{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HYLOJDOYKPPZZTJEAZ32X3IAKT","short_pith_number":"pith:HYLOJDOY","canonical_record":{"source":{"id":"1402.3900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-17T05:53:42Z","cross_cats_sorted":[],"title_canon_sha256":"504daf12ca9ab18efddb8d593411f8537ed2f9f1fb2632f4b788fb05cacc6cc0","abstract_canon_sha256":"240ff2d251cbb45ef99e96f3b8bf5a9d93f94c944abac09705ad049dc95b23cd"},"schema_version":"1.0"},"canonical_sha256":"3e16e48dd853df9ccd240677abed0054d55f3de53dc3434d73a70b0e51543d02","source":{"kind":"arxiv","id":"1402.3900","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3900","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3900v2","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3900","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"HYLOJDOYKPPZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYLOJDOYKPPZZTJE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYLOJDOY","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HYLOJDOYKPPZZTJEAZ32X3IAKT","target":"record","payload":{"canonical_record":{"source":{"id":"1402.3900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-17T05:53:42Z","cross_cats_sorted":[],"title_canon_sha256":"504daf12ca9ab18efddb8d593411f8537ed2f9f1fb2632f4b788fb05cacc6cc0","abstract_canon_sha256":"240ff2d251cbb45ef99e96f3b8bf5a9d93f94c944abac09705ad049dc95b23cd"},"schema_version":"1.0"},"canonical_sha256":"3e16e48dd853df9ccd240677abed0054d55f3de53dc3434d73a70b0e51543d02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:09.007579Z","signature_b64":"lezZEtrPx4kwXKqC92JAXka7/6FuDwUQCOUxvzAtUdy4a36Xl40zvnXakLOqhoCQkprmKziwgMjTpVjJcLs0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e16e48dd853df9ccd240677abed0054d55f3de53dc3434d73a70b0e51543d02","last_reissued_at":"2026-05-18T01:23:09.007161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:09.007161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.3900","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":"2026-05-18T01:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KIjVHpQDSZxTmldU9/Ez5PplsIE1cBHAVOTRw6IVzUFBnMVqnJc6IeJXAiiLFPCEZLLhQ21kg6virLml3cm9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:07:37.702467Z"},"content_sha256":"5b4b3db267934d0df4aa15e79dfad2cc802659befc7f2a0fa059889997682f5d","schema_version":"1.0","event_id":"sha256:5b4b3db267934d0df4aa15e79dfad2cc802659befc7f2a0fa059889997682f5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HYLOJDOYKPPZZTJEAZ32X3IAKT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the placement of an obstacle so as to optimize the Dirichlet heat trace","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Ahmad El Soufi (LMPT), Evans Harrell","submitted_at":"2014-02-17T05:53:42Z","abstract_excerpt":"We prove that among all doubly connected domains of $\\R^n$ bounded by two spheres of given radii, $Z(t)$, the trace of the heat kernel with Dirichlet boundary conditions, achieves its minimum when the spheres are concentric (i.e., for the spherical shell).  The supremum is attained when the interior sphere is in contact with the outer sphere.This is shown to be a special case of a more general theorem characterizing the optimal placement of a spherical obstacle inside a convex domain so as to maximize or minimize the trace of the Dirichlet heat kernel.  In this case the minimizing position of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3900","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":""},"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":"2026-05-18T01:23:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BkYv2ue2QsoEqaOFVWmZcWZlh0L5laFKm/8RGSrzhwfqj+xPKxBxandjaYhnK78jDwuLnn2SsmDDKqSF/rteAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:07:37.702948Z"},"content_sha256":"9305fa878461c9fbe9ee772ab7037ab44b82d9b8cf0421dbbe4036adcd627cb3","schema_version":"1.0","event_id":"sha256:9305fa878461c9fbe9ee772ab7037ab44b82d9b8cf0421dbbe4036adcd627cb3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYLOJDOYKPPZZTJEAZ32X3IAKT/bundle.json","state_url":"https://pith.science/pith/HYLOJDOYKPPZZTJEAZ32X3IAKT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYLOJDOYKPPZZTJEAZ32X3IAKT/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":"2026-06-22T22:07:37Z","links":{"resolver":"https://pith.science/pith/HYLOJDOYKPPZZTJEAZ32X3IAKT","bundle":"https://pith.science/pith/HYLOJDOYKPPZZTJEAZ32X3IAKT/bundle.json","state":"https://pith.science/pith/HYLOJDOYKPPZZTJEAZ32X3IAKT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYLOJDOYKPPZZTJEAZ32X3IAKT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HYLOJDOYKPPZZTJEAZ32X3IAKT","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":"240ff2d251cbb45ef99e96f3b8bf5a9d93f94c944abac09705ad049dc95b23cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-17T05:53:42Z","title_canon_sha256":"504daf12ca9ab18efddb8d593411f8537ed2f9f1fb2632f4b788fb05cacc6cc0"},"schema_version":"1.0","source":{"id":"1402.3900","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.3900","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"arxiv_version","alias_value":"1402.3900v2","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.3900","created_at":"2026-05-18T01:23:09Z"},{"alias_kind":"pith_short_12","alias_value":"HYLOJDOYKPPZ","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"HYLOJDOYKPPZZTJE","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"HYLOJDOY","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:9305fa878461c9fbe9ee772ab7037ab44b82d9b8cf0421dbbe4036adcd627cb3","target":"graph","created_at":"2026-05-18T01:23:09Z","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 prove that among all doubly connected domains of $\\R^n$ bounded by two spheres of given radii, $Z(t)$, the trace of the heat kernel with Dirichlet boundary conditions, achieves its minimum when the spheres are concentric (i.e., for the spherical shell).  The supremum is attained when the interior sphere is in contact with the outer sphere.This is shown to be a special case of a more general theorem characterizing the optimal placement of a spherical obstacle inside a convex domain so as to maximize or minimize the trace of the Dirichlet heat kernel.  In this case the minimizing position of ","authors_text":"Ahmad El Soufi (LMPT), Evans Harrell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-17T05:53:42Z","title":"On the placement of an obstacle so as to optimize the Dirichlet heat trace"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3900","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":"sha256:5b4b3db267934d0df4aa15e79dfad2cc802659befc7f2a0fa059889997682f5d","target":"record","created_at":"2026-05-18T01:23:09Z","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":"240ff2d251cbb45ef99e96f3b8bf5a9d93f94c944abac09705ad049dc95b23cd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-02-17T05:53:42Z","title_canon_sha256":"504daf12ca9ab18efddb8d593411f8537ed2f9f1fb2632f4b788fb05cacc6cc0"},"schema_version":"1.0","source":{"id":"1402.3900","kind":"arxiv","version":2}},"canonical_sha256":"3e16e48dd853df9ccd240677abed0054d55f3de53dc3434d73a70b0e51543d02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e16e48dd853df9ccd240677abed0054d55f3de53dc3434d73a70b0e51543d02","first_computed_at":"2026-05-18T01:23:09.007161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:09.007161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lezZEtrPx4kwXKqC92JAXka7/6FuDwUQCOUxvzAtUdy4a36Xl40zvnXakLOqhoCQkprmKziwgMjTpVjJcLs0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:09.007579Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.3900","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b4b3db267934d0df4aa15e79dfad2cc802659befc7f2a0fa059889997682f5d","sha256:9305fa878461c9fbe9ee772ab7037ab44b82d9b8cf0421dbbe4036adcd627cb3"],"state_sha256":"051231a5b1e6dae01cdd4339704e7c820e3601629c52462cd50c70b74f08d0b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LZNMj1/TkjmM6q75oKgRY5nKKfTmBnElTtsY6uL7gr3WmBMgSJUMzG5GW2MbcQZ96lE+c45rmZZAOTNBkP0IDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:07:37.705559Z","bundle_sha256":"295df126dc94cb0c65b111d702c837a6e78ee6d24d312c4a356e95735a4692ac"}}