{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:MH56FSVLZUPF22LC5SFDQ2A363","short_pith_number":"pith:MH56FSVL","canonical_record":{"source":{"id":"2508.00461","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-08-01T09:33:38Z","cross_cats_sorted":[],"title_canon_sha256":"a3e2f65561607af295cd5262b6877190b204522b3c0fe2e032dd9da67a68a4ff","abstract_canon_sha256":"b2e28b7e85fc2926b53afb2390ed1914e5d935478e50f2f19ba12803e63a9706"},"schema_version":"1.0"},"canonical_sha256":"61fbe2caabcd1e5d6962ec8a38681bf6e7a2fb08922be104f4114a0ddb8042de","source":{"kind":"arxiv","id":"2508.00461","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.00461","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"arxiv_version","alias_value":"2508.00461v1","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00461","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"pith_short_12","alias_value":"MH56FSVLZUPF","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"pith_short_16","alias_value":"MH56FSVLZUPF22LC","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"pith_short_8","alias_value":"MH56FSVL","created_at":"2026-07-05T11:46:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:MH56FSVLZUPF22LC5SFDQ2A363","target":"record","payload":{"canonical_record":{"source":{"id":"2508.00461","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-08-01T09:33:38Z","cross_cats_sorted":[],"title_canon_sha256":"a3e2f65561607af295cd5262b6877190b204522b3c0fe2e032dd9da67a68a4ff","abstract_canon_sha256":"b2e28b7e85fc2926b53afb2390ed1914e5d935478e50f2f19ba12803e63a9706"},"schema_version":"1.0"},"canonical_sha256":"61fbe2caabcd1e5d6962ec8a38681bf6e7a2fb08922be104f4114a0ddb8042de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:46:56.579162Z","signature_b64":"wqtE52TK8wffH+fT0ryjSXGmt5gL9dRKNlK9I5OHza1n/b6NiwJ9+jY1xMzim39V07NqdWX9EouehNz+rNYOAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"61fbe2caabcd1e5d6962ec8a38681bf6e7a2fb08922be104f4114a0ddb8042de","last_reissued_at":"2026-07-05T11:46:56.578767Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:46:56.578767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2508.00461","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":"2026-07-05T11:46:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DzcPoPWbIp2YsIz6cy9doi92mVSfQ4v0wfTvDWMDSGVOB/2cw9CK4ZG25jOX2IY4r1RioY400obbEMn5gVmnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T12:11:22.446079Z"},"content_sha256":"9c84b24fdc881b2399339ff98776af89271faaa0644f85c7259b958c293b2344","schema_version":"1.0","event_id":"sha256:9c84b24fdc881b2399339ff98776af89271faaa0644f85c7259b958c293b2344"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:MH56FSVLZUPF22LC5SFDQ2A363","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flexibility versus genericity of phase diagrams of perturbed continuous maps on the Cantor set","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hugo Marsan, Mathieu Sablik","submitted_at":"2025-08-01T09:33:38Z","abstract_excerpt":"Consider the dynamical system constitued by a continuous function $F:\\mathcal{A}^\\mathbb{N}\\to\\mathcal{A}^\\mathbb{N}$ where $\\mathcal{A}$ is a finite alphabet. The perturbed counterpart, denoted by $F_\\epsilon$, is obtained after each iteration of $F$ by modifying each cell independently with probability $\\epsilon\\in[0,1]$ and choosing the new value uniformly. We characterize the possible sets of $\\epsilon\\in[0,1]$ such that $F_\\epsilon$ has a unique measure. These sets are exactly the $G_\\delta$ sets (countable intersection of open sets) of $[0, 1]$ which contain 1. However, we show that gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00461","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/2508.00461/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":"2026-07-05T11:46:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fMyTiAVAaTYd1sMakWwiSqWq86hkr55qSqMiCfQfrToIJ/03BgYxrlbGRXYztfzzYz1k3vxzNKkYRFjP+q+nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T12:11:22.446681Z"},"content_sha256":"2127921c2ac0b02001231bea9616af61e20d12d3e300ca5f8da2e0534eb2f4d2","schema_version":"1.0","event_id":"sha256:2127921c2ac0b02001231bea9616af61e20d12d3e300ca5f8da2e0534eb2f4d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MH56FSVLZUPF22LC5SFDQ2A363/bundle.json","state_url":"https://pith