{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:W2OXHKSMAF7U3ZQZMHLEVXLQJQ","short_pith_number":"pith:W2OXHKSM","canonical_record":{"source":{"id":"1410.7493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-28T02:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"b76b33057bb6791015d27dce96b75b6d448b321af148950a9f6eb5216fe11641","abstract_canon_sha256":"c109f144df0c36cde6f57121112b50532091c410575ec6c14284a25de7ddeb60"},"schema_version":"1.0"},"canonical_sha256":"b69d73aa4c017f4de61961d64add704c11fd6e39f014bd889ade78924f0501d2","source":{"kind":"arxiv","id":"1410.7493","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7493","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7493v2","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7493","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"pith_short_12","alias_value":"W2OXHKSMAF7U","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2OXHKSMAF7U3ZQZ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2OXHKSM","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:W2OXHKSMAF7U3ZQZMHLEVXLQJQ","target":"record","payload":{"canonical_record":{"source":{"id":"1410.7493","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-28T02:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"b76b33057bb6791015d27dce96b75b6d448b321af148950a9f6eb5216fe11641","abstract_canon_sha256":"c109f144df0c36cde6f57121112b50532091c410575ec6c14284a25de7ddeb60"},"schema_version":"1.0"},"canonical_sha256":"b69d73aa4c017f4de61961d64add704c11fd6e39f014bd889ade78924f0501d2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:10.450888Z","signature_b64":"GZyEkb3oa2KL8CUl0VQ7Bv5tGH780MFA0DE94lFsbRHrEndtSYWC+aDHDhe2kqGuKB5YOLC5z5ods2Vzs2MiDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b69d73aa4c017f4de61961d64add704c11fd6e39f014bd889ade78924f0501d2","last_reissued_at":"2026-05-18T02:29:10.450420Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:10.450420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.7493","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":"2026-05-18T02:29:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SiCvrRsw7tqhbPs+9Ll99RkMvTk1a8tF5FxxVaKYPPLe9cIUndVoKF4hNt8j/qK1nDWZtkwqwsJaCt+QKbIDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:37:57.123575Z"},"content_sha256":"b28b3afbc5796fd9050a7529da85b1170036ca4070e260170332223ce785cfed","schema_version":"1.0","event_id":"sha256:b28b3afbc5796fd9050a7529da85b1170036ca4070e260170332223ce785cfed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:W2OXHKSMAF7U3ZQZMHLEVXLQJQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Contractivity, complete contractivity and curvature inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Avijit Pal, Gadadhar Misra","submitted_at":"2014-10-28T02:27:45Z","abstract_excerpt":"For any bounded domain $\\Omega$ in $\\mathbb C^m,$ let ${\\mathrm B}_1(\\Omega)$ denote the Cowen-Douglas class of commuting $m$-tuples of bounded linear operators. For an $m$-tuple $\\boldsymbol T$ in the Cowen-Douglas class ${\\mathrm B}_1(\\Omega),$ let $N_{\\boldsymbol T}(w)$ denote the restriction of $\\boldsymbol T$ to the subspace ${\\cap_{i,j=1}^m\\ker(T_i-w_iI)(T_j-w_jI)}.$ This commuting $m$-tuple $N_{\\boldsymbol T}(w)$ of $m+1$ dimensional operators induces a homomorphism $\\rho_{_{\\!N_{\\boldsymbol T}(w)}}$ of the polynomial ring $P[z_1, ..., z_m],$ namely, $\\rho_{_{\\!N_{\\boldsymbol T}(w)}}(p)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7493","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":"2026-05-18T02:29:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pZkvZ2A/KpL3GfEhHAq2uy5kRitt05MTU6gUzeb8lRTi9dagwYcYPLoGoPw7mt0qQPpniDIUCYcXUpfgnud8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T01:37:57.124281Z"},"content_sha256":"651e13b798bc0228318b81a361b5605b35d80cca80dca55b03f080ac544ff136","schema_version":"1.0","event_id":"sha256:651e13b798bc0228318b81a361b5605b35d80cca80dca55b03f080ac544ff136"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2OXHKSMAF7U3ZQZMHLEVXLQJQ/bundle.json","state_url":"https://pith.science/pith/W2OXHKSMAF7U3ZQZMHLEVXLQJQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2OXHKSMAF7U3ZQZMHLEVXLQJQ/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":"2026-06-08T01:37:57Z","links":{"resolver":"https://pith.science/pith/W2OXHKSMAF7U3ZQZMHLEVXLQJQ","bundle":"https://pith.science/pith/W2OXHKSMAF7U3ZQZMHLEVXLQJQ/bundle.json","state":"https://pith.science/pith/W2OXHKSMAF7U3ZQZMHLEVXLQJQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2OXHKSMAF7U3ZQZMHLEVXLQJQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:W2OXHKSMAF7U3ZQZMHLEVXLQJQ","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":"c109f144df0c36cde6f57121112b50532091c410575ec6c14284a25de7ddeb60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-28T02:27:45Z","title_canon_sha256":"b76b33057bb6791015d27dce96b75b6d448b321af148950a9f6eb5216fe11641"},"schema_version":"1.0","source":{"id":"1410.7493","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.7493","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"arxiv_version","alias_value":"1410.7493v2","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.7493","created_at":"2026-05-18T02:29:10Z"},{"alias_kind":"pith_short_12","alias_value":"W2OXHKSMAF7U","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"W2OXHKSMAF7U3ZQZ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"W2OXHKSM","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:651e13b798bc0228318b81a361b5605b35d80cca80dca55b03f080ac544ff136","target":"graph","created_at":"2026-05-18T02:29:10Z","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":"For any bounded domain $\\Omega$ in $\\mathbb C^m,$ let ${\\mathrm B}_1(\\Omega)$ denote the Cowen-Douglas class of commuting $m$-tuples of bounded linear operators. For an $m$-tuple $\\boldsymbol T$ in the Cowen-Douglas class ${\\mathrm B}_1(\\Omega),$ let $N_{\\boldsymbol T}(w)$ denote the restriction of $\\boldsymbol T$ to the subspace ${\\cap_{i,j=1}^m\\ker(T_i-w_iI)(T_j-w_jI)}.$ This commuting $m$-tuple $N_{\\boldsymbol T}(w)$ of $m+1$ dimensional operators induces a homomorphism $\\rho_{_{\\!N_{\\boldsymbol T}(w)}}$ of the polynomial ring $P[z_1, ..., z_m],$ namely, $\\rho_{_{\\!N_{\\boldsymbol T}(w)}}(p)","authors_text":"Avijit Pal, Gadadhar Misra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-28T02:27:45Z","title":"Contractivity, complete contractivity and curvature inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7493","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:b28b3afbc5796fd9050a7529da85b1170036ca4070e260170332223ce785cfed","target":"record","created_at":"2026-05-18T02:29:10Z","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":"c109f144df0c36cde6f57121112b50532091c410575ec6c14284a25de7ddeb60","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-28T02:27:45Z","title_canon_sha256":"b76b33057bb6791015d27dce96b75b6d448b321af148950a9f6eb5216fe11641"},"schema_version":"1.0","source":{"id":"1410.7493","kind":"arxiv","version":2}},"canonical_sha256":"b69d73aa4c017f4de61961d64add704c11fd6e39f014bd889ade78924f0501d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b69d73aa4c017f4de61961d64add704c11fd6e39f014bd889ade78924f0501d2","first_computed_at":"2026-05-18T02:29:10.450420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:10.450420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GZyEkb3oa2KL8CUl0VQ7Bv5tGH780MFA0DE94lFsbRHrEndtSYWC+aDHDhe2kqGuKB5YOLC5z5ods2Vzs2MiDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:10.450888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.7493","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b28b3afbc5796fd9050a7529da85b1170036ca4070e260170332223ce785cfed","sha256:651e13b798bc0228318b81a361b5605b35d80cca80dca55b03f080ac544ff136"],"state_sha256":"86dc20578b57085bd5ada61db075be697fbb590e036ed2af32ef291a47c739e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MURMVEQIEdPlZ0GsTciuu2qzpn8RKX3hNkq2PVhE8pq4xtTI9l8wNocfdZSycNme5T3mhbpzEBfVn7nAjWNSCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T01:37:57.128054Z","bundle_sha256":"f3c8ef05e8b4c4cc00a3f88a719f0c6815bde11faaa1b22894ccdc54bd9d8042"}}