{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:OIKYYUPMWYE3OY6XNJG64TSNK7","short_pith_number":"pith:OIKYYUPM","canonical_record":{"source":{"id":"1407.2434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-09T11:10:32Z","cross_cats_sorted":[],"title_canon_sha256":"4d07cfdcbd3d1e7e1a22122e7499580a189ea171f06cab4ee6578344a6c5fc6d","abstract_canon_sha256":"85656fa9b8fd3717d92494d1384264af00004926474104c1a11d8be1b4523ba3"},"schema_version":"1.0"},"canonical_sha256":"72158c51ecb609b763d76a4dee4e4d57eb0bfee7a3b087787a2faf3b8d942c9b","source":{"kind":"arxiv","id":"1407.2434","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2434","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2434v2","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2434","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"pith_short_12","alias_value":"OIKYYUPMWYE3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OIKYYUPMWYE3OY6X","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OIKYYUPM","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:OIKYYUPMWYE3OY6XNJG64TSNK7","target":"record","payload":{"canonical_record":{"source":{"id":"1407.2434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-09T11:10:32Z","cross_cats_sorted":[],"title_canon_sha256":"4d07cfdcbd3d1e7e1a22122e7499580a189ea171f06cab4ee6578344a6c5fc6d","abstract_canon_sha256":"85656fa9b8fd3717d92494d1384264af00004926474104c1a11d8be1b4523ba3"},"schema_version":"1.0"},"canonical_sha256":"72158c51ecb609b763d76a4dee4e4d57eb0bfee7a3b087787a2faf3b8d942c9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:34.911886Z","signature_b64":"By6yegiVkztu7aLAoquRu7MyroQyf9qAb1hYnzGbYRI+3nIvSleEj+2B3rgU4pcdubzE63xoxuGBVml2iAL9DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72158c51ecb609b763d76a4dee4e4d57eb0bfee7a3b087787a2faf3b8d942c9b","last_reissued_at":"2026-05-18T01:28:34.911391Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:34.911391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.2434","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":"2026-05-18T01:28:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bpJ17AxB2hN/7OMm1njopdTbDRwp3CH0fJEq9fRVBXKMzaIp7V7l8+bqLekP83zUKwzl6xRQFz2FFXEUBk74Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:42:54.399178Z"},"content_sha256":"8ac7b9e4959f5197e99fddb2fcbc5f91e0ba61a326ff26893280f79bf5ff3518","schema_version":"1.0","event_id":"sha256:8ac7b9e4959f5197e99fddb2fcbc5f91e0ba61a326ff26893280f79bf5ff3518"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:OIKYYUPMWYE3OY6XNJG64TSNK7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric duality theory of cones in dual pairs of vector spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Miek Messerschmidt","submitted_at":"2014-07-09T11:10:32Z","abstract_excerpt":"This paper will generalize what may be termed the \"geometric duality theory\" of real pre-ordered Banach spaces which relates geometric properties of a closed cone in a real Banach space, to geometric properties of the dual cone in the dual Banach space. We show that geometric duality theory is not restricted to real pre-ordered Banach spaces, as is done classically, but can be extended to real Banach spaces endowed with arbitrary collections of closed cones.\n  We define geometric notions of normality, conormality, additivity and coadditivity for members of dual pairs of real vector spaces as c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2434","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":"2026-05-18T01:28:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2RkdVL3TctyfoSriu5MdSvluZ/QiLKOuj/VVRMObTmXClbwprSBRBxXrlohzxHbBI6W2MSfktc7CGNul5Kc4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T18:42:54.399540Z"},"content_sha256":"6e4c034e1edefc7638e69d96fceeb4492a44a850b2d7cdc82feb68e0a187d8db","schema_version":"1.0","event_id":"sha256:6e4c034e1edefc7638e69d96fceeb4492a44a850b2d7cdc82feb68e0a187d8db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OIKYYUPMWYE3OY6XNJG64TSNK7/bundle.json","state_url":"https://pith.science