{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QU3FIQWJ6TQSA5IH3CCX3L7ISC","short_pith_number":"pith:QU3FIQWJ","canonical_record":{"source":{"id":"2606.08746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-07T17:35:59Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"5e51b5ba68d41b200a589c655405fa5f989226e767999c303ee474175f0e0e6a","abstract_canon_sha256":"f062f5ee168f681dcce0f367a0ee132a4c183fe7a25f15c0b05fd2432577c320"},"schema_version":"1.0"},"canonical_sha256":"85365442c9f4e1207507d8857dafe890a0b19619f8b19cf33a39f3d1624b162e","source":{"kind":"arxiv","id":"2606.08746","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08746","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08746v1","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08746","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"pith_short_12","alias_value":"QU3FIQWJ6TQS","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"pith_short_16","alias_value":"QU3FIQWJ6TQSA5IH","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"pith_short_8","alias_value":"QU3FIQWJ","created_at":"2026-06-09T02:07:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QU3FIQWJ6TQSA5IH3CCX3L7ISC","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08746","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-07T17:35:59Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"5e51b5ba68d41b200a589c655405fa5f989226e767999c303ee474175f0e0e6a","abstract_canon_sha256":"f062f5ee168f681dcce0f367a0ee132a4c183fe7a25f15c0b05fd2432577c320"},"schema_version":"1.0"},"canonical_sha256":"85365442c9f4e1207507d8857dafe890a0b19619f8b19cf33a39f3d1624b162e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T02:07:36.938514Z","signature_b64":"bJFby2xNAGj3liMifEvSs5PYgqgjtbsPOvaT//UmNPHgdNKQpzcVEOW3LVWka4M/I9+0pAduPQ+wN9sOeK5rCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85365442c9f4e1207507d8857dafe890a0b19619f8b19cf33a39f3d1624b162e","last_reissued_at":"2026-06-09T02:07:36.937405Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T02:07:36.937405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08746","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":"2026-06-09T02:07:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZOSIdjvSprEG6uAPMN88/W8Fx3zFrDVpx7cweAofblHXSMfO5+Ge4lYDNfTNZrz7Otk7dKGG3a+tMG3i2RycCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:11:05.860249Z"},"content_sha256":"15087f91020a427639ab4ace46bf4728bd208c83f7d3b172bf47f582b7c415f7","schema_version":"1.0","event_id":"sha256:15087f91020a427639ab4ace46bf4728bd208c83f7d3b172bf47f582b7c415f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QU3FIQWJ6TQSA5IH3CCX3L7ISC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the support of measures of large entropy for automorphisms of K\\\"ahler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DS","authors_text":"Fabrizio Bianchi, Karim Rakhimov, Sobir Boymurodov","submitted_at":"2026-06-07T17:35:59Z","abstract_excerpt":"Let $f$ be a holomorphic automorphism of a compact K\\\"ahler manifold $X$ with simple action on cohomology. We show that every ergodic measure with sufficiently large entropy is supported on the Julia set of $f$. In particular, when $X$ is a surface, any ergodic measure with positive entropy is supported on the Julia set. The proof relies on quantitative estimates for the speed of convergence towards the Green currents of $f$, with respect to a suitable norm on an adapted functional space of non-necessarily closed currents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08746","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/2606.08746/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":"2026-06-09T02:07:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p7DDmFImUhk2t1Ggp9ptgyudaDSE6K0nJ/AhoYzPO4cuno9fCqIgeaKIslU1e6voH0RXkfAXYXz2ARctoIKkDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T01:11:05.861055Z"},"content_sha256":"95a23860fc69b0a62f304b85301f1b269aa5faddaee2966ad9e24cdeb375fc0b","schema_version":"1.0","event_id":"sha256:95a23860fc69b0a62f304b85301f1b269aa5faddaee2966ad9e24cdeb375fc0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QU3FIQWJ6TQSA5IH3CCX3L7ISC/bundle.json","state_url":"https://pith.science