{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QASJUHOOSIX7OMV5PQGWUL4A3U","short_pith_number":"pith:QASJUHOO","canonical_record":{"source":{"id":"2606.12052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-10T13:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"2098427d75cbd874bd63545a11478a8204b25ff9aa6af48da42ef4aa115fb1a3","abstract_canon_sha256":"45167f1d8d41330af566eee4323a9ba39a2ce512e5c3ba902fb7cc20f34b6cef"},"schema_version":"1.0"},"canonical_sha256":"80249a1dce922ff732bd7c0d6a2f80dd15b7c0bdb9605af80a8b82ad39d95f52","source":{"kind":"arxiv","id":"2606.12052","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.12052","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"2606.12052v1","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.12052","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"QASJUHOOSIX7","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"pith_short_16","alias_value":"QASJUHOOSIX7OMV5","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"pith_short_8","alias_value":"QASJUHOO","created_at":"2026-06-11T01:10:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QASJUHOOSIX7OMV5PQGWUL4A3U","target":"record","payload":{"canonical_record":{"source":{"id":"2606.12052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-10T13:16:29Z","cross_cats_sorted":[],"title_canon_sha256":"2098427d75cbd874bd63545a11478a8204b25ff9aa6af48da42ef4aa115fb1a3","abstract_canon_sha256":"45167f1d8d41330af566eee4323a9ba39a2ce512e5c3ba902fb7cc20f34b6cef"},"schema_version":"1.0"},"canonical_sha256":"80249a1dce922ff732bd7c0d6a2f80dd15b7c0bdb9605af80a8b82ad39d95f52","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-11T01:10:45.176789Z","signature_b64":"C4Vdxw/Aqwy1cVvOx2kNclYMfN3eSYJkHKeMpMqIFFPjHto0i7frLpUJwf64tjtAB3MhtzD5HuHWJB4PcFX/Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80249a1dce922ff732bd7c0d6a2f80dd15b7c0bdb9605af80a8b82ad39d95f52","last_reissued_at":"2026-06-11T01:10:45.175976Z","signature_status":"signed_v1","first_computed_at":"2026-06-11T01:10:45.175976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.12052","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":"2026-06-11T01:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7IsbU8Km5AoniHHNzURCjCV8ZeLecMHJ1+WcHJfKbHbUAYtJZ/72nsdn417NQ465ykR07jONFlT/npZGrU9DCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:13:09.488363Z"},"content_sha256":"a647963f0297ba46bf39bc13a48b1c8ccba46888b6b8d181df5746b036c27676","schema_version":"1.0","event_id":"sha256:a647963f0297ba46bf39bc13a48b1c8ccba46888b6b8d181df5746b036c27676"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QASJUHOOSIX7OMV5PQGWUL4A3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension of the Feigenbaum Attractor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mark Pollicott","submitted_at":"2026-06-10T13:16:29Z","abstract_excerpt":"In this note we propose an effective method to estimate the dimension of the Feigenbaum attractor for the period doubling phenomenon. In particular, we will describe a way to convert the highly accurate estimates for $g$ into better estimates on $\\dim(X)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12052","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/2606.12052/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":"2026-06-11T01:10:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u+R+04aHeSv6/aQMTexBo+v3Uwp9roCQBeXKs25UUk5yizHL/UfRS9c2o7rRBXzCDQTouXgU5fD1BC5dk9zuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:13:09.488730Z"},"content_sha256":"a82fba88200e13cd066d59dbcfb029a9fbb47c7181234f2f4c95d261e76646e2","schema_version":"1.0","event_id":"sha256:a82fba88200e13cd066d59dbcfb029a9fbb47c7181234f2f4c95d261e76646e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QASJUHOOSIX7OMV5PQGWUL4A3U/bundle.json","state_url":"https://pith.science/pith/QASJUHOOSIX7