{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:VQC76GQQKTFX76URFAUMKN3KPR","short_pith_number":"pith:VQC76GQQ","canonical_record":{"source":{"id":"math/0411648","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2004-11-30T09:28:53Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"017e9b8fccfd711288e5a14be21147eb572ece55f491bcefbef149cb455cdeab","abstract_canon_sha256":"2e4e11eb0cd4647127d433ea42cc3574a6608d6a18ac7e545b1de2a6821f254f"},"schema_version":"1.0"},"canonical_sha256":"ac05ff1a1054cb7ffa912828c5376a7c67a2103d9932b70272ccd0d0579662de","source":{"kind":"arxiv","id":"math/0411648","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411648","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411648v1","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411648","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"pith_short_12","alias_value":"VQC76GQQKTFX","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"pith_short_16","alias_value":"VQC76GQQKTFX76UR","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"pith_short_8","alias_value":"VQC76GQQ","created_at":"2026-07-04T14:39:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:VQC76GQQKTFX76URFAUMKN3KPR","target":"record","payload":{"canonical_record":{"source":{"id":"math/0411648","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2004-11-30T09:28:53Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"017e9b8fccfd711288e5a14be21147eb572ece55f491bcefbef149cb455cdeab","abstract_canon_sha256":"2e4e11eb0cd4647127d433ea42cc3574a6608d6a18ac7e545b1de2a6821f254f"},"schema_version":"1.0"},"canonical_sha256":"ac05ff1a1054cb7ffa912828c5376a7c67a2103d9932b70272ccd0d0579662de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:39:25.076662Z","signature_b64":"NPjsGKnGRjRaBF86uuoQGGsBVNIPNZuhCMbQoJ8zE7FJ/QAvBIL8be7PguGtC8oUXYl4Q+7Uj9a5Gk8xtdFiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac05ff1a1054cb7ffa912828c5376a7c67a2103d9932b70272ccd0d0579662de","last_reissued_at":"2026-07-04T14:39:25.076326Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:39:25.076326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0411648","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":"2026-07-04T14:39:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tjLlrElsviiqay5qXNLRXmrX3aa56UqC8bBE1QaHzUTrw5NYULT61VVMyVBsRXGuc6XDXR3t0t6FzUOljyPeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:58:59.437620Z"},"content_sha256":"839baba8d721ddf84a55583afd2e82f7d4555c17e52f0838e1a2629f1f8783aa","schema_version":"1.0","event_id":"sha256:839baba8d721ddf84a55583afd2e82f7d4555c17e52f0838e1a2629f1f8783aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:VQC76GQQKTFX76URFAUMKN3KPR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riesz transform and $L^p$ cohomology for manifolds with Euclidean ends","license":"","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Andrew Hassell, Gilles Carron (LMJL), Thierry Coulhon","submitted_at":"2004-11-30T09:28:53Z","abstract_excerpt":"Let $M$ be a smooth Riemannian manifold which is the union of a compact part and a finite number of Euclidean ends, $\\RR^n \\setminus B(0,R)$ for some $R > 0$, each of which carries the standard metric. Our main result is that the Riesz transform on $M$ is bounded from $L^p(M) \\to L^p(M; T^*M)$ for $1 < p < n$ and unbounded for $p \\geq n$ if there is more than one end. It follows from known results that in such a case the Riesz transform on $M$ is bounded for $1 < p \\leq 2$ and unbounded for $p > n$; the result is new for $2 < p \\leq n$. We also give some heat kernel estimates on such manifolds"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411648","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0411648/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:39:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3kT6p075w/wLYN3GteQWujosOFSwr0xKNQGAhD+3K9TzVtU+lrVlIlvwJhyZ3dzduoVQ67WMDgcyb0r31GIZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T04:58:59.437989Z"},"content_sha256":"dda6d12968f9631eaf3390ca69d1ebadd19257be55679c97801172af1ee9a58c","schema_version":"1.0","event_id":"sha256:dda6d12968f9631eaf3390ca69d1ebadd19257be55679c97801172af1ee9a58c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQC76GQQKTFX76URFAUMKN3KPR/bundle.json","state_url":"https://pith.science/pith/VQC76GQQKTFX76URFAUMKN3KPR