.science/pith/MH56FSVLZUPF22LC5SFDQ2A363/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MH56FSVLZUPF22LC5SFDQ2A363/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":"2026-08-17T12:11:22Z","links":{"resolver":"https://pith.science/pith/MH56FSVLZUPF22LC5SFDQ2A363","bundle":"https://pith.science/pith/MH56FSVLZUPF22LC5SFDQ2A363/bundle.json","state":"https://pith.science/pith/MH56FSVLZUPF22LC5SFDQ2A363/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MH56FSVLZUPF22LC5SFDQ2A363/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:MH56FSVLZUPF22LC5SFDQ2A363","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":"b2e28b7e85fc2926b53afb2390ed1914e5d935478e50f2f19ba12803e63a9706","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-08-01T09:33:38Z","title_canon_sha256":"a3e2f65561607af295cd5262b6877190b204522b3c0fe2e032dd9da67a68a4ff"},"schema_version":"1.0","source":{"id":"2508.00461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.00461","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"arxiv_version","alias_value":"2508.00461v1","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.00461","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"pith_short_12","alias_value":"MH56FSVLZUPF","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"pith_short_16","alias_value":"MH56FSVLZUPF22LC","created_at":"2026-07-05T11:46:56Z"},{"alias_kind":"pith_short_8","alias_value":"MH56FSVL","created_at":"2026-07-05T11:46:56Z"}],"graph_snapshots":[{"event_id":"sha256:2127921c2ac0b02001231bea9616af61e20d12d3e300ca5f8da2e0534eb2f4d2","target":"graph","created_at":"2026-07-05T11:46:56Z","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/2508.00461/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Consider the dynamical system constitued by a continuous function $F:\\mathcal{A}^\\mathbb{N}\\to\\mathcal{A}^\\mathbb{N}$ where $\\mathcal{A}$ is a finite alphabet. The perturbed counterpart, denoted by $F_\\epsilon$, is obtained after each iteration of $F$ by modifying each cell independently with probability $\\epsilon\\in[0,1]$ and choosing the new value uniformly. We characterize the possible sets of $\\epsilon\\in[0,1]$ such that $F_\\epsilon$ has a unique measure. These sets are exactly the $G_\\delta$ sets (countable intersection of open sets) of $[0, 1]$ which contain 1. However, we show that gene","authors_text":"Hugo Marsan, Mathieu Sablik","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-08-01T09:33:38Z","title":"Flexibility versus genericity of phase diagrams of perturbed continuous maps on the Cantor set"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00461","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":"sha256:9c84b24fdc881b2399339ff98776af89271faaa0644f85c7259b958c293b2344","target":"record","created_at":"2026-07-05T11:46:56Z","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":"b2e28b7e85fc2926b53afb2390ed1914e5d935478e50f2f19ba12803e63a9706","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-08-01T09:33:38Z","title_canon_sha256":"a3e2f65561607af295cd5262b6877190b204522b3c0fe2e032dd9da67a68a4ff"},"schema_version":"1.0","source":{"id":"2508.00461","kind":"arxiv","version":1}},"canonical_sha256":"61fbe2caabcd1e5d6962ec8a38681bf6e7a2fb08922be104f4114a0ddb8042de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61fbe2caabcd1e5d6962ec8a38681bf6e7a2fb08922be104f4114a0ddb8042de","first_computed_at":"2026-07-05T11:46:56.578767Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:46:56.578767Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wqtE52TK8wffH+fT0ryjSXGmt5gL9dRKNlK9I5OHza1n/b6NiwJ9+jY1xMzim39V07NqdWX9EouehNz+rNYOAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:46:56.579162Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.00461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c84b24fdc881b2399339ff98776af89271faaa0644f85c7259b958c293b2344","sha256:2127921c2ac0b02001231bea9616af61e20d12d3e300ca5f8da2e0534eb2f4d2"],"state_sha256":"0647dcfa731411a5758a9804358b03b73cc8efb27d31f117442d0f1d073c475d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wXuxqhbhu+fFAHfBQ80q6XcZNYgSDA31X2N6+E7SwRWxgo2IkMwF7VN9mBw//hDpgvIHiBN0jRv5ojVYL0lqDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T12:11:22.450859Z","bundle_sha256":"004a82975fd503103bd87cb50ba9d69a250628d7e4747de2d719c03376a36764"}}