{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:LZ45NR6BXXZKOA7ZWTTTTODQRN","short_pith_number":"pith:LZ45NR6B","canonical_record":{"source":{"id":"2405.05948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-05-09T17:37:02Z","cross_cats_sorted":[],"title_canon_sha256":"4b400ce82a629b89c3bc56b4f056b3edb053b20b3cff2b49ab9663e5c3452498","abstract_canon_sha256":"bbb2e950057b0fc5c6508f5c5f24e44a4ed127e42ed300b8f96e5f506329fe0a"},"schema_version":"1.0"},"canonical_sha256":"5e79d6c7c1bdf2a703f9b4e739b8708b60d5de399022fe1d33bf7ad81f9b8d65","source":{"kind":"arxiv","id":"2405.05948","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.05948","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"2405.05948v1","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05948","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"LZ45NR6BXXZK","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"pith_short_16","alias_value":"LZ45NR6BXXZKOA7Z","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"pith_short_8","alias_value":"LZ45NR6B","created_at":"2026-07-05T08:17:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:LZ45NR6BXXZKOA7ZWTTTTODQRN","target":"record","payload":{"canonical_record":{"source":{"id":"2405.05948","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-05-09T17:37:02Z","cross_cats_sorted":[],"title_canon_sha256":"4b400ce82a629b89c3bc56b4f056b3edb053b20b3cff2b49ab9663e5c3452498","abstract_canon_sha256":"bbb2e950057b0fc5c6508f5c5f24e44a4ed127e42ed300b8f96e5f506329fe0a"},"schema_version":"1.0"},"canonical_sha256":"5e79d6c7c1bdf2a703f9b4e739b8708b60d5de399022fe1d33bf7ad81f9b8d65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:25.152682Z","signature_b64":"0Em8+ZIow2+IfXZwGmaC4PjktGBMNiFMc8Y35oleZE/SSWcW3/y0jzbC3bXCGjjScT98bnGQ0oBcTKC0fDAsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e79d6c7c1bdf2a703f9b4e739b8708b60d5de399022fe1d33bf7ad81f9b8d65","last_reissued_at":"2026-07-05T08:17:25.152273Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:25.152273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.05948","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":"2026-07-05T08:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dm6ET/bM5YQPoZf7N30nZ5hnTBTTa0fwbRI3Jv2DvzjEHGmYs7qEgHCq/qZvhi0ABOjlf2kq+rVKYZeQYebYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:42.228180Z"},"content_sha256":"5c5e699f52446d14ba9f98fccac241d80410609632674a7e5e3535d787fc57e5","schema_version":"1.0","event_id":"sha256:5c5e699f52446d14ba9f98fccac241d80410609632674a7e5e3535d787fc57e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:LZ45NR6BXXZKOA7ZWTTTTODQRN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniformly global observables for 1D maps with an indifferent fixed point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Giovanni Canestrari, Marco Lenci","submitted_at":"2024-05-09T17:37:02Z","abstract_excerpt":"We study the property of global-local mixing for full-branched expanding maps of either the half-line or the interval, with one indifferent fixed point. Global-local mixing expresses the decorrelation of global vs local observables w.r.t. to an infinite measure $\\mu$. Global observables are essentially bounded functions admitting an infinite-volume average, i.e., a limit for the average of the function over bigger and bigger intervals; local observables are integrable functions (both notions are relative to $\\mu$). Of course, the definition of global observable depends on the exact definition "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05948","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.05948/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MOvkdYxdns5HN6obLwVI8qaCmAiupu5pbZDD6CB61OqBLkH4XLEZhDojQo0pu1ZlFNONykwxUl/vIfQD6zHODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T11:07:42.228766Z"},"content_sha256":"00fd40924a4167b5603537b6570c956df8bdcf849b5d86d870534d5226a40943","schema_version":"1.0","event_id":"sha256:00fd40924a4167b5603537b6570c956df8bdcf849b5d86d870534d5226a40943"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LZ45NR6BXXZKOA7ZWTTTTODQRN/bundle.json","state_url":"https://pith.science/pith/LZ45NR6BXXZKOA7ZWTTTTODQRN