{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZSITOWRQEYVZI3B6V6OOEZRI4L","short_pith_number":"pith:ZSITOWRQ","canonical_record":{"source":{"id":"1503.02895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-10T13:17:35Z","cross_cats_sorted":["math.PR","math.SP"],"title_canon_sha256":"5f31c60162f5c5a9637196dd6f28fdbd5688ff32c099a021e5a335f6aec033de","abstract_canon_sha256":"a8c8da89bfd25c5de097311cf8bfc6df2ca37d5fedf801fc681556364d12ec1d"},"schema_version":"1.0"},"canonical_sha256":"cc91375a30262b946c3eaf9ce26628e2e63c00038961bebee3e63be45234602f","source":{"kind":"arxiv","id":"1503.02895","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02895","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02895v2","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02895","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZSITOWRQEYVZ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZSITOWRQEYVZI3B6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZSITOWRQ","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZSITOWRQEYVZI3B6V6OOEZRI4L","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-10T13:17:35Z","cross_cats_sorted":["math.PR","math.SP"],"title_canon_sha256":"5f31c60162f5c5a9637196dd6f28fdbd5688ff32c099a021e5a335f6aec033de","abstract_canon_sha256":"a8c8da89bfd25c5de097311cf8bfc6df2ca37d5fedf801fc681556364d12ec1d"},"schema_version":"1.0"},"canonical_sha256":"cc91375a30262b946c3eaf9ce26628e2e63c00038961bebee3e63be45234602f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:34.992917Z","signature_b64":"mHHrTKrCvfutQ/GR8VR0YuV4YLTkExDLgOYhCqhAPFZcdKRVHnylgVQSUNbaHwZl2plCIiH0xfHIZF8lTPe4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc91375a30262b946c3eaf9ce26628e2e63c00038961bebee3e63be45234602f","last_reissued_at":"2026-05-18T01:34:34.992221Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:34.992221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02895","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":"2026-05-18T01:34:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eJNijOCea0dDyAnBCfHSfmLuabF7iykabK3ZyB90cEjUcvt+mr67h1TooAOZpxESOQ0eOTJW4G0Zl3Z3ghFNBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:25:37.264153Z"},"content_sha256":"3daf2d57bc86bf52093069f96483b5d4f44a1744edb6f59ee02820f7faa1e3e6","schema_version":"1.0","event_id":"sha256:3daf2d57bc86bf52093069f96483b5d4f44a1744edb6f59ee02820f7faa1e3e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZSITOWRQEYVZI3B6V6OOEZRI4L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Form Inequalities for Symmetric Contraction Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.SP"],"primary_cat":"math.FA","authors_text":"Markus Haase","submitted_at":"2015-03-10T13:17:35Z","abstract_excerpt":"Consider --- for the generator \\({-}A\\) of a symmetric contraction semigroup over some measure space $\\mathrm{X}$, $1\\le p < \\infty$, $q$ the dual exponent and given measurable functions $F_j,\\: G_j : \\mathbb{C}^d \\to \\mathbb{C}$ --- the statement: $$ \\mathrm{Re}\\, \\sum_{j=1}^m \\int_{\\mathrm{X}} A F_j(\\mathbf{f}) \\cdot G_j(\\mathbf{f}) \\,\\,\\ge \\,\\,0 $$ {\\em for all $\\mathbb{C}^d$-valued measurable functions $\\mathbf{f}$ on $\\mathrm{X}$ such that $F_j(\\mathbf{f}) \\in \\mathrm{dom}(A_p)$ and $G_j(\\mathbf{f}) \\in \\mathrm{L}^q(\\mathrm{X})$ for all $j$.}\n  It is shown that this statement is valid in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02895","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":"2026-05-18T01:34:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d4GsSKFYHc6M3LLUeZqCqO+oxvSbz3O/On3zL/jBi/zgQIr0Li0/acYk8BunJNeACEn2DRmZbJXE8Bmk+4v+CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:25:37.264520Z"},"content_sha256":"9eef4f1f0aa5407720b6354dc6e15a90521383a8faa0db47f77e1d41291cf986","schema_version":"1.0","event_id":"sha256:9eef4f1f0aa5407720b6354dc6e15a90521383a8faa0db47f77e1d41291cf986"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/bundle.json","state_url":