/pith/OIKYYUPMWYE3OY6XNJG64TSNK7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OIKYYUPMWYE3OY6XNJG64TSNK7/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":"2026-06-22T18:42:54Z","links":{"resolver":"https://pith.science/pith/OIKYYUPMWYE3OY6XNJG64TSNK7","bundle":"https://pith.science/pith/OIKYYUPMWYE3OY6XNJG64TSNK7/bundle.json","state":"https://pith.science/pith/OIKYYUPMWYE3OY6XNJG64TSNK7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OIKYYUPMWYE3OY6XNJG64TSNK7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OIKYYUPMWYE3OY6XNJG64TSNK7","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":"85656fa9b8fd3717d92494d1384264af00004926474104c1a11d8be1b4523ba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-09T11:10:32Z","title_canon_sha256":"4d07cfdcbd3d1e7e1a22122e7499580a189ea171f06cab4ee6578344a6c5fc6d"},"schema_version":"1.0","source":{"id":"1407.2434","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2434","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2434v2","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2434","created_at":"2026-05-18T01:28:34Z"},{"alias_kind":"pith_short_12","alias_value":"OIKYYUPMWYE3","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OIKYYUPMWYE3OY6X","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OIKYYUPM","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:6e4c034e1edefc7638e69d96fceeb4492a44a850b2d7cdc82feb68e0a187d8db","target":"graph","created_at":"2026-05-18T01:28:34Z","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":"This paper will generalize what may be termed the \"geometric duality theory\" of real pre-ordered Banach spaces which relates geometric properties of a closed cone in a real Banach space, to geometric properties of the dual cone in the dual Banach space. We show that geometric duality theory is not restricted to real pre-ordered Banach spaces, as is done classically, but can be extended to real Banach spaces endowed with arbitrary collections of closed cones.\n  We define geometric notions of normality, conormality, additivity and coadditivity for members of dual pairs of real vector spaces as c","authors_text":"Miek Messerschmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-09T11:10:32Z","title":"Geometric duality theory of cones in dual pairs of vector spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2434","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":"sha256:8ac7b9e4959f5197e99fddb2fcbc5f91e0ba61a326ff26893280f79bf5ff3518","target":"record","created_at":"2026-05-18T01:28:34Z","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":"85656fa9b8fd3717d92494d1384264af00004926474104c1a11d8be1b4523ba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-09T11:10:32Z","title_canon_sha256":"4d07cfdcbd3d1e7e1a22122e7499580a189ea171f06cab4ee6578344a6c5fc6d"},"schema_version":"1.0","source":{"id":"1407.2434","kind":"arxiv","version":2}},"canonical_sha256":"72158c51ecb609b763d76a4dee4e4d57eb0bfee7a3b087787a2faf3b8d942c9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72158c51ecb609b763d76a4dee4e4d57eb0bfee7a3b087787a2faf3b8d942c9b","first_computed_at":"2026-05-18T01:28:34.911391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:34.911391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"By6yegiVkztu7aLAoquRu7MyroQyf9qAb1hYnzGbYRI+3nIvSleEj+2B3rgU4pcdubzE63xoxuGBVml2iAL9DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:34.911886Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2434","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ac7b9e4959f5197e99fddb2fcbc5f91e0ba61a326ff26893280f79bf5ff3518","sha256:6e4c034e1edefc7638e69d96fceeb4492a44a850b2d7cdc82feb68e0a187d8db"],"state_sha256":"241434dacf57fc77806d13b0aa467aff8c1ec0ed5b226feeb3034a4865bcbe6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2boSL+bzXHThWhpFhBOKIFNzVkDf8/k8aRMyXQIbDWHJQRUoz6jzPxqlnvVea2UVvjJTKNRoLdNqNqRDhrzgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T18:42:54.401469Z","bundle_sha256":"30f01bcdab711da14a1c22655802ae26534ffce292325c0558ee0e919ee9885a"}}