{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PUNGPWTNW3YRYSN2XLCO5VBECF","short_pith_number":"pith:PUNGPWTN","canonical_record":{"source":{"id":"1507.08016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-29T04:47:54Z","cross_cats_sorted":[],"title_canon_sha256":"01a575e1cdf59f4117ae2482ba39ab6ff40aa5ecabaf25714703bf7731801385","abstract_canon_sha256":"4a0bdf42732283ad68e2deef4db09e34fc0439ea9301d2643b2ac36fde1012c2"},"schema_version":"1.0"},"canonical_sha256":"7d1a67da6db6f11c49babac4eed42411545fe25b2d015275c49ccd823563131d","source":{"kind":"arxiv","id":"1507.08016","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08016","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08016v1","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08016","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"PUNGPWTNW3YR","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PUNGPWTNW3YRYSN2","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PUNGPWTN","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PUNGPWTNW3YRYSN2XLCO5VBECF","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08016","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-29T04:47:54Z","cross_cats_sorted":[],"title_canon_sha256":"01a575e1cdf59f4117ae2482ba39ab6ff40aa5ecabaf25714703bf7731801385","abstract_canon_sha256":"4a0bdf42732283ad68e2deef4db09e34fc0439ea9301d2643b2ac36fde1012c2"},"schema_version":"1.0"},"canonical_sha256":"7d1a67da6db6f11c49babac4eed42411545fe25b2d015275c49ccd823563131d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:08.640439Z","signature_b64":"KkSl2sX3k5rF3+0Gb3rrsJokK9B0NofKArXcYE1SEQ/ESybT4xYCX5NivUrg6OePV1TwvE/lfJsdF3wqn+raCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d1a67da6db6f11c49babac4eed42411545fe25b2d015275c49ccd823563131d","last_reissued_at":"2026-05-18T01:36:08.639982Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:08.639982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08016","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":"2026-05-18T01:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"572rR/ITcrdKCbt2BmEqq1sSFU2oALvBKCZ5CKbKrrHEDuLGiAjzcFeAf9lr+X4tYekbqGF+bywMzaj6MJJyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:21:23.333740Z"},"content_sha256":"6745fc5c60b1b3833d0c13e8a6360b6d186fe5d1e13a9f23b434de29c4e6a54f","schema_version":"1.0","event_id":"sha256:6745fc5c60b1b3833d0c13e8a6360b6d186fe5d1e13a9f23b434de29c4e6a54f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PUNGPWTNW3YRYSN2XLCO5VBECF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diamagnetism versus Robin condition and concentration of ground states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"A. Kachmar","submitted_at":"2015-07-29T04:47:54Z","abstract_excerpt":"We estimate the ground state energy for the magnetic Laplacian with a Robin condition. In a special asymptotic limit, we find that the magnetic field does not contribute to the two-term expansion of the ground state energy, thereby proving that the Robin condition weakens diamagnetism. We discuss a semi-classical version of the operator and prove that the ground states concentrate near the boundary points of maximal curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08016","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":"2026-05-18T01:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QbP/lFIuwzbWeu0egdZzz41AklUb4XJfun1OFR+7yYY/74B+60ZLQhrFLKAgZhRn4WifThymck8qAcYkVGkOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:21:23.334404Z"},"content_sha256":"6b7cd548324eb4fdcd23cf7a98178bfac08b233ee977bf60c385179587515c86","schema_version":"1.0","event_id":"sha256:6b7cd548324eb4fdcd23cf7a98178bfac08b233ee977bf60c385179587515c86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PUNGPWTNW3YRYSN2XLCO5VBECF/bundle.json","state_url":"https://pith.science/pith/PUNGPWTNW3YRYSN2XLCO5VBECF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PUNGPWTNW3YRYSN2XLCO5VBECF/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":"2026-06-22T14:21:23Z","links":{"resolver":"https://pith.science/pith/PUNGPWTNW3YRYSN2XLCO5VBECF","bundle":"https://pith.science/pith/PUNGPWTNW3YRYSN2XLCO5VBECF/bundle.json","state":"https://pith.science/pith/PUNGPWTNW3YRYSN2XLCO5VBECF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PUNGPWTNW3YRYSN2XLCO5VBECF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PUNGPWTNW3YRYSN2XLCO5VBECF","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":"4a0bdf42732283ad68e2deef4db09e34fc0439ea9301d2643b2ac36fde1012c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-29T04:47:54Z","title_canon_sha256":"01a575e1cdf59f4117ae2482ba39ab6ff40aa5ecabaf25714703bf7731801385"},"schema_version":"1.0","source":{"id":"1507.08016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08016","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08016v1","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08016","created_at":"2026-05-18T01:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"PUNGPWTNW3YR","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PUNGPWTNW3YRYSN2","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PUNGPWTN","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:6b7cd548324eb4fdcd23cf7a98178bfac08b233ee977bf60c385179587515c86","target":"graph","created_at":"2026-05-18T01:36:08Z","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 estimate the ground state energy for the magnetic Laplacian with a Robin condition. In a special asymptotic limit, we find that the magnetic field does not contribute to the two-term expansion of the ground state energy, thereby proving that the Robin condition weakens diamagnetism. We discuss a semi-classical version of the operator and prove that the ground states concentrate near the boundary points of maximal curvature.","authors_text":"A. Kachmar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-29T04:47:54Z","title":"Diamagnetism versus Robin condition and concentration of ground states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08016","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":"sha256:6745fc5c60b1b3833d0c13e8a6360b6d186fe5d1e13a9f23b434de29c4e6a54f","target":"record","created_at":"2026-05-18T01:36:08Z","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":"4a0bdf42732283ad68e2deef4db09e34fc0439ea9301d2643b2ac36fde1012c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2015-07-29T04:47:54Z","title_canon_sha256":"01a575e1cdf59f4117ae2482ba39ab6ff40aa5ecabaf25714703bf7731801385"},"schema_version":"1.0","source":{"id":"1507.08016","kind":"arxiv","version":1}},"canonical_sha256":"7d1a67da6db6f11c49babac4eed42411545fe25b2d015275c49ccd823563131d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d1a67da6db6f11c49babac4eed42411545fe25b2d015275c49ccd823563131d","first_computed_at":"2026-05-18T01:36:08.639982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:08.639982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KkSl2sX3k5rF3+0Gb3rrsJokK9B0NofKArXcYE1SEQ/ESybT4xYCX5NivUrg6OePV1TwvE/lfJsdF3wqn+raCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:08.640439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6745fc5c60b1b3833d0c13e8a6360b6d186fe5d1e13a9f23b434de29c4e6a54f","sha256:6b7cd548324eb4fdcd23cf7a98178bfac08b233ee977bf60c385179587515c86"],"state_sha256":"15c1628c871f3138752685f93931a4c84bdd575fefc63d0f727a7873cd844588"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mKDd3mEbVgxoFTC2Rh74tObGot4pYS196U0CaoAmf5T5gSSzIhfB6A0i4Wq8jQgo2E19BUZ/L+dksqmRyyH9Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:21:23.337439Z","bundle_sha256":"d9eda1d77a1dd39026205f38e051948e421ae50184d8bcc20b3a7100d16b67d0"}}