{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:KMTKA2TU6XQAATAYBKY6GSWCOI","short_pith_number":"pith:KMTKA2TU","canonical_record":{"source":{"id":"1407.7264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-27T17:44:36Z","cross_cats_sorted":[],"title_canon_sha256":"cd8d3a25cb8d1465ec2ee9f53e9ede69e5de283164d1a88511ad9eab1b6bcc5e","abstract_canon_sha256":"9055ab5be64b9fd8846c8c01a9fbee67d138fa0af51de7bdf3572e431a53d56d"},"schema_version":"1.0"},"canonical_sha256":"5326a06a74f5e0004c180ab1e34ac27228b6c2efa2bac7edbbd63f7be2bd9d43","source":{"kind":"arxiv","id":"1407.7264","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7264","created_at":"2026-05-18T00:47:16Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7264v1","created_at":"2026-05-18T00:47:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7264","created_at":"2026-05-18T00:47:16Z"},{"alias_kind":"pith_short_12","alias_value":"KMTKA2TU6XQA","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KMTKA2TU6XQAATAY","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KMTKA2TU","created_at":"2026-05-18T12:28:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:KMTKA2TU6XQAATAYBKY6GSWCOI","target":"record","payload":{"canonical_record":{"source":{"id":"1407.7264","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-27T17:44:36Z","cross_cats_sorted":[],"title_canon_sha256":"cd8d3a25cb8d1465ec2ee9f53e9ede69e5de283164d1a88511ad9eab1b6bcc5e","abstract_canon_sha256":"9055ab5be64b9fd8846c8c01a9fbee67d138fa0af51de7bdf3572e431a53d56d"},"schema_version":"1.0"},"canonical_sha256":"5326a06a74f5e0004c180ab1e34ac27228b6c2efa2bac7edbbd63f7be2bd9d43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:16.017174Z","signature_b64":"cPlg8NWAMfiZeRK0JFAYJFkle4GMgFX6eCz9nAvNFLereobKcfYI52trfMim4ZXGDUAmzZao2gvMqE1GsZgHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5326a06a74f5e0004c180ab1e34ac27228b6c2efa2bac7edbbd63f7be2bd9d43","last_reissued_at":"2026-05-18T00:47:16.016469Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:16.016469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.7264","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":"2026-05-18T00:47:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LvH1gBGppTlG/xqjGVAGZLtp4d4pyGWaCndVlTbP9TUeKesUl+iDujIvbBKWgHmLtWOBomTBmvMf+GDO8OgiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:03:30.512689Z"},"content_sha256":"d5a9517dedb454e962ce9ac3bd982792fb4088ab0d6654b18a411abc8cacc1ab","schema_version":"1.0","event_id":"sha256:d5a9517dedb454e962ce9ac3bd982792fb4088ab0d6654b18a411abc8cacc1ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:KMTKA2TU6XQAATAYBKY6GSWCOI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Cohomology for Product Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Jeong Hee Hong, Mi Jung Son, Wojciech Szymanski","submitted_at":"2014-07-27T17:44:36Z","abstract_excerpt":"A cohomology for product systems of Hilbert bimodules is defined via the Ext functor. For the class of product systems corresponding to irreversible algebraic dynamics, relevant resolutions are found explicitly and it is shown how the underlying product system can be twisted by the 2-cocycles. In particular, this process gives rise to cohomological deformations of the C*-algebras associated with the product system. Concrete examples of deformations of the Cuntz's algebra Q_N arising this way are investigated and we show they are simple and purely infinite."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7264","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":"2026-05-18T00:47:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LoHNdCZ+ZCMVynqCsFM9o1KrfXez6/82kvMftgad1835MxqMlo4MdqoAA8kHWgS7Zyp26LMuVeUTiK5ygwQ7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T04:03:30.513045Z"},"content_sha256":"0a8630a3324df94018da6659d2c2a7922f0209717a5e62594c500b543732f980","schema_version":"1.0","event_id":"sha256:0a8630a3324df94018da6659d2c2a7922f0209717a5e62594c500b543732f980"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KMTKA2TU6XQAATAYBKY6GSWCOI/bundle.json","state_url":"