{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ECWB3DGSYEIWBDGXZKN2D3EYKO","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":"d082dcc025b56d031694031cfa13b590788c7ed9896a717747611a216c666bb1","cross_cats_sorted":["math.FA","math.KT","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-04-21T17:00:44Z","title_canon_sha256":"59a051de4fc13fe40dc9908ad944ed22c666aabafcf1485ba9835c9b8c6f8ae5"},"schema_version":"1.0","source":{"id":"1604.06387","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06387","created_at":"2026-05-18T01:15:22Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06387v2","created_at":"2026-05-18T01:15:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06387","created_at":"2026-05-18T01:15:22Z"},{"alias_kind":"pith_short_12","alias_value":"ECWB3DGSYEIW","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"ECWB3DGSYEIWBDGX","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"ECWB3DGS","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:bf89bd229bcc90e399fab095495feb6eb120d4838a30c1ee9ea5f3ade48de0b6","target":"graph","created_at":"2026-05-18T01:15:22Z","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":"This is an introduction to the Rapid Decay property, with a survey of known results and equivalent definitions of this property. We also discuss in details the easy case when G = Z. Everything in this paper is well-known by different sets of people.","authors_text":"Indira Chatterji","cross_cats":["math.FA","math.KT","math.OA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-04-21T17:00:44Z","title":"Introduction to the Rapid Decay property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06387","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:b4774a17fbfa4ed762252e6afa972604691d382f945738c227c829285c501a45","target":"record","created_at":"2026-05-18T01:15:22Z","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":"d082dcc025b56d031694031cfa13b590788c7ed9896a717747611a216c666bb1","cross_cats_sorted":["math.FA","math.KT","math.OA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-04-21T17:00:44Z","title_canon_sha256":"59a051de4fc13fe40dc9908ad944ed22c666aabafcf1485ba9835c9b8c6f8ae5"},"schema_version":"1.0","source":{"id":"1604.06387","kind":"arxiv","version":2}},"canonical_sha256":"20ac1d8cd2c111608cd7ca9ba1ec98538caba912b70ec0119f17b89b31acef7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20ac1d8cd2c111608cd7ca9ba1ec98538caba912b70ec0119f17b89b31acef7d","first_computed_at":"2026-05-18T01:15:22.325995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:22.325995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Avt9z52KZO3mPU2pIpdAtIL042sj0pa7V0k+6l79H1rzdlTuBRP7w2OMwP2eVzf8rSupzxGnP3nUpuGUpOIXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:22.326614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06387","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4774a17fbfa4ed762252e6afa972604691d382f945738c227c829285c501a45","sha256:bf89bd229bcc90e399fab095495feb6eb120d4838a30c1ee9ea5f3ade48de0b6"],"state_sha256":"9d81a337a82f99d888d9a7e99a5fd2c9cecb350e4855f8e1f9abd1767e8009dc"}