{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LZM35R7EEICVYMXHHZD5API6PI","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":"11b89d0486a40ccf9beec86afa7c9d42864cf45dd609df485318c20a8a7fec2d","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-19T08:37:05Z","title_canon_sha256":"92f0a88c6bdaf4ea3f8650ad8e179ebea6f20761f856c5445641aa79fe17256e"},"schema_version":"1.0","source":{"id":"1701.05330","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05330","created_at":"2026-05-18T00:52:30Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05330v1","created_at":"2026-05-18T00:52:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05330","created_at":"2026-05-18T00:52:30Z"},{"alias_kind":"pith_short_12","alias_value":"LZM35R7EEICV","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LZM35R7EEICVYMXH","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LZM35R7E","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:e095ac627a9d87808e026d90bb8c6559fb41697532337c761bdee06cd68f4dfb","target":"graph","created_at":"2026-05-18T00:52:30Z","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":"It is proved that a norm-decreasing homomorphism of commutative Banach algebras is an effective descent morphism for Banach modules if and only if it is a weak retract.","authors_text":"Bachuki Mesablishvili","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-19T08:37:05Z","title":"Effective descent morphisms for Banach modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05330","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:a49609356e4875121ec8eb8bb5f19ba991534e4359fc2643397a0400cf122768","target":"record","created_at":"2026-05-18T00:52:30Z","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":"11b89d0486a40ccf9beec86afa7c9d42864cf45dd609df485318c20a8a7fec2d","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-19T08:37:05Z","title_canon_sha256":"92f0a88c6bdaf4ea3f8650ad8e179ebea6f20761f856c5445641aa79fe17256e"},"schema_version":"1.0","source":{"id":"1701.05330","kind":"arxiv","version":1}},"canonical_sha256":"5e59bec7e422055c32e73e47d03d1e7a0dcdda619a18ff9948fec748e7c37586","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e59bec7e422055c32e73e47d03d1e7a0dcdda619a18ff9948fec748e7c37586","first_computed_at":"2026-05-18T00:52:30.218165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:30.218165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TGiV0+4CaBAqjRa8lk8W9C7EK9vdfP6tUxMeJnYhYRp47MZNNqSfJIGBDAo8/1kE3pzf9Ly4Ne0yuinvjmjdCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:30.218890Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05330","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a49609356e4875121ec8eb8bb5f19ba991534e4359fc2643397a0400cf122768","sha256:e095ac627a9d87808e026d90bb8c6559fb41697532337c761bdee06cd68f4dfb"],"state_sha256":"5347e9fdc72f39a6c70e9d53a277ce7a176c4d8cca93dd0b9ed7394a72a25467"}