{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UETUP3Q4TS5EYJCA5YJWAWRKFU","short_pith_number":"pith:UETUP3Q4","canonical_record":{"source":{"id":"2507.23731","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-31T17:05:51Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"5849ae0c36a1c01e03937dca019105a19182dfa7db389f78afe4ff27acbce05c","abstract_canon_sha256":"e7d68a6cefc03e023850b0662ad9dd5ab6b8706d0676603e0e94c017a9da8b1c"},"schema_version":"1.0"},"canonical_sha256":"a12747ee1c9cba4c2440ee13605a2a2d28650587faacd1e942de264c17fdf620","source":{"kind":"arxiv","id":"2507.23731","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.23731","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"2507.23731v1","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.23731","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"UETUP3Q4TS5E","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"pith_short_16","alias_value":"UETUP3Q4TS5EYJCA","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"pith_short_8","alias_value":"UETUP3Q4","created_at":"2026-07-05T11:46:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UETUP3Q4TS5EYJCA5YJWAWRKFU","target":"record","payload":{"canonical_record":{"source":{"id":"2507.23731","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-31T17:05:51Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"5849ae0c36a1c01e03937dca019105a19182dfa7db389f78afe4ff27acbce05c","abstract_canon_sha256":"e7d68a6cefc03e023850b0662ad9dd5ab6b8706d0676603e0e94c017a9da8b1c"},"schema_version":"1.0"},"canonical_sha256":"a12747ee1c9cba4c2440ee13605a2a2d28650587faacd1e942de264c17fdf620","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:46:30.156414Z","signature_b64":"PsqoZX0KFA9yBIjazcP4nnS7d0rBFdERrwM3UrKKaleg9SjxNHv6c/3veKvm/sxMh+9FLNNG91UIh7TFI6QfAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a12747ee1c9cba4c2440ee13605a2a2d28650587faacd1e942de264c17fdf620","last_reissued_at":"2026-07-05T11:46:30.155883Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:46:30.155883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2507.23731","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":"2026-07-05T11:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mswEhxG7p0vjG78rf0GJkjXPemdyX/yeKzXrdywPcROoiqaAaWl+5J8WOK2CjWNZjhHNM/sJpiYtHDNdX0okAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:13:23.159635Z"},"content_sha256":"e3441d9e5e54dce7b70be911f55e51f6ff33a285221a663632068f51c51bd907","schema_version":"1.0","event_id":"sha256:e3441d9e5e54dce7b70be911f55e51f6ff33a285221a663632068f51c51bd907"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UETUP3Q4TS5EYJCA5YJWAWRKFU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fourier decay of equilibrium states and the Fibonacci Hamiltonian","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.DS","authors_text":"Ga\\'etan Leclerc","submitted_at":"2025-07-31T17:05:51Z","abstract_excerpt":"We show positivity of the lower Fourier dimension for equilibrium states of nonlinear, area preserving, Axiom A diffeomorphisms on surfaces. To do so, we use the sum-product phenomenon to reduce Fourier decay to the study of some temporal distance function for a well chosen suspension flow, whose mixing properties reflects the nonlinearity of our base dynamics. We then generalize in an Axiom A setting the methods of Tsujii-Zhang, dealing with exponential mixing of three-dimensional Anosov flows arXiv:2006.04293. The nonlinearity condition is generic and can be checked in concrete contexts. As "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23731","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/2507.23731/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":"2026-07-05T11:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKomdWdbe+afUyUSskTiTYEX2k6u1aJRGxo9NdlGh8KjcjU2dWbNaNSFsoyKxdiKOJKkofYC/7iBvFgDrDmkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T02:13:23.160230Z"},"content_sha256":"3cb83c0185cb8a795ac8051d9e1635091973edf996d4742fbf5c3b51b360d878","schema_version":"1.0","event_id":"sha256:3cb83c0185cb8a795ac8051d9e1635091973edf996d4742fbf5c3b51b360d878"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UETUP3Q4TS5EYJCA5YJWAWRKFU/bundle.json","state_url":"https://pith.science/pith/UETUP3Q4TS5EYJCA5YJWAWRKFU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UETUP3Q4TS5EYJCA5YJWAWRKFU/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":"2026-08-10T02:13:23Z","links":{"resolver":"https://pith.science/pith/UETUP3Q4TS5EYJCA5YJWAWRKFU","bundle":"https://pith.science/pith/UETUP3Q4TS5EYJCA5YJWAWRKFU/bundle.json","state":"https://pith.science/pith/UETUP3Q4TS5EYJCA5YJWAWRKFU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UETUP3Q4TS5EYJCA5YJWAWRKFU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UETUP3Q4TS5EYJCA5YJWAWRKFU","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":"e7d68a6cefc03e023850b0662ad9dd5ab6b8706d0676603e0e94c017a9da8b1c","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-31T17:05:51Z","title_canon_sha256":"5849ae0c36a1c01e03937dca019105a19182dfa7db389f78afe4ff27acbce05c"},"schema_version":"1.0","source":{"id":"2507.23731","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.23731","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"2507.23731v1","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.23731","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"UETUP3Q4TS5E","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"pith_short_16","alias_value":"UETUP3Q4TS5EYJCA","created_at":"2026-07-05T11:46:30Z"},{"alias_kind":"pith_short_8","alias_value":"UETUP3Q4","created_at":"2026-07-05T11:46:30Z"}],"graph_snapshots":[{"event_id":"sha256:3cb83c0185cb8a795ac8051d9e1635091973edf996d4742fbf5c3b51b360d878","target":"graph","created_at":"2026-07-05T11:46:30Z","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/2507.23731/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show positivity of the lower Fourier dimension for equilibrium states of nonlinear, area preserving, Axiom A diffeomorphisms on surfaces. To do so, we use the sum-product phenomenon to reduce Fourier decay to the study of some temporal distance function for a well chosen suspension flow, whose mixing properties reflects the nonlinearity of our base dynamics. We then generalize in an Axiom A setting the methods of Tsujii-Zhang, dealing with exponential mixing of three-dimensional Anosov flows arXiv:2006.04293. The nonlinearity condition is generic and can be checked in concrete contexts. As ","authors_text":"Ga\\'etan Leclerc","cross_cats":["math-ph","math.MP","math.SP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-31T17:05:51Z","title":"Fourier decay of equilibrium states and the Fibonacci Hamiltonian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.23731","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:e3441d9e5e54dce7b70be911f55e51f6ff33a285221a663632068f51c51bd907","target":"record","created_at":"2026-07-05T11:46:30Z","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":"e7d68a6cefc03e023850b0662ad9dd5ab6b8706d0676603e0e94c017a9da8b1c","cross_cats_sorted":["math-ph","math.MP","math.SP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2025-07-31T17:05:51Z","title_canon_sha256":"5849ae0c36a1c01e03937dca019105a19182dfa7db389f78afe4ff27acbce05c"},"schema_version":"1.0","source":{"id":"2507.23731","kind":"arxiv","version":1}},"canonical_sha256":"a12747ee1c9cba4c2440ee13605a2a2d28650587faacd1e942de264c17fdf620","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a12747ee1c9cba4c2440ee13605a2a2d28650587faacd1e942de264c17fdf620","first_computed_at":"2026-07-05T11:46:30.155883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:46:30.155883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PsqoZX0KFA9yBIjazcP4nnS7d0rBFdERrwM3UrKKaleg9SjxNHv6c/3veKvm/sxMh+9FLNNG91UIh7TFI6QfAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:46:30.156414Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.23731","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3441d9e5e54dce7b70be911f55e51f6ff33a285221a663632068f51c51bd907","sha256:3cb83c0185cb8a795ac8051d9e1635091973edf996d4742fbf5c3b51b360d878"],"state_sha256":"e1b4c7671d2f6e15b852f988061cc6c84b16f37170e1b9d3ad1b3c94f9ea2a4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GpueRJ8lhAW3yZpFkcoKCuqmuH1dquqP/g7gOW2JckwIqwjlq2T9mtI2HLae9aq9OyISyHw0c6AExYpD+NxrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T02:13:23.165274Z","bundle_sha256":"8a0bfeec73338bae4aa0ee814392bf2a2aa6ca141e467586164035b8492e74ec"}}