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/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":"2026-06-26T21:25:37Z","links":{"resolver":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L","bundle":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/bundle.json","state":"https://pith.science/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZSITOWRQEYVZI3B6V6OOEZRI4L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZSITOWRQEYVZI3B6V6OOEZRI4L","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":"a8c8da89bfd25c5de097311cf8bfc6df2ca37d5fedf801fc681556364d12ec1d","cross_cats_sorted":["math.PR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-10T13:17:35Z","title_canon_sha256":"5f31c60162f5c5a9637196dd6f28fdbd5688ff32c099a021e5a335f6aec033de"},"schema_version":"1.0","source":{"id":"1503.02895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02895","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02895v2","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02895","created_at":"2026-05-18T01:34:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZSITOWRQEYVZ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZSITOWRQEYVZI3B6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZSITOWRQ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:9eef4f1f0aa5407720b6354dc6e15a90521383a8faa0db47f77e1d41291cf986","target":"graph","created_at":"2026-05-18T01:34:34Z","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":"Consider --- for the generator \\({-}A\\) of a symmetric contraction semigroup over some measure space $\\mathrm{X}$, $1\\le p < \\infty$, $q$ the dual exponent and given measurable functions $F_j,\\: G_j : \\mathbb{C}^d \\to \\mathbb{C}$ --- the statement: $$ \\mathrm{Re}\\, \\sum_{j=1}^m \\int_{\\mathrm{X}} A F_j(\\mathbf{f}) \\cdot G_j(\\mathbf{f}) \\,\\,\\ge \\,\\,0 $$ {\\em for all $\\mathbb{C}^d$-valued measurable functions $\\mathbf{f}$ on $\\mathrm{X}$ such that $F_j(\\mathbf{f}) \\in \\mathrm{dom}(A_p)$ and $G_j(\\mathbf{f}) \\in \\mathrm{L}^q(\\mathrm{X})$ for all $j$.}\n  It is shown that this statement is valid in ","authors_text":"Markus Haase","cross_cats":["math.PR","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-10T13:17:35Z","title":"Form Inequalities for Symmetric Contraction Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02895","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":"sha256:3daf2d57bc86bf52093069f96483b5d4f44a1744edb6f59ee02820f7faa1e3e6","target":"record","created_at":"2026-05-18T01:34:34Z","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":"a8c8da89bfd25c5de097311cf8bfc6df2ca37d5fedf801fc681556364d12ec1d","cross_cats_sorted":["math.PR","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-03-10T13:17:35Z","title_canon_sha256":"5f31c60162f5c5a9637196dd6f28fdbd5688ff32c099a021e5a335f6aec033de"},"schema_version":"1.0","source":{"id":"1503.02895","kind":"arxiv","version":2}},"canonical_sha256":"cc91375a30262b946c3eaf9ce26628e2e63c00038961bebee3e63be45234602f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc91375a30262b946c3eaf9ce26628e2e63c00038961bebee3e63be45234602f","first_computed_at":"2026-05-18T01:34:34.992221Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:34.992221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mHHrTKrCvfutQ/GR8VR0YuV4YLTkExDLgOYhCqhAPFZcdKRVHnylgVQSUNbaHwZl2plCIiH0xfHIZF8lTPe4DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:34.992917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3daf2d57bc86bf52093069f96483b5d4f44a1744edb6f59ee02820f7faa1e3e6","sha256:9eef4f1f0aa5407720b6354dc6e15a90521383a8faa0db47f77e1d41291cf986"],"state_sha256":"c9b1743e007064050e1144eb80e9282cbc392cbfc4d4908fc697d97a26c51bbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nobp1HHH8eW0Shwk+NrcoJ1xcX/OSzDfTcaZbu47MbrJxXOENusiDTmdABwra8E0aF6IBvcV/ZAaAkT+bxmiAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T21:25:37.266449Z","bundle_sha256":"49bcb1f17e1a804b4faebf75e94e3119d94ae421d1b204f3dcaba4f24b35c383"}}