{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:KTYSICHXUHKKA5KCHI26REKHTN","short_pith_number":"pith:KTYSICHX","canonical_record":{"source":{"id":"1511.05755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-18T12:23:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"86dd326a2981b34e9b90b7a02bc3131abbe5d17f60d0e0690351182b19b35ee0","abstract_canon_sha256":"1a2b7f36bb2fec535731fa9476d144d7b658ba9cf6e548a99a6dad99d231deed"},"schema_version":"1.0"},"canonical_sha256":"54f12408f7a1d4a075423a35e891479b5e000262767978219c13c60c713ceb08","source":{"kind":"arxiv","id":"1511.05755","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05755","created_at":"2026-05-18T00:13:48Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05755v1","created_at":"2026-05-18T00:13:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05755","created_at":"2026-05-18T00:13:48Z"},{"alias_kind":"pith_short_12","alias_value":"KTYSICHXUHKK","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KTYSICHXUHKKA5KC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KTYSICHX","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:KTYSICHXUHKKA5KCHI26REKHTN","target":"record","payload":{"canonical_record":{"source":{"id":"1511.05755","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-18T12:23:24Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"86dd326a2981b34e9b90b7a02bc3131abbe5d17f60d0e0690351182b19b35ee0","abstract_canon_sha256":"1a2b7f36bb2fec535731fa9476d144d7b658ba9cf6e548a99a6dad99d231deed"},"schema_version":"1.0"},"canonical_sha256":"54f12408f7a1d4a075423a35e891479b5e000262767978219c13c60c713ceb08","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:48.548728Z","signature_b64":"Qq389Eo0dD1cFfqPRLeYF0bmFAT6M+zKzNqM7XQRsdDNocXH7N1CJ8bgTJ0tNtRpZaR08gLIJqHtTSjYrTtUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"54f12408f7a1d4a075423a35e891479b5e000262767978219c13c60c713ceb08","last_reissued_at":"2026-05-18T00:13:48.548021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:48.548021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.05755","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":"2026-05-18T00:13:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMbXLjs4fN5QMF79AYkqo6mNIdFRtPjZXxf49YRT6HW0g69nG2+p+8L1xOaQ4eD5U4Xli+mdVBP+1qAmUjslDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:26:34.917733Z"},"content_sha256":"07017ae9095ec6dd229d7d30b639e7ccc7ab5385c367ec4c666f45e1c275f11b","schema_version":"1.0","event_id":"sha256:07017ae9095ec6dd229d7d30b639e7ccc7ab5385c367ec4c666f45e1c275f11b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:KTYSICHXUHKKA5KCHI26REKHTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"KSGNS construction for $\\tau$-maps on S-modules and $\\mathfrak{K}$-families","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Harsh Trivedi, Santanu Dey","submitted_at":"2015-11-18T12:23:24Z","abstract_excerpt":"We introduce S-modules, generalizing the notion of Krein $C^*$-modules, where a fixed unitary replaces the symmetry of Krein $C^*$-modules. The representation theory on S-modules is explored and for a given $*$-automorphism $\\alpha$ on a $C^*$-algebra the KSGNS construction for $\\alpha$-completely positive maps is proved. An extention of this theorem for $\\tau$-maps is also achieved, when $\\tau$ is an $\\alpha$-completely positive map, along with a decomposition theorem for $\\mathfrak K$-families."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05755","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":"2026-05-18T00:13:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5/LphxcjPq4DbqitDdBn7Ieretku07y7T2MgAWNlqe2D/9zZgzHVsa1+QWqh2ZBKcosGU5NEOWTskK8KxiK5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T04:26:34.918109Z"},"content_sha256":"b184626fe1f9e9dc58bc6fc55774d3d5723fa12103353782b9bc573bcc10901e","schema_version":"1.0","event_id":"sha256:b184626fe1f9e9dc58bc6fc55774d3d5723fa12103353782b9bc573bcc10901e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KTYSICHXUHKKA5KCHI26REKHTN/bundle.json","state_url":"https://pith.science