{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RZDDJO6WOG4TMI4M2IE2JWFJ2T","short_pith_number":"pith:RZDDJO6W","canonical_record":{"source":{"id":"1701.02172","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-01-09T13:40:39Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"b89c8305df07b8fe4d7dbbcd6476e045f26e52de64b9ab44548b38a4dee32479","abstract_canon_sha256":"1cdcf1c29571376757ac47749faec0e82547ae71c95f146cc29f140b6a420233"},"schema_version":"1.0"},"canonical_sha256":"8e4634bbd671b936238cd209a4d8a9d4f16ffc6d71580733c5222e18b9fc45a9","source":{"kind":"arxiv","id":"1701.02172","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02172","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02172v2","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02172","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"RZDDJO6WOG4T","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RZDDJO6WOG4TMI4M","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RZDDJO6W","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RZDDJO6WOG4TMI4M2IE2JWFJ2T","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02172","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-01-09T13:40:39Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"b89c8305df07b8fe4d7dbbcd6476e045f26e52de64b9ab44548b38a4dee32479","abstract_canon_sha256":"1cdcf1c29571376757ac47749faec0e82547ae71c95f146cc29f140b6a420233"},"schema_version":"1.0"},"canonical_sha256":"8e4634bbd671b936238cd209a4d8a9d4f16ffc6d71580733c5222e18b9fc45a9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:37.946361Z","signature_b64":"/lxSKYHGyQc0DaXRQCWbns9Es0exIdLIOq5209cVSXly58/WUwu77ti1+ZVRe4wkqWcWc9HndQaCCBAUIW07Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e4634bbd671b936238cd209a4d8a9d4f16ffc6d71580733c5222e18b9fc45a9","last_reissued_at":"2026-05-18T00:47:37.945776Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:37.945776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02172","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":"2026-05-18T00:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RGsrshnm+2AlT8gBK700cDc91GND3hBBv/EPkTUtYYCYmPWaePMaWfv8vP7EZ8U1gFr5sLu1olkRI++DeiLJAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T11:16:16.754092Z"},"content_sha256":"324eceed24302f66558a850474e40a82bf3a1a0530497b8b3f12281eeb654885","schema_version":"1.0","event_id":"sha256:324eceed24302f66558a850474e40a82bf3a1a0530497b8b3f12281eeb654885"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RZDDJO6WOG4TMI4M2IE2JWFJ2T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spectral bounds for the torsion function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Michiel van den Berg","submitted_at":"2017-01-09T13:40:39Z","abstract_excerpt":"Let $\\Omega$ be an open set in Euclidean space $\\R^m,\\, m=2,3,...$, and let $v_{\\Omega}$ denote the torsion function for $\\Omega$. It is known that $v_{\\Omega}$ is bounded if and only if the bottom of the spectrum of the Dirichlet Laplacian acting in $\\Leb^2(\\Omega)$, denoted by $\\lambda(\\Omega)$, is bounded away from $0$. It is shown that the previously obtained bound $\\|v_{\\Omega}\\|_{\\Leb^{\\infty}(\\Omega)}\\lambda(\\Omega)\\ge 1$ is sharp: for $m\\in\\{2,3,...\\}$, and any $\\epsilon>0$ we construct an open, bounded and connected set $\\Omega_{\\epsilon}\\subset \\R^m$ such that $\\|v_{\\Omega_{\\epsilon}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02172","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":"2026-05-18T00:47:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iu1PbHnTCBQAq+Bl/2h0ydqVjRutWLHHimnu7R/16rQOkU5jLws6d48p9u2J2l32FIsfhcFm56WDcelgO0hHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T11:16:16.754782Z"},"content_sha256":"eb2e5206f5465554934f2fb6e9eae264efac3fb8ec4c54ae685ef62a5684f0ef","schema_version":"1.0","event_id":"sha256:eb2e5206f5465554934f2fb6e9eae264efac3fb8ec4c54ae685ef62a5684f0ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RZDDJO6WOG4TMI4M2IE2JWFJ2T/bundle.json","state_url":"https://pith.science/pith/RZDDJO6WOG4TMI4M2IE2JWFJ2T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RZDDJO6WOG4TMI4M2IE2JWFJ2T/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":"2026-05-20T11:16:16Z","links":{"resolver":"https://pith.science/pith/RZDDJO6WOG4TMI4M2IE2JWFJ2T","bundle":"https://pith.science/pith/RZDDJO6WOG4TMI4M2IE2JWFJ2T/bundle.json","state":"https://pith.science/pith/RZDDJO6WOG4TMI4M2IE2JWFJ2T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RZDDJO6WOG4TMI4M2IE2JWFJ2T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RZDDJO6WOG4TMI4M2IE2JWFJ2T","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":"1cdcf1c29571376757ac47749faec0e82547ae71c95f146cc29f140b6a420233","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-01-09T13:40:39Z","title_canon_sha256":"b89c8305df07b8fe4d7dbbcd6476e045f26e52de64b9ab44548b38a4dee32479"},"schema_version":"1.0","source":{"id":"1701.02172","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02172","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02172v2","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02172","created_at":"2026-05-18T00:47:37Z"},{"alias_kind":"pith_short_12","alias_value":"RZDDJO6WOG4T","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"RZDDJO6WOG4TMI4M","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"RZDDJO6W","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:eb2e5206f5465554934f2fb6e9eae264efac3fb8ec4c54ae685ef62a5684f0ef","target":"graph","created_at":"2026-05-18T00:47:37Z","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":"Let $\\Omega$ be an open set in Euclidean space $\\R^m,\\, m=2,3,...$, and let $v_{\\Omega}$ denote the torsion function for $\\Omega$. It is known that $v_{\\Omega}$ is bounded if and only if the bottom of the spectrum of the Dirichlet Laplacian acting in $\\Leb^2(\\Omega)$, denoted by $\\lambda(\\Omega)$, is bounded away from $0$. It is shown that the previously obtained bound $\\|v_{\\Omega}\\|_{\\Leb^{\\infty}(\\Omega)}\\lambda(\\Omega)\\ge 1$ is sharp: for $m\\in\\{2,3,...\\}$, and any $\\epsilon>0$ we construct an open, bounded and connected set $\\Omega_{\\epsilon}\\subset \\R^m$ such that $\\|v_{\\Omega_{\\epsilon}","authors_text":"Michiel van den Berg","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-01-09T13:40:39Z","title":"Spectral bounds for the torsion function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02172","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":"sha256:324eceed24302f66558a850474e40a82bf3a1a0530497b8b3f12281eeb654885","target":"record","created_at":"2026-05-18T00:47:37Z","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":"1cdcf1c29571376757ac47749faec0e82547ae71c95f146cc29f140b6a420233","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2017-01-09T13:40:39Z","title_canon_sha256":"b89c8305df07b8fe4d7dbbcd6476e045f26e52de64b9ab44548b38a4dee32479"},"schema_version":"1.0","source":{"id":"1701.02172","kind":"arxiv","version":2}},"canonical_sha256":"8e4634bbd671b936238cd209a4d8a9d4f16ffc6d71580733c5222e18b9fc45a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e4634bbd671b936238cd209a4d8a9d4f16ffc6d71580733c5222e18b9fc45a9","first_computed_at":"2026-05-18T00:47:37.945776Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:37.945776Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/lxSKYHGyQc0DaXRQCWbns9Es0exIdLIOq5209cVSXly58/WUwu77ti1+ZVRe4wkqWcWc9HndQaCCBAUIW07Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:37.946361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02172","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:324eceed24302f66558a850474e40a82bf3a1a0530497b8b3f12281eeb654885","sha256:eb2e5206f5465554934f2fb6e9eae264efac3fb8ec4c54ae685ef62a5684f0ef"],"state_sha256":"980195587396c45478579b1e9622d19995ba346fd524270726b70f0a576acfac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YYix63ltdIbVLpXgmxGl7mR/uHOdUiryQaFWWdP78a+nm1ceucYnSQIHBnKJgi232H0C9EhbKnpjeaiGzW/mAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T11:16:16.757651Z","bundle_sha256":"2d68bdf37aa0ab501a876d5268f729fc922fe894c964902d55a4f8cb453138a0"}}