{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PXBYHFREMACD4HRPNDBEM64KCR","short_pith_number":"pith:PXBYHFRE","canonical_record":{"source":{"id":"1209.0694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-04T16:37:02Z","cross_cats_sorted":[],"title_canon_sha256":"aad0c7d10b8f6db7ad108b14fc8a68a85d5517dc96383b5a3512d151ea07b3a4","abstract_canon_sha256":"900499ee6ac8c09cd3573d616345e2e7046c4cbcdf7c656da7b9278f4f601a1d"},"schema_version":"1.0"},"canonical_sha256":"7dc383962460043e1e2f68c2467b8a146b696e33f7ca4fee4ca2bea3843fcbc5","source":{"kind":"arxiv","id":"1209.0694","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0694","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0694v1","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0694","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"pith_short_12","alias_value":"PXBYHFREMACD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PXBYHFREMACD4HRP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PXBYHFRE","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PXBYHFREMACD4HRPNDBEM64KCR","target":"record","payload":{"canonical_record":{"source":{"id":"1209.0694","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-04T16:37:02Z","cross_cats_sorted":[],"title_canon_sha256":"aad0c7d10b8f6db7ad108b14fc8a68a85d5517dc96383b5a3512d151ea07b3a4","abstract_canon_sha256":"900499ee6ac8c09cd3573d616345e2e7046c4cbcdf7c656da7b9278f4f601a1d"},"schema_version":"1.0"},"canonical_sha256":"7dc383962460043e1e2f68c2467b8a146b696e33f7ca4fee4ca2bea3843fcbc5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:17.432069Z","signature_b64":"HN4oyzEPHW6s0WjvFvfAXActltyKePYEI1H/rfy/fYqckdODC5lwspusNCmPsUsQ/aAtqPbUMdth3ROqUq4zDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dc383962460043e1e2f68c2467b8a146b696e33f7ca4fee4ca2bea3843fcbc5","last_reissued_at":"2026-05-18T03:46:17.431387Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:17.431387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.0694","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":"2026-05-18T03:46:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j3syDuIA9P+8Ae4UBiZZp5ABoTBzWxUiMqqNKxiORfeP3jMB/lFWCSxbrr730i4dhL5zVbM9cB+88FlhYP29Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:28:14.589179Z"},"content_sha256":"e1e06f625a40379c1866a0f92cc573dc14d681a2a8d7d9695fe972d7de4ffee9","schema_version":"1.0","event_id":"sha256:e1e06f625a40379c1866a0f92cc573dc14d681a2a8d7d9695fe972d7de4ffee9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PXBYHFREMACD4HRPNDBEM64KCR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^p$-spectral multipliers for some elliptic systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Matthias Uhl, Peer Christian Kunstmann","submitted_at":"2012-09-04T16:37:02Z","abstract_excerpt":"We show results on $L^p$-spectral multipliers for Maxwell operators with bounded measurable coefficients. We also present similar results for the Stokes operator with Hodge boundary conditions and the Lam\\'e system. Here we rely on resolvent estimates established recently by M.\\ Mitrea and S.\\ Monniaux."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0694","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":"2026-05-18T03:46:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UedDfPxcvRUAkipMhn8MWRRT4INVIlhxY7wKChZQrrtOyzMjUzDvmsSoiMYBenesfI5SipCGOtN/9kmXW1uBBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T16:28:14.589540Z"},"content_sha256":"32c19f4561c6cfba2afb3b11a8c7451f1728bd9fade3d479aecd2cd1ecfe71f8","schema_version":"1.0","event_id":"sha256:32c19f4561c6cfba2afb3b11a8c7451f1728bd9fade3d479aecd2cd1ecfe71f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXBYHFREMACD4HRPNDBEM64KCR/bundle.json","state_url":"https://pith.science/pith/PXBYHFREMACD4HRPNDBEM64KCR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXBYHFREMACD4HRPNDBEM64KCR/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":"2026-06-02T16:28:14Z","links":{"resolver":"https://pith.science/pith/PXBYHFREMACD4HRPNDBEM64KCR","bundle":"https://pith.science/pith/PXBYHFREMACD4HRPNDBEM64KCR/bundle.json","state":"https://pith.science/pith/PXBYHFREMACD4HRPNDBEM64KCR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXBYHFREMACD4HRPNDBEM64KCR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PXBYHFREMACD4HRPNDBEM64KCR","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":"900499ee6ac8c09cd3573d616345e2e7046c4cbcdf7c656da7b9278f4f601a1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-04T16:37:02Z","title_canon_sha256":"aad0c7d10b8f6db7ad108b14fc8a68a85d5517dc96383b5a3512d151ea07b3a4"},"schema_version":"1.0","source":{"id":"1209.0694","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.0694","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"arxiv_version","alias_value":"1209.0694v1","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0694","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"pith_short_12","alias_value":"PXBYHFREMACD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PXBYHFREMACD4HRP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PXBYHFRE","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:32c19f4561c6cfba2afb3b11a8c7451f1728bd9fade3d479aecd2cd1ecfe71f8","target":"graph","created_at":"2026-05-18T03:46:17Z","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 show results on $L^p$-spectral multipliers for Maxwell operators with bounded measurable coefficients. We also present similar results for the Stokes operator with Hodge boundary conditions and the Lam\\'e system. Here we rely on resolvent estimates established recently by M.\\ Mitrea and S.\\ Monniaux.","authors_text":"Matthias Uhl, Peer Christian Kunstmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-04T16:37:02Z","title":"$L^p$-spectral multipliers for some elliptic systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0694","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:e1e06f625a40379c1866a0f92cc573dc14d681a2a8d7d9695fe972d7de4ffee9","target":"record","created_at":"2026-05-18T03:46:17Z","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":"900499ee6ac8c09cd3573d616345e2e7046c4cbcdf7c656da7b9278f4f601a1d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-09-04T16:37:02Z","title_canon_sha256":"aad0c7d10b8f6db7ad108b14fc8a68a85d5517dc96383b5a3512d151ea07b3a4"},"schema_version":"1.0","source":{"id":"1209.0694","kind":"arxiv","version":1}},"canonical_sha256":"7dc383962460043e1e2f68c2467b8a146b696e33f7ca4fee4ca2bea3843fcbc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dc383962460043e1e2f68c2467b8a146b696e33f7ca4fee4ca2bea3843fcbc5","first_computed_at":"2026-05-18T03:46:17.431387Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:17.431387Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HN4oyzEPHW6s0WjvFvfAXActltyKePYEI1H/rfy/fYqckdODC5lwspusNCmPsUsQ/aAtqPbUMdth3ROqUq4zDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:17.432069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.0694","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e1e06f625a40379c1866a0f92cc573dc14d681a2a8d7d9695fe972d7de4ffee9","sha256:32c19f4561c6cfba2afb3b11a8c7451f1728bd9fade3d479aecd2cd1ecfe71f8"],"state_sha256":"83d42c8dc74f9e3fcf2b6bb1fb0ff6f4eee30b7c17168dfb5d1f37f9b2bc82cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EGLO+Aw+j+E/7+j7zaF0y5sUzEg8bUZXseZPhu35rlG5IDt4Z6/BXwsrmN02FgUvs44ptw5xYDvSeH9nGg7LAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T16:28:14.591452Z","bundle_sha256":"b6a358bb60d5cbd98810f0ef5c71b4aa5da9b052d6fab9b98304e972045e634d"}}