/pith/KTYSICHXUHKKA5KCHI26REKHTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KTYSICHXUHKKA5KCHI26REKHTN/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":"2026-05-27T04:26:34Z","links":{"resolver":"https://pith.science/pith/KTYSICHXUHKKA5KCHI26REKHTN","bundle":"https://pith.science/pith/KTYSICHXUHKKA5KCHI26REKHTN/bundle.json","state":"https://pith.science/pith/KTYSICHXUHKKA5KCHI26REKHTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KTYSICHXUHKKA5KCHI26REKHTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KTYSICHXUHKKA5KCHI26REKHTN","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":"1a2b7f36bb2fec535731fa9476d144d7b658ba9cf6e548a99a6dad99d231deed","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-18T12:23:24Z","title_canon_sha256":"86dd326a2981b34e9b90b7a02bc3131abbe5d17f60d0e0690351182b19b35ee0"},"schema_version":"1.0","source":{"id":"1511.05755","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05755","created_at":"2026-05-18T00:13:48Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05755v1","created_at":"2026-05-18T00:13:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05755","created_at":"2026-05-18T00:13:48Z"},{"alias_kind":"pith_short_12","alias_value":"KTYSICHXUHKK","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"KTYSICHXUHKKA5KC","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"KTYSICHX","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:b184626fe1f9e9dc58bc6fc55774d3d5723fa12103353782b9bc573bcc10901e","target":"graph","created_at":"2026-05-18T00:13:48Z","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 introduce S-modules, generalizing the notion of Krein $C^*$-modules, where a fixed unitary replaces the symmetry of Krein $C^*$-modules. The representation theory on S-modules is explored and for a given $*$-automorphism $\\alpha$ on a $C^*$-algebra the KSGNS construction for $\\alpha$-completely positive maps is proved. An extention of this theorem for $\\tau$-maps is also achieved, when $\\tau$ is an $\\alpha$-completely positive map, along with a decomposition theorem for $\\mathfrak K$-families.","authors_text":"Harsh Trivedi, Santanu Dey","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-18T12:23:24Z","title":"KSGNS construction for $\\tau$-maps on S-modules and $\\mathfrak{K}$-families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05755","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":"sha256:07017ae9095ec6dd229d7d30b639e7ccc7ab5385c367ec4c666f45e1c275f11b","target":"record","created_at":"2026-05-18T00:13:48Z","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":"1a2b7f36bb2fec535731fa9476d144d7b658ba9cf6e548a99a6dad99d231deed","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-11-18T12:23:24Z","title_canon_sha256":"86dd326a2981b34e9b90b7a02bc3131abbe5d17f60d0e0690351182b19b35ee0"},"schema_version":"1.0","source":{"id":"1511.05755","kind":"arxiv","version":1}},"canonical_sha256":"54f12408f7a1d4a075423a35e891479b5e000262767978219c13c60c713ceb08","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"54f12408f7a1d4a075423a35e891479b5e000262767978219c13c60c713ceb08","first_computed_at":"2026-05-18T00:13:48.548021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:48.548021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qq389Eo0dD1cFfqPRLeYF0bmFAT6M+zKzNqM7XQRsdDNocXH7N1CJ8bgTJ0tNtRpZaR08gLIJqHtTSjYrTtUCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:48.548728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05755","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07017ae9095ec6dd229d7d30b639e7ccc7ab5385c367ec4c666f45e1c275f11b","sha256:b184626fe1f9e9dc58bc6fc55774d3d5723fa12103353782b9bc573bcc10901e"],"state_sha256":"e617e1fb4cf26d5813846e811f80c442461d03041205f1f2a230b612f802165a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5as9cN6//r9hexahwCDnAvSi3ucJU+v93kuqxv1Mf2m61gYPV06n9A7pSmg7vuoC5SdAmQgtl69L3ZXaJ1ABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:26:34.921026Z","bundle_sha256":"ca7b17de34fd11cb9a8a5660931453188be23c1ce3a1eb76717837eb1ec61402"}}