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LZ45NR6BXXZKOA7ZWTTTTODQRN/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":"2026-08-22T11:07:42Z","links":{"resolver":"https://pith.science/pith/LZ45NR6BXXZKOA7ZWTTTTODQRN","bundle":"https://pith.science/pith/LZ45NR6BXXZKOA7ZWTTTTODQRN/bundle.json","state":"https://pith.science/pith/LZ45NR6BXXZKOA7ZWTTTTODQRN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LZ45NR6BXXZKOA7ZWTTTTODQRN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:LZ45NR6BXXZKOA7ZWTTTTODQRN","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":"bbb2e950057b0fc5c6508f5c5f24e44a4ed127e42ed300b8f96e5f506329fe0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-05-09T17:37:02Z","title_canon_sha256":"4b400ce82a629b89c3bc56b4f056b3edb053b20b3cff2b49ab9663e5c3452498"},"schema_version":"1.0","source":{"id":"2405.05948","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.05948","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"2405.05948v1","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.05948","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"LZ45NR6BXXZK","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"pith_short_16","alias_value":"LZ45NR6BXXZKOA7Z","created_at":"2026-07-05T08:17:25Z"},{"alias_kind":"pith_short_8","alias_value":"LZ45NR6B","created_at":"2026-07-05T08:17:25Z"}],"graph_snapshots":[{"event_id":"sha256:00fd40924a4167b5603537b6570c956df8bdcf849b5d86d870534d5226a40943","target":"graph","created_at":"2026-07-05T08:17:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.05948/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the property of global-local mixing for full-branched expanding maps of either the half-line or the interval, with one indifferent fixed point. Global-local mixing expresses the decorrelation of global vs local observables w.r.t. to an infinite measure $\\mu$. Global observables are essentially bounded functions admitting an infinite-volume average, i.e., a limit for the average of the function over bigger and bigger intervals; local observables are integrable functions (both notions are relative to $\\mu$). Of course, the definition of global observable depends on the exact definition ","authors_text":"Giovanni Canestrari, Marco Lenci","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-05-09T17:37:02Z","title":"Uniformly global observables for 1D maps with an indifferent fixed point"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.05948","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":"sha256:5c5e699f52446d14ba9f98fccac241d80410609632674a7e5e3535d787fc57e5","target":"record","created_at":"2026-07-05T08:17:25Z","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":"bbb2e950057b0fc5c6508f5c5f24e44a4ed127e42ed300b8f96e5f506329fe0a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2024-05-09T17:37:02Z","title_canon_sha256":"4b400ce82a629b89c3bc56b4f056b3edb053b20b3cff2b49ab9663e5c3452498"},"schema_version":"1.0","source":{"id":"2405.05948","kind":"arxiv","version":1}},"canonical_sha256":"5e79d6c7c1bdf2a703f9b4e739b8708b60d5de399022fe1d33bf7ad81f9b8d65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e79d6c7c1bdf2a703f9b4e739b8708b60d5de399022fe1d33bf7ad81f9b8d65","first_computed_at":"2026-07-05T08:17:25.152273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:17:25.152273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0Em8+ZIow2+IfXZwGmaC4PjktGBMNiFMc8Y35oleZE/SSWcW3/y0jzbC3bXCGjjScT98bnGQ0oBcTKC0fDAsCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:17:25.152682Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.05948","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c5e699f52446d14ba9f98fccac241d80410609632674a7e5e3535d787fc57e5","sha256:00fd40924a4167b5603537b6570c956df8bdcf849b5d86d870534d5226a40943"],"state_sha256":"a84bec07e7637332c021f49ef33ff72708a8569ed7cc99f13c897333d9a0eca9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTb+rJjC1lQLn9I5zZ8lGsEnt9kcolanY9EVCFaAs46ezP1doyi89ikeg6d12TBAryXadYNJc/6me1dAmHh8AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T11:07:42.233189Z","bundle_sha256":"6708449abc35818deb9b692f0243c1b015a097e457546cd8e4054ac3f3685f84"}}