/pith/QU3FIQWJ6TQSA5IH3CCX3L7ISC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QU3FIQWJ6TQSA5IH3CCX3L7ISC/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":"2026-06-11T01:11:05Z","links":{"resolver":"https://pith.science/pith/QU3FIQWJ6TQSA5IH3CCX3L7ISC","bundle":"https://pith.science/pith/QU3FIQWJ6TQSA5IH3CCX3L7ISC/bundle.json","state":"https://pith.science/pith/QU3FIQWJ6TQSA5IH3CCX3L7ISC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QU3FIQWJ6TQSA5IH3CCX3L7ISC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QU3FIQWJ6TQSA5IH3CCX3L7ISC","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":"f062f5ee168f681dcce0f367a0ee132a4c183fe7a25f15c0b05fd2432577c320","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-07T17:35:59Z","title_canon_sha256":"5e51b5ba68d41b200a589c655405fa5f989226e767999c303ee474175f0e0e6a"},"schema_version":"1.0","source":{"id":"2606.08746","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08746","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08746v1","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08746","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"pith_short_12","alias_value":"QU3FIQWJ6TQS","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"pith_short_16","alias_value":"QU3FIQWJ6TQSA5IH","created_at":"2026-06-09T02:07:36Z"},{"alias_kind":"pith_short_8","alias_value":"QU3FIQWJ","created_at":"2026-06-09T02:07:36Z"}],"graph_snapshots":[{"event_id":"sha256:95a23860fc69b0a62f304b85301f1b269aa5faddaee2966ad9e24cdeb375fc0b","target":"graph","created_at":"2026-06-09T02:07:36Z","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/2606.08746/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f$ be a holomorphic automorphism of a compact K\\\"ahler manifold $X$ with simple action on cohomology. We show that every ergodic measure with sufficiently large entropy is supported on the Julia set of $f$. In particular, when $X$ is a surface, any ergodic measure with positive entropy is supported on the Julia set. The proof relies on quantitative estimates for the speed of convergence towards the Green currents of $f$, with respect to a suitable norm on an adapted functional space of non-necessarily closed currents.","authors_text":"Fabrizio Bianchi, Karim Rakhimov, Sobir Boymurodov","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-07T17:35:59Z","title":"On the support of measures of large entropy for automorphisms of K\\\"ahler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08746","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":"sha256:15087f91020a427639ab4ace46bf4728bd208c83f7d3b172bf47f582b7c415f7","target":"record","created_at":"2026-06-09T02:07:36Z","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":"f062f5ee168f681dcce0f367a0ee132a4c183fe7a25f15c0b05fd2432577c320","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-06-07T17:35:59Z","title_canon_sha256":"5e51b5ba68d41b200a589c655405fa5f989226e767999c303ee474175f0e0e6a"},"schema_version":"1.0","source":{"id":"2606.08746","kind":"arxiv","version":1}},"canonical_sha256":"85365442c9f4e1207507d8857dafe890a0b19619f8b19cf33a39f3d1624b162e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85365442c9f4e1207507d8857dafe890a0b19619f8b19cf33a39f3d1624b162e","first_computed_at":"2026-06-09T02:07:36.937405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T02:07:36.937405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bJFby2xNAGj3liMifEvSs5PYgqgjtbsPOvaT//UmNPHgdNKQpzcVEOW3LVWka4M/I9+0pAduPQ+wN9sOeK5rCw==","signature_status":"signed_v1","signed_at":"2026-06-09T02:07:36.938514Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08746","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15087f91020a427639ab4ace46bf4728bd208c83f7d3b172bf47f582b7c415f7","sha256:95a23860fc69b0a62f304b85301f1b269aa5faddaee2966ad9e24cdeb375fc0b"],"state_sha256":"466035ef5454a3608289d68192a6b875b53fe3bde1044d94257ee81fedfd497e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9gJsd8Is7ISpQCGpyz30VNcoiWvHX2Bqvc8RErWYDKh9rjO0P0zukjiQe8L+vBj6n8zjErBELhIqTDqg+1ebDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T01:11:05.864960Z","bundle_sha256":"245797bdc3274494cadbea64383f8b05f5f5fb90858624fb93cfa7727c6e5264"}}