{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MFZVUXCASJ2Q3DWJEH6YAZMS2W","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":"884697eeadbe13c2ec34d5902d2ab15e53e1f033dadcc3d681f547fd4fd8fb33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-27T16:05:30Z","title_canon_sha256":"866e67d513ddee57db3ef72f4feb9678c0b0a77303d40ab4129dc0fc9809cee5"},"schema_version":"1.0","source":{"id":"1606.08338","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.08338","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"arxiv_version","alias_value":"1606.08338v2","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.08338","created_at":"2026-05-18T01:07:53Z"},{"alias_kind":"pith_short_12","alias_value":"MFZVUXCASJ2Q","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MFZVUXCASJ2Q3DWJ","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MFZVUXCA","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:1fd086a3a6634ff80af652a504c3b5f57c7d1a2552a779c0b028f9bb66279794","target":"graph","created_at":"2026-05-18T01:07:53Z","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":"In this paper, for a Banach algebra A, we introduced the new notions of approximately left $\\phi$-biprojective and approximately left character biprojective, where $\\phi$ is a non-zero multiplicative linear functional on A. We show that for SIN group G, Segal algebra S(G) is approximately left $\\phi_1$- biprojective if and only if G is amenable, where $\\phi_1$ is the augmentation character on S(G). Also we showed that the measure algebra M(G) is approximately left character biprojective if and only if G is discrete and amenable. For a Clifford semigroup S, we show that `1(S) is approximately l","authors_text":"Amir Sahami","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-27T16:05:30Z","title":"On approximately left phi-biprojective Banach algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.08338","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":"sha256:2766010fcf153f4d2e2c206762385c6f28befc43ee85e09488483b8df0474fce","target":"record","created_at":"2026-05-18T01:07:53Z","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":"884697eeadbe13c2ec34d5902d2ab15e53e1f033dadcc3d681f547fd4fd8fb33","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-27T16:05:30Z","title_canon_sha256":"866e67d513ddee57db3ef72f4feb9678c0b0a77303d40ab4129dc0fc9809cee5"},"schema_version":"1.0","source":{"id":"1606.08338","kind":"arxiv","version":2}},"canonical_sha256":"61735a5c4092750d8ec921fd806592d58f358de9f36ae59a98d8f8bcc5dcd7a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61735a5c4092750d8ec921fd806592d58f358de9f36ae59a98d8f8bcc5dcd7a8","first_computed_at":"2026-05-18T01:07:53.559723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:53.559723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pJbYCNz/lW20rz1Djn4E8vl/Yd7gj4xVMDjQuCljpxCKrq4/6VkFfmgtczNtOkYikf4UrXaVcYOYhP3Yz0nMDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:53.560154Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.08338","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2766010fcf153f4d2e2c206762385c6f28befc43ee85e09488483b8df0474fce","sha256:1fd086a3a6634ff80af652a504c3b5f57c7d1a2552a779c0b028f9bb66279794"],"state_sha256":"f8dccd21b997fd8f12c0fba2f1137203a98d3b50fa8dea864b880cc6882ec6f5"}