{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5K4PH2QRPQUOVV2754RDBSYGOR","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":"ec95471296297cdd46f8bcc86250223786cc21db32c154abe6a9e40c7eaf044a","cross_cats_sorted":["math.DS","math.FA","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-10T15:57:35Z","title_canon_sha256":"dc451d05e045553af8093a678a62de18d92f6985022e207d73d5cd2c5230af4f"},"schema_version":"1.0","source":{"id":"1612.03309","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03309","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03309v1","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03309","created_at":"2026-05-18T00:26:01Z"},{"alias_kind":"pith_short_12","alias_value":"5K4PH2QRPQUO","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5K4PH2QRPQUOVV27","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5K4PH2QR","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:aba08a1dba4bb5523dd673cb1c5a0e514021a1881a1859d283bc65a6a29df89f","target":"graph","created_at":"2026-05-18T00:26:01Z","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":"Given an action $\\alpha$ of a discrete group $G$ on a unital C*-algebra $A$, we introduce a natural concept of $\\alpha$-negative definiteness for functions from $G$ to $A$, and examine some of the first consequences of such a notion. In particular, we prove analogs of theorems due to Delorme-Guichardet and Schoenberg in the classical case where $A$ is trivial. We also give a characterization of the Haagerup property for the action $\\alpha$ when $G$ is countable.","authors_text":"Erik Bedos, Roberto Conti","cross_cats":["math.DS","math.FA","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-10T15:57:35Z","title":"Negative definite functions for C*-dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03309","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":"sha256:527e2e8975a79488c446140cf86a7285e93770d4264d2140cd2e0951f30f24fd","target":"record","created_at":"2026-05-18T00:26:01Z","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":"ec95471296297cdd46f8bcc86250223786cc21db32c154abe6a9e40c7eaf044a","cross_cats_sorted":["math.DS","math.FA","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-12-10T15:57:35Z","title_canon_sha256":"dc451d05e045553af8093a678a62de18d92f6985022e207d73d5cd2c5230af4f"},"schema_version":"1.0","source":{"id":"1612.03309","kind":"arxiv","version":1}},"canonical_sha256":"eab8f3ea117c28ead75fef2230cb06746e16f2a4e37f81ef5d52f60aa6620090","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eab8f3ea117c28ead75fef2230cb06746e16f2a4e37f81ef5d52f60aa6620090","first_computed_at":"2026-05-18T00:26:01.606835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:01.606835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/ptLJAmiJNfV3V+E1lkwavnwhh98Fu6K/1hjrOrVwrljwAZ2p8rbcTe90q0CtStu2o1kbLhMWTD4O1x4WZLcDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:01.607509Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03309","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:527e2e8975a79488c446140cf86a7285e93770d4264d2140cd2e0951f30f24fd","sha256:aba08a1dba4bb5523dd673cb1c5a0e514021a1881a1859d283bc65a6a29df89f"],"state_sha256":"1d1de43705f97274f8ccb098c997ce05c3eabdadfc9503f3276431419fb4bcf4"}