{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CK3T7IBVUHHP3KSUNHGMPYUT2Q","short_pith_number":"pith:CK3T7IBV","canonical_record":{"source":{"id":"1406.4810","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-18T17:53:02Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"7b81d215d1365063d52277edd1920430bbdc9730c9777798ae8eeb7c02e304fc","abstract_canon_sha256":"f1d0fc0a34b5015390656dbd6033d732c01c39f7494cd105b43e4aeefe6ae0ca"},"schema_version":"1.0"},"canonical_sha256":"12b73fa035a1cefdaa5469ccc7e293d4153d5c6201c73ec1b8a2d8831a24dae2","source":{"kind":"arxiv","id":"1406.4810","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4810","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4810v2","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4810","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"pith_short_12","alias_value":"CK3T7IBVUHHP","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CK3T7IBVUHHP3KSU","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CK3T7IBV","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CK3T7IBVUHHP3KSUNHGMPYUT2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4810","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-18T17:53:02Z","cross_cats_sorted":["math-ph","math.DS","math.MP"],"title_canon_sha256":"7b81d215d1365063d52277edd1920430bbdc9730c9777798ae8eeb7c02e304fc","abstract_canon_sha256":"f1d0fc0a34b5015390656dbd6033d732c01c39f7494cd105b43e4aeefe6ae0ca"},"schema_version":"1.0"},"canonical_sha256":"12b73fa035a1cefdaa5469ccc7e293d4153d5c6201c73ec1b8a2d8831a24dae2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:37.633747Z","signature_b64":"P210zhU/JN9JOm9W4ZKVaMD8uPsZ+al8PDlLZWnLx36Gd1Kgwa1Ife0tGFT/iVQTy3nq0D98GCep3xZqTs4CBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12b73fa035a1cefdaa5469ccc7e293d4153d5c6201c73ec1b8a2d8831a24dae2","last_reissued_at":"2026-05-18T02:03:37.633168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:37.633168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4810","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":"2026-05-18T02:03:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ejVKhKh7iJYcliwl3T14F3UeDz+GUwsqHifQSGbuTZhXOJzLMkXr+6YLr6YBXxDcXEnXQQQEK7kXYKGNYfXgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:54:45.728878Z"},"content_sha256":"df3392e94c241a014bc45511d3b0ee249b8d21fc9b940c36709ea5bdff62d1d8","schema_version":"1.0","event_id":"sha256:df3392e94c241a014bc45511d3b0ee249b8d21fc9b940c36709ea5bdff62d1d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CK3T7IBVUHHP3KSUNHGMPYUT2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.SP","authors_text":"Anton Gorodetski (UC Irvine), David Damanik (Rice University)","submitted_at":"2014-06-18T17:53:02Z","abstract_excerpt":"We consider the spectrum of discrete Schr\\\"odinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value of the frequency."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4810","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":"2026-05-18T02:03:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rHT5b05yb//4qhP30uBO1Y7hQiVSFwGMXVJ+zjw3sjUlnQmeyQHVpyIqXnMSic8+x9KETXpn/wwxbaX2mN38AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T10:54:45.729257Z"},"content_sha256":"9dcffebd4a9c0947ccc52eb5c069d9ab7791e4bf0e7beb7f2fce04e5475802b5","schema_version":"1.0","event_id":"sha256:9dcffebd4a9c0947ccc52eb5c069d9ab7791e4bf0e7beb7f2fce04e5475802b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CK3T7IBVUHHP3KSUNHGMPYUT2Q/bundle.json","state_url":"https://pith.science/pith/CK3T7IBVUHHP3KSUNHGMPYUT2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CK3T7IBVUHHP3KSUNHGMPYUT2Q/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":"2026-05-27T10:54:45Z","links":{"resolver":"https://pith.science/pith/CK3T7IBVUHHP3KSUNHGMPYUT2Q","bundle":"https://pith.science/pith/CK3T7IBVUHHP3KSUNHGMPYUT2Q/bundle.json","state":"https://pith.science/pith/CK3T7IBVUHHP3KSUNHGMPYUT2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CK3T7IBVUHHP3KSUNHGMPYUT2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CK3T7IBVUHHP3KSUNHGMPYUT2Q","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":"f1d0fc0a34b5015390656dbd6033d732c01c39f7494cd105b43e4aeefe6ae0ca","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-18T17:53:02Z","title_canon_sha256":"7b81d215d1365063d52277edd1920430bbdc9730c9777798ae8eeb7c02e304fc"},"schema_version":"1.0","source":{"id":"1406.4810","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4810","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4810v2","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4810","created_at":"2026-05-18T02:03:37Z"},{"alias_kind":"pith_short_12","alias_value":"CK3T7IBVUHHP","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CK3T7IBVUHHP3KSU","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CK3T7IBV","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:9dcffebd4a9c0947ccc52eb5c069d9ab7791e4bf0e7beb7f2fce04e5475802b5","target":"graph","created_at":"2026-05-18T02:03:37Z","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 consider the spectrum of discrete Schr\\\"odinger operators with Sturmian potentials and show that for sufficiently large coupling, its Hausdorff dimension and its upper box counting dimension are the same for Lebesgue almost every value of the frequency.","authors_text":"Anton Gorodetski (UC Irvine), David Damanik (Rice University)","cross_cats":["math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-18T17:53:02Z","title":"Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4810","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:df3392e94c241a014bc45511d3b0ee249b8d21fc9b940c36709ea5bdff62d1d8","target":"record","created_at":"2026-05-18T02:03:37Z","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":"f1d0fc0a34b5015390656dbd6033d732c01c39f7494cd105b43e4aeefe6ae0ca","cross_cats_sorted":["math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2014-06-18T17:53:02Z","title_canon_sha256":"7b81d215d1365063d52277edd1920430bbdc9730c9777798ae8eeb7c02e304fc"},"schema_version":"1.0","source":{"id":"1406.4810","kind":"arxiv","version":2}},"canonical_sha256":"12b73fa035a1cefdaa5469ccc7e293d4153d5c6201c73ec1b8a2d8831a24dae2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12b73fa035a1cefdaa5469ccc7e293d4153d5c6201c73ec1b8a2d8831a24dae2","first_computed_at":"2026-05-18T02:03:37.633168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:37.633168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P210zhU/JN9JOm9W4ZKVaMD8uPsZ+al8PDlLZWnLx36Gd1Kgwa1Ife0tGFT/iVQTy3nq0D98GCep3xZqTs4CBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:37.633747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4810","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df3392e94c241a014bc45511d3b0ee249b8d21fc9b940c36709ea5bdff62d1d8","sha256:9dcffebd4a9c0947ccc52eb5c069d9ab7791e4bf0e7beb7f2fce04e5475802b5"],"state_sha256":"98cb1c1abf193d19a45c80541b5b6b96992bbdf619702cb319e4e702b7d4a0f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H2+EqgYwh6VPfKFRUNzws8FkaKTGTq8UvH4+CICu3XYQmUnALLOQ7sNlalcqZXCpYwLBeiZtdYBE7jWLxri/Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T10:54:45.732698Z","bundle_sha256":"d8bd419e629df5f86db8781cc651ced1d370534b3417a7f358f3990de0dffdca"}}