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":"2026-05-18T03:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vQ9HFK9VGAJQ/wcUq5RcAoich2tdT9/Fu0O9xm0F4N/8d4E5xK18kIZYYtMDNcTEb1hwdsrLzfKWm53cYPCwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:38:07.741985Z"},"content_sha256":"b596a02363d5fbbcfa0c549e1eb3777e81a89ceb6b8c9d2a2ace316e97c95900","schema_version":"1.0","event_id":"sha256:b596a02363d5fbbcfa0c549e1eb3777e81a89ceb6b8c9d2a2ace316e97c95900"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FS2Q2WRYBZXLP6LPMO3UN5X4WR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The improved decay rate for the heat semigroup with local magnetic field in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"David Krejcirik","submitted_at":"2011-01-10T13:22:37Z","abstract_excerpt":"We consider the heat equation in the presence of compactly supported magnetic field in the plane. We show that the magnetic field leads to an improvement of the decay rate of the heat semigroup by a polynomial factor with power proportional to the distance of the total magnetic flux to the discrete set of flux quanta. The proof employs Hardy-type inequalities due to Laptev and Weidl for the two-dimensional magnetic Schroedinger operator and the method of self-similar variables and weighted Sobolev spaces for the heat equation. A careful analysis of the asymptotic behaviour of the heat equation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1806","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":"2026-05-18T03:17:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PeNGRF40I0cvte+D73sa56O2noVFQDQ0UGsqqvXnWmV749FPNcJxtoLm79L8HaH5u9YCnsYH0ucFNw7lSZhxBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:38:07.742422Z"},"content_sha256":"c6ebbe6fb96e1705eca1ae91634036113a7c71d667e6df776b31b6d1a79a633e","schema_version":"1.0","event_id":"sha256:c6ebbe6fb96e1705eca1ae91634036113a7c71d667e6df776b31b6d1a79a633e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FS2Q2WRYBZXLP6LPMO3UN5X4WR/bundle.json","state_url":"https://pith.science/pith/FS2Q2WRYBZXLP6LPMO3UN5X4WR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FS2Q2WRYBZXLP6LPMO3UN5X4WR/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":"2026-05-26T15:38:07Z","links":{"resolver":"https://pith.science/pith/FS2Q2WRYBZXLP6LPMO3UN5X4WR","bundle":"https://pith.science/pith/FS2Q2WRYBZXLP6LPMO3UN5X4WR/bundle.json","state":"https://pith.science/pith/FS2Q2WRYBZXLP6LPMO3UN5X4WR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FS2Q2WRYBZXLP6LPMO3UN5X4WR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FS2Q2WRYBZXLP6LPMO3UN5X4WR","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":"66882ddf4a9b19304262b0e2dd355d885a0e704c6ec6b38155dd88da0e145066","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-10T13:22:37Z","title_canon_sha256":"294a805fa2db514a1196141ddc42fdb283df04799456be038650aa1d55f7410d"},"schema_version":"1.0","source":{"id":"1101.1806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.1806","created_at":"2026-05-18T03:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1101.1806v1","created_at":"2026-05-18T03:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.1806","created_at":"2026-05-18T03:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"FS2Q2WRYBZXL","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FS2Q2WRYBZXLP6LP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FS2Q2WRY","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:c6ebbe6fb96e1705eca1ae91634036113a7c71d667e6df776b31b6d1a79a633e","target":"graph","created_at":"2026-05-18T03:17:14Z","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 consider the heat equation in the presence of compactly supported magnetic field in the plane. We show that the magnetic field leads to an improvement of the decay rate of the heat semigroup by a polynomial factor with power proportional to the distance of the total magnetic flux to the discrete set of flux quanta. The proof employs Hardy-type inequalities due to Laptev and Weidl for the two-dimensional magnetic Schroedinger operator and the method of self-similar variables and weighted Sobolev spaces for the heat equation. A careful analysis of the asymptotic behaviour of the heat equation","authors_text":"David Krejcirik","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-10T13:22:37Z","title":"The improved decay rate for the heat semigroup with local magnetic field in the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1806","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:b596a02363d5fbbcfa0c549e1eb3777e81a89ceb6b8c9d2a2ace316e97c95900","target":"record","created_at":"2026-05-18T03:17:14Z","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":"66882ddf4a9b19304262b0e2dd355d885a0e704c6ec6b38155dd88da0e145066","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-01-10T13:22:37Z","title_canon_sha256":"294a805fa2db514a1196141ddc42fdb283df04799456be038650aa1d55f7410d"},"schema_version":"1.0","source":{"id":"1101.1806","kind":"arxiv","version":1}},"canonical_sha256":"2cb50d5a380e6eb7f96f63b746f6fcb45f92c2692d8de1af588fc3a1b07f8306","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cb50d5a380e6eb7f96f63b746f6fcb45f92c2692d8de1af588fc3a1b07f8306","first_computed_at":"2026-05-18T03:17:14.982513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:14.982513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q4ynOOmN30vMO1ruLVlGpVp51t9vMI99spJ7Uqkchp8sU/MBlqZGxn7V6KXj0IA7CPQ/K51cBm3ah5kLJsXrDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:14.983101Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.1806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b596a02363d5fbbcfa0c549e1eb3777e81a89ceb6b8c9d2a2ace316e97c95900","sha256:c6ebbe6fb96e1705eca1ae91634036113a7c71d667e6df776b31b6d1a79a633e"],"state_sha256":"5ca2a654898cbfdc093cd91d4103ca9dd27d8c415207af7d5c1e038850516f63"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aR2IVGKOmJj0UhEyKpkYuCdoxZvMZxP0jaadoID8Y+e7ETfpSypc7N6E0snsfOTlS8nglqqBgbkXhufODcN+CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:38:07.745686Z","bundle_sha256":"23c9dd209fd167944dc062b290d12d34afa474b7a9ef4c7efae2208b80e910b4"}}