https://pith.science/pith/KMTKA2TU6XQAATAYBKY6GSWCOI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KMTKA2TU6XQAATAYBKY6GSWCOI/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":"2026-05-28T04:03:30Z","links":{"resolver":"https://pith.science/pith/KMTKA2TU6XQAATAYBKY6GSWCOI","bundle":"https://pith.science/pith/KMTKA2TU6XQAATAYBKY6GSWCOI/bundle.json","state":"https://pith.science/pith/KMTKA2TU6XQAATAYBKY6GSWCOI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KMTKA2TU6XQAATAYBKY6GSWCOI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KMTKA2TU6XQAATAYBKY6GSWCOI","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":"9055ab5be64b9fd8846c8c01a9fbee67d138fa0af51de7bdf3572e431a53d56d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-27T17:44:36Z","title_canon_sha256":"cd8d3a25cb8d1465ec2ee9f53e9ede69e5de283164d1a88511ad9eab1b6bcc5e"},"schema_version":"1.0","source":{"id":"1407.7264","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7264","created_at":"2026-05-18T00:47:16Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7264v1","created_at":"2026-05-18T00:47:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7264","created_at":"2026-05-18T00:47:16Z"},{"alias_kind":"pith_short_12","alias_value":"KMTKA2TU6XQA","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KMTKA2TU6XQAATAY","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KMTKA2TU","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:0a8630a3324df94018da6659d2c2a7922f0209717a5e62594c500b543732f980","target":"graph","created_at":"2026-05-18T00:47:16Z","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":"A cohomology for product systems of Hilbert bimodules is defined via the Ext functor. For the class of product systems corresponding to irreversible algebraic dynamics, relevant resolutions are found explicitly and it is shown how the underlying product system can be twisted by the 2-cocycles. In particular, this process gives rise to cohomological deformations of the C*-algebras associated with the product system. Concrete examples of deformations of the Cuntz's algebra Q_N arising this way are investigated and we show they are simple and purely infinite.","authors_text":"Jeong Hee Hong, Mi Jung Son, Wojciech Szymanski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-27T17:44:36Z","title":"On Cohomology for Product Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7264","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:d5a9517dedb454e962ce9ac3bd982792fb4088ab0d6654b18a411abc8cacc1ab","target":"record","created_at":"2026-05-18T00:47:16Z","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":"9055ab5be64b9fd8846c8c01a9fbee67d138fa0af51de7bdf3572e431a53d56d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-27T17:44:36Z","title_canon_sha256":"cd8d3a25cb8d1465ec2ee9f53e9ede69e5de283164d1a88511ad9eab1b6bcc5e"},"schema_version":"1.0","source":{"id":"1407.7264","kind":"arxiv","version":1}},"canonical_sha256":"5326a06a74f5e0004c180ab1e34ac27228b6c2efa2bac7edbbd63f7be2bd9d43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5326a06a74f5e0004c180ab1e34ac27228b6c2efa2bac7edbbd63f7be2bd9d43","first_computed_at":"2026-05-18T00:47:16.016469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:16.016469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cPlg8NWAMfiZeRK0JFAYJFkle4GMgFX6eCz9nAvNFLereobKcfYI52trfMim4ZXGDUAmzZao2gvMqE1GsZgHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:16.017174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7264","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5a9517dedb454e962ce9ac3bd982792fb4088ab0d6654b18a411abc8cacc1ab","sha256:0a8630a3324df94018da6659d2c2a7922f0209717a5e62594c500b543732f980"],"state_sha256":"d3459ec1337c2274c6c00114902f8b8e6626bca62e106129f10c9451b9a992bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVH92p7MZT/gfMVHBNqqFOAjPkwxo3h9o5bdHyEXG/RqlVS2Ru6KcGKtgZ/Fcbnn0bWrnC9731rIK3EMhwojAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T04:03:30.515225Z","bundle_sha256":"274a8f8fca74c998297aa82d705df01dcb63ab9b8b800f4fbfd459ad32332e42"}}