OMV5PQGWUL4A3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QASJUHOOSIX7OMV5PQGWUL4A3U/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":"2026-06-11T12:13:09Z","links":{"resolver":"https://pith.science/pith/QASJUHOOSIX7OMV5PQGWUL4A3U","bundle":"https://pith.science/pith/QASJUHOOSIX7OMV5PQGWUL4A3U/bundle.json","state":"https://pith.science/pith/QASJUHOOSIX7OMV5PQGWUL4A3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QASJUHOOSIX7OMV5PQGWUL4A3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QASJUHOOSIX7OMV5PQGWUL4A3U","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":"45167f1d8d41330af566eee4323a9ba39a2ce512e5c3ba902fb7cc20f34b6cef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-10T13:16:29Z","title_canon_sha256":"2098427d75cbd874bd63545a11478a8204b25ff9aa6af48da42ef4aa115fb1a3"},"schema_version":"1.0","source":{"id":"2606.12052","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.12052","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"arxiv_version","alias_value":"2606.12052v1","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.12052","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"pith_short_12","alias_value":"QASJUHOOSIX7","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"pith_short_16","alias_value":"QASJUHOOSIX7OMV5","created_at":"2026-06-11T01:10:45Z"},{"alias_kind":"pith_short_8","alias_value":"QASJUHOO","created_at":"2026-06-11T01:10:45Z"}],"graph_snapshots":[{"event_id":"sha256:a82fba88200e13cd066d59dbcfb029a9fbb47c7181234f2f4c95d261e76646e2","target":"graph","created_at":"2026-06-11T01:10:45Z","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/2606.12052/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note we propose an effective method to estimate the dimension of the Feigenbaum attractor for the period doubling phenomenon. In particular, we will describe a way to convert the highly accurate estimates for $g$ into better estimates on $\\dim(X)$.","authors_text":"Mark Pollicott","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-10T13:16:29Z","title":"Dimension of the Feigenbaum Attractor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12052","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:a647963f0297ba46bf39bc13a48b1c8ccba46888b6b8d181df5746b036c27676","target":"record","created_at":"2026-06-11T01:10:45Z","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":"45167f1d8d41330af566eee4323a9ba39a2ce512e5c3ba902fb7cc20f34b6cef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-10T13:16:29Z","title_canon_sha256":"2098427d75cbd874bd63545a11478a8204b25ff9aa6af48da42ef4aa115fb1a3"},"schema_version":"1.0","source":{"id":"2606.12052","kind":"arxiv","version":1}},"canonical_sha256":"80249a1dce922ff732bd7c0d6a2f80dd15b7c0bdb9605af80a8b82ad39d95f52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80249a1dce922ff732bd7c0d6a2f80dd15b7c0bdb9605af80a8b82ad39d95f52","first_computed_at":"2026-06-11T01:10:45.175976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-11T01:10:45.175976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"C4Vdxw/Aqwy1cVvOx2kNclYMfN3eSYJkHKeMpMqIFFPjHto0i7frLpUJwf64tjtAB3MhtzD5HuHWJB4PcFX/Dg==","signature_status":"signed_v1","signed_at":"2026-06-11T01:10:45.176789Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.12052","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a647963f0297ba46bf39bc13a48b1c8ccba46888b6b8d181df5746b036c27676","sha256:a82fba88200e13cd066d59dbcfb029a9fbb47c7181234f2f4c95d261e76646e2"],"state_sha256":"b862cfe035d78057ef718f0b4db8c6174d32d74dd13b733936c6aae67c328b23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bJpCUU7D9b5V/4eNBILNUoHhZ4mQ0+Ri9C9n7aXeO4VC+KcQEdGE5EV4CJ5PHyar8m9bW9sOe/pxOh06l7suDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:13:09.490672Z","bundle_sha256":"e114242ea8ada68f73f3f4ec45ad97bfbb44c4ae44dcb38b74bcb6b756c5c98e"}}