{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:A2CU4EWAXHN4WS3R6BBOWCXKAM","short_pith_number":"pith:A2CU4EWA","canonical_record":{"source":{"id":"1610.07941","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-10-24T01:45:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"800675ed12bf513e3e031f5a41c4614d482cf87b4302e7aa8eef0813938cb0c8","abstract_canon_sha256":"f39a6f476cb7dc49d3b15a05b587a5359039f2095c21bfb131bf3ae48c4e33cf"},"schema_version":"1.0"},"canonical_sha256":"06854e12c0b9dbcb4b71f042eb0aea03066e45e7e92538572d712c3571ab3d6a","source":{"kind":"arxiv","id":"1610.07941","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07941","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07941v2","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07941","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"A2CU4EWAXHN4","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A2CU4EWAXHN4WS3R","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A2CU4EWA","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:A2CU4EWAXHN4WS3R6BBOWCXKAM","target":"record","payload":{"canonical_record":{"source":{"id":"1610.07941","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-10-24T01:45:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"800675ed12bf513e3e031f5a41c4614d482cf87b4302e7aa8eef0813938cb0c8","abstract_canon_sha256":"f39a6f476cb7dc49d3b15a05b587a5359039f2095c21bfb131bf3ae48c4e33cf"},"schema_version":"1.0"},"canonical_sha256":"06854e12c0b9dbcb4b71f042eb0aea03066e45e7e92538572d712c3571ab3d6a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:24.452080Z","signature_b64":"Vdch80cT5OHykyxs+O9lyyjsIuJOTnt+h6FVRrHb+xl/EYGCRoRD/r/PeSvjzWWVRGKHhaoU0KBcOGBc4+NkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06854e12c0b9dbcb4b71f042eb0aea03066e45e7e92538572d712c3571ab3d6a","last_reissued_at":"2026-05-18T00:35:24.451620Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:24.451620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.07941","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h10iQOK7CEycazJcdxsCQGzfW1JRUEj9aOuXDT/rJnHfjO5Lui9XMZacf/SNlb9HEjArVbZBTX9lHXVvf1v2Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:33:40.785269Z"},"content_sha256":"a36f0fe3e05526ab21715055b9d44e66d7952b92c69aa348f147ff626e6d3473","schema_version":"1.0","event_id":"sha256:a36f0fe3e05526ab21715055b9d44e66d7952b92c69aa348f147ff626e6d3473"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:A2CU4EWAXHN4WS3R6BBOWCXKAM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distinguishability notion based on Wootters statistical distance: application to discrete maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.CD","authors_text":"Ignacio S. Gomez, Mariela Portesi, Pedro W. Lamberti","submitted_at":"2016-10-24T01:45:54Z","abstract_excerpt":"We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a distance in chaotic unidimensional maps. Based on that definition, we provide a metric $\\overline{d}$ for an arbitrary discrete map. Moreover, from this we associate a metric space to each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07941","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:35:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/HKN0jGuMAf6bOj761NKwpJnCn92YShYGrd/7Fa289V2ASTWaaI0YbbrF/EPOFW7h/OYNJ51BEilgWP0STLrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T21:33:40.785665Z"},"content_sha256":"601dc8a468d6b9b2ec095d3008ac65c70bd02d2b8e4eeaa60e5d5bf12e801e05","schema_version":"1.0","event_id":"sha256:601dc8a468d6b9b2ec095d3008ac65c70bd02d2b8e4eeaa60e5d5bf12e801e05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A2CU4EWAXHN4WS3R6BBOWCXKAM/bundle.json","state_url":"https://pith.science/pith/A2CU4EWAXHN4WS3R6BBOWCXKAM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A2CU4EWAXHN4WS3R6BBOWCXKAM/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":"2026-06-02T21:33:40Z","links":{"resolver":"https://pith.science/pith/A2CU4EWAXHN4WS3R6BBOWCXKAM","bundle":"https://pith.science/pith/A2CU4EWAXHN4WS3R6BBOWCXKAM/bundle.json","state":"https://pith.science/pith/A2CU4EWAXHN4WS3R6BBOWCXKAM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A2CU4EWAXHN4WS3R6BBOWCXKAM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A2CU4EWAXHN4WS3R6BBOWCXKAM","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":"f39a6f476cb7dc49d3b15a05b587a5359039f2095c21bfb131bf3ae48c4e33cf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-10-24T01:45:54Z","title_canon_sha256":"800675ed12bf513e3e031f5a41c4614d482cf87b4302e7aa8eef0813938cb0c8"},"schema_version":"1.0","source":{"id":"1610.07941","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.07941","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"arxiv_version","alias_value":"1610.07941v2","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.07941","created_at":"2026-05-18T00:35:24Z"},{"alias_kind":"pith_short_12","alias_value":"A2CU4EWAXHN4","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A2CU4EWAXHN4WS3R","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A2CU4EWA","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:601dc8a468d6b9b2ec095d3008ac65c70bd02d2b8e4eeaa60e5d5bf12e801e05","target":"graph","created_at":"2026-05-18T00:35:24Z","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":"We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a distance in chaotic unidimensional maps. Based on that definition, we provide a metric $\\overline{d}$ for an arbitrary discrete map. Moreover, from this we associate a metric space to each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of ","authors_text":"Ignacio S. Gomez, Mariela Portesi, Pedro W. Lamberti","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-10-24T01:45:54Z","title":"Distinguishability notion based on Wootters statistical distance: application to discrete maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.07941","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:a36f0fe3e05526ab21715055b9d44e66d7952b92c69aa348f147ff626e6d3473","target":"record","created_at":"2026-05-18T00:35:24Z","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":"f39a6f476cb7dc49d3b15a05b587a5359039f2095c21bfb131bf3ae48c4e33cf","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2016-10-24T01:45:54Z","title_canon_sha256":"800675ed12bf513e3e031f5a41c4614d482cf87b4302e7aa8eef0813938cb0c8"},"schema_version":"1.0","source":{"id":"1610.07941","kind":"arxiv","version":2}},"canonical_sha256":"06854e12c0b9dbcb4b71f042eb0aea03066e45e7e92538572d712c3571ab3d6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06854e12c0b9dbcb4b71f042eb0aea03066e45e7e92538572d712c3571ab3d6a","first_computed_at":"2026-05-18T00:35:24.451620Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:24.451620Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vdch80cT5OHykyxs+O9lyyjsIuJOTnt+h6FVRrHb+xl/EYGCRoRD/r/PeSvjzWWVRGKHhaoU0KBcOGBc4+NkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:24.452080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.07941","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a36f0fe3e05526ab21715055b9d44e66d7952b92c69aa348f147ff626e6d3473","sha256:601dc8a468d6b9b2ec095d3008ac65c70bd02d2b8e4eeaa60e5d5bf12e801e05"],"state_sha256":"f468c675c4778db90bc4f20d2c448df8771d5f08ed6c0d752fe99c22253956ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fPYV7+DIAhSGkdNFBxBslNlWmim/eiXMP3uQcPz1R83wnpTkPJcwHCrdCrtJb2wM8H/WSh6f0BB6AnwxM+2JAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T21:33:40.787777Z","bundle_sha256":"d645740e24af941be56284f703ab058e0f75e0c69c04df2971593ee66e597f5e"}}