{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:FQE74DA527KHSGUHSXYVG6QZ7A","short_pith_number":"pith:FQE74DA5","canonical_record":{"source":{"id":"1503.02273","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-08T13:12:32Z","cross_cats_sorted":[],"title_canon_sha256":"42a440d1dd3a55dec4aea7d9bd0b07657ba7e8aa8440770455dd37af4c8c9928","abstract_canon_sha256":"887681e5a816c244e073c168192a16c8c4efacb29a65e907df4aadd0bb6cf7d9"},"schema_version":"1.0"},"canonical_sha256":"2c09fe0c1dd7d4791a8795f1537a19f838c5be62fe04cb7c6d1d4238022b343c","source":{"kind":"arxiv","id":"1503.02273","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02273","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02273v2","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02273","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"FQE74DA527KH","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FQE74DA527KHSGUH","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FQE74DA5","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:FQE74DA527KHSGUHSXYVG6QZ7A","target":"record","payload":{"canonical_record":{"source":{"id":"1503.02273","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-08T13:12:32Z","cross_cats_sorted":[],"title_canon_sha256":"42a440d1dd3a55dec4aea7d9bd0b07657ba7e8aa8440770455dd37af4c8c9928","abstract_canon_sha256":"887681e5a816c244e073c168192a16c8c4efacb29a65e907df4aadd0bb6cf7d9"},"schema_version":"1.0"},"canonical_sha256":"2c09fe0c1dd7d4791a8795f1537a19f838c5be62fe04cb7c6d1d4238022b343c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:45.054256Z","signature_b64":"pDKVdc8BbIuS+3fru5aiAVYy1aKjPCZOmQLW19GG5rYp4sWCo3B8vFk9D1VienEPgeDs10FuMYrPj8YE7CKTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c09fe0c1dd7d4791a8795f1537a19f838c5be62fe04cb7c6d1d4238022b343c","last_reissued_at":"2026-05-18T01:21:45.053587Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:45.053587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.02273","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":"2026-05-18T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yE9cIHjAFSyucvqw5UZSEmm9hGZqQ4muMpMpq+DPNFPQWg6gFse+fasBSWh+ZvKajdqkw4sKzm4o6lI+5Q80CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:44:50.328848Z"},"content_sha256":"463b57537f4b299631682de43c66aa9061c8cb1fed63541f182001d553479712","schema_version":"1.0","event_id":"sha256:463b57537f4b299631682de43c66aa9061c8cb1fed63541f182001d553479712"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:FQE74DA527KHSGUHSXYVG6QZ7A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nondense orbits for Anosov diffeomorphisms of the $2$-torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jimmy Tseng","submitted_at":"2015-03-08T13:12:32Z","abstract_excerpt":"Let $\\lambda$ denote the probability Lebesgue measure on ${\\mathbb T}^2$. For any $C^2$-Anosov diffeomorphism of the $2$-torus preserving $\\lambda$ with measure-theoretic entropy equal to topological entropy, we show that the set of points with nondense orbits is hyperplane absolute winning (HAW). This generalizes the result in~\\cite[Theorem~1.4]{T4} for $C^2$-expanding maps of the circle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02273","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":"2026-05-18T01:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e02C8LERNnzur6rNZyHUSCTTYXYxT+6NvpT3qFm3qEflz1hcn7QS9JqaRPvAQpqWpnR3+MSfHQH530zI2hwfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:44:50.329217Z"},"content_sha256":"9bb2571888c5561e3a612fecbb538f463dded2e5a3493cef8983b5af592a6e67","schema_version":"1.0","event_id":"sha256:9bb2571888c5561e3a612fecbb538f463dded2e5a3493cef8983b5af592a6e67"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQE74DA527KHSGUHSXYVG6QZ7A/bundle.json","state_url":"https://pith.science/pith/FQE74DA527KHSGUHSXYVG6QZ7A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQE74DA527KHSGUHSXYVG6QZ7A/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":"2026-06-25T08:44:50Z","links":{"resolver":"https://pith.science/pith/FQE74DA527KHSGUHSXYVG6QZ7A","bundle":"https://pith.science/pith/FQE74DA527KHSGUHSXYVG6QZ7A/bundle.json","state":"https://pith.science/pith/FQE74DA527KHSGUHSXYVG6QZ7A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQE74DA527KHSGUHSXYVG6QZ7A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FQE74DA527KHSGUHSXYVG6QZ7A","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":"887681e5a816c244e073c168192a16c8c4efacb29a65e907df4aadd0bb6cf7d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-08T13:12:32Z","title_canon_sha256":"42a440d1dd3a55dec4aea7d9bd0b07657ba7e8aa8440770455dd37af4c8c9928"},"schema_version":"1.0","source":{"id":"1503.02273","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.02273","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1503.02273v2","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02273","created_at":"2026-05-18T01:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"FQE74DA527KH","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FQE74DA527KHSGUH","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FQE74DA5","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:9bb2571888c5561e3a612fecbb538f463dded2e5a3493cef8983b5af592a6e67","target":"graph","created_at":"2026-05-18T01:21:45Z","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"},"paper":{"abstract_excerpt":"Let $\\lambda$ denote the probability Lebesgue measure on ${\\mathbb T}^2$. For any $C^2$-Anosov diffeomorphism of the $2$-torus preserving $\\lambda$ with measure-theoretic entropy equal to topological entropy, we show that the set of points with nondense orbits is hyperplane absolute winning (HAW). This generalizes the result in~\\cite[Theorem~1.4]{T4} for $C^2$-expanding maps of the circle.","authors_text":"Jimmy Tseng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-08T13:12:32Z","title":"Nondense orbits for Anosov diffeomorphisms of the $2$-torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02273","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":"sha256:463b57537f4b299631682de43c66aa9061c8cb1fed63541f182001d553479712","target":"record","created_at":"2026-05-18T01:21:45Z","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":"887681e5a816c244e073c168192a16c8c4efacb29a65e907df4aadd0bb6cf7d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-08T13:12:32Z","title_canon_sha256":"42a440d1dd3a55dec4aea7d9bd0b07657ba7e8aa8440770455dd37af4c8c9928"},"schema_version":"1.0","source":{"id":"1503.02273","kind":"arxiv","version":2}},"canonical_sha256":"2c09fe0c1dd7d4791a8795f1537a19f838c5be62fe04cb7c6d1d4238022b343c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c09fe0c1dd7d4791a8795f1537a19f838c5be62fe04cb7c6d1d4238022b343c","first_computed_at":"2026-05-18T01:21:45.053587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:45.053587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pDKVdc8BbIuS+3fru5aiAVYy1aKjPCZOmQLW19GG5rYp4sWCo3B8vFk9D1VienEPgeDs10FuMYrPj8YE7CKTBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:45.054256Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.02273","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:463b57537f4b299631682de43c66aa9061c8cb1fed63541f182001d553479712","sha256:9bb2571888c5561e3a612fecbb538f463dded2e5a3493cef8983b5af592a6e67"],"state_sha256":"66b2fd06b084dfeaf52934410780221d14e6c2d9e9fd697889eb0111c02c1638"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lTyyLkrd7l+Y+R2forHox4vye8aTrBO024dvdObVaFdTBKDejElKihoiNZvqjr2kf2SVUqha/HitMtGhadT3Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:44:50.331164Z","bundle_sha256":"e7acdf4c7964dd584dcce369cd4a33b3219b3a7076e7f4a21238b6a477cc379c"}}