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQC76GQQKTFX76URFAUMKN3KPR/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":"2026-07-05T04:58:59Z","links":{"resolver":"https://pith.science/pith/VQC76GQQKTFX76URFAUMKN3KPR","bundle":"https://pith.science/pith/VQC76GQQKTFX76URFAUMKN3KPR/bundle.json","state":"https://pith.science/pith/VQC76GQQKTFX76URFAUMKN3KPR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQC76GQQKTFX76URFAUMKN3KPR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:VQC76GQQKTFX76URFAUMKN3KPR","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":"2e4e11eb0cd4647127d433ea42cc3574a6608d6a18ac7e545b1de2a6821f254f","cross_cats_sorted":["math.DG","math.FA"],"license":"","primary_cat":"math.AP","submitted_at":"2004-11-30T09:28:53Z","title_canon_sha256":"017e9b8fccfd711288e5a14be21147eb572ece55f491bcefbef149cb455cdeab"},"schema_version":"1.0","source":{"id":"math/0411648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0411648","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/0411648v1","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411648","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"pith_short_12","alias_value":"VQC76GQQKTFX","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"pith_short_16","alias_value":"VQC76GQQKTFX76UR","created_at":"2026-07-04T14:39:25Z"},{"alias_kind":"pith_short_8","alias_value":"VQC76GQQ","created_at":"2026-07-04T14:39:25Z"}],"graph_snapshots":[{"event_id":"sha256:dda6d12968f9631eaf3390ca69d1ebadd19257be55679c97801172af1ee9a58c","target":"graph","created_at":"2026-07-04T14:39:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0411648/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $M$ be a smooth Riemannian manifold which is the union of a compact part and a finite number of Euclidean ends, $\\RR^n \\setminus B(0,R)$ for some $R > 0$, each of which carries the standard metric. Our main result is that the Riesz transform on $M$ is bounded from $L^p(M) \\to L^p(M; T^*M)$ for $1 < p < n$ and unbounded for $p \\geq n$ if there is more than one end. It follows from known results that in such a case the Riesz transform on $M$ is bounded for $1 < p \\leq 2$ and unbounded for $p > n$; the result is new for $2 < p \\leq n$. We also give some heat kernel estimates on such manifolds","authors_text":"Andrew Hassell, Gilles Carron (LMJL), Thierry Coulhon","cross_cats":["math.DG","math.FA"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2004-11-30T09:28:53Z","title":"Riesz transform and $L^p$ cohomology for manifolds with Euclidean ends"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411648","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":"sha256:839baba8d721ddf84a55583afd2e82f7d4555c17e52f0838e1a2629f1f8783aa","target":"record","created_at":"2026-07-04T14:39:25Z","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":"2e4e11eb0cd4647127d433ea42cc3574a6608d6a18ac7e545b1de2a6821f254f","cross_cats_sorted":["math.DG","math.FA"],"license":"","primary_cat":"math.AP","submitted_at":"2004-11-30T09:28:53Z","title_canon_sha256":"017e9b8fccfd711288e5a14be21147eb572ece55f491bcefbef149cb455cdeab"},"schema_version":"1.0","source":{"id":"math/0411648","kind":"arxiv","version":1}},"canonical_sha256":"ac05ff1a1054cb7ffa912828c5376a7c67a2103d9932b70272ccd0d0579662de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac05ff1a1054cb7ffa912828c5376a7c67a2103d9932b70272ccd0d0579662de","first_computed_at":"2026-07-04T14:39:25.076326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:39:25.076326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NPjsGKnGRjRaBF86uuoQGGsBVNIPNZuhCMbQoJ8zE7FJ/QAvBIL8be7PguGtC8oUXYl4Q+7Uj9a5Gk8xtdFiBg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:39:25.076662Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0411648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:839baba8d721ddf84a55583afd2e82f7d4555c17e52f0838e1a2629f1f8783aa","sha256:dda6d12968f9631eaf3390ca69d1ebadd19257be55679c97801172af1ee9a58c"],"state_sha256":"6528739cf997024fde083231a16dced5c983f3fb5a7ae0de6e28b00adaa36f20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"We6SEC9FjVqyfjU41ox6eH4vX/wzbvtakPLbIbOQ/ppbuLb6xm7jug4PE+UPTIukJUOcewrmTE8cdVAmoVASBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T04:58:59.439937Z","bundle_sha256":"a9378e6b7469e239d60a936e8229d4f56d222b8d222c306a7780e23